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Title:
MODIFYING THE CONTRAST BASIS WHEN USING CONTRAST SOURCE INVERSION METHOD TO IMAGE A STORED COMMODITY IN A GRAIN BIN
Document Type and Number:
WIPO Patent Application WO/2023/187529
Kind Code:
A1
Abstract:
An electromagnetic imaging method uses a reduced set of whole domain basis functions that is chosen in an informed manner from prior information about the imaging problem, using prior information to tailor the choice of 'alternative' basis functions, e.g., first seeking layered structure in a grain storage bin, then providing support for hot-spots. In one embodiment, the method first uses a pulse basis and then projects the basis onto the 'alternative' basis. This allows for more than one 'alternative' basis at each iteration. Similarities and differences between the target reconstruction in different alternative bases can be used to guide the reconstruction procedure. In an alternate embodiment the method constructs the 'alternative basis' directly and modifies the underlying inversion algorithm to accommodate the new basis. The method uses the information to parametrically describe a state of a stored commodity.

Inventors:
BANTING LUCAS (CA)
LOVETRI JOE (CA)
JEFFREY IAN (CA)
FOGEL HANNAH CLAIRE (CA)
ASEFI MOHAMMAD (CA)
Application Number:
PCT/IB2023/052533
Publication Date:
October 05, 2023
Filing Date:
March 15, 2023
Export Citation:
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Assignee:
GSI ELECTRONIQUE INC (CA)
UNIV MANITOBA (CA)
International Classes:
G01N22/04; A01F25/14; B65D90/48
Domestic Patent References:
WO2021001796A12021-01-07
Foreign References:
US20170199134A12017-07-13
KR20140082376A2014-07-02
Other References:
E. KIM: "Imaging and Calibration of Electromagnetic Inversion Data With a Single Data Set", IEEE OPEN JOURNAL OF ANTENNAS AND PROPAGATION, vol. 3, 2 December 2021 (2021-12-02), pages 12 - 23, XP011896692, DOI: 10.1109/OJAP.2021.3132100
N. JAVANBAKHT: "Portable Microwave Sensor Based on Frequency-Selective Surface for Grain Moisture Content Monitoring", IEEE SENSORS LETTERS, vol. 5, no. 11, 29 September 2021 (2021-09-29), pages 1 - 4, XP011884150, DOI: 10.1109/LSENS.2021.3115397
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Claims:
CLAIMS What is claimed is: 1. A method of imaging contents of a storage bin, the method comprising: receiving radio frequency data from one or more antenna probes of an antenna array mounting within the storage bin; applying a parametric inversion to at least one or more portions of the radio frequency data to estimate a height of the contents, a cone-angle of the contents, or a bulk permittivity of the contents; setting an imaging domain to reflect the estimated height of the contents and the cone-angle of the contents; generating calibrated scattered-field data based at least partially on the estimated bulk permittivity of the contents and utilizing a one-shot calibration technique; applying a contrast source inversion technique to the calibrated scattered-field data to determine variations of permittivity within a volume of the contents; and based at least partially on the estimated bulk permittivity of the contents and the determined variations of the permittivity within a volume of the contents, generating one or more graphical representations depicting moisture content within at least a portion of the contents within the storage bin. 2. The method of claim 1, wherein applying the contrast source inversion technique to the calibrated scattered-field data comprises incrementally increasing a number of basis functions during iterations of the contrast source inversion technique. 3. The method of claim 2, wherein the number of basis functions are increased based at least partially on about a 2.0% change in a relative norm of basis function coefficients.

4. The method of claim 1, wherein applying the contrast source inversion technique to the calibrated scattered-field data comprises selecting and utilizing Gaussian radial basis functions in cylindrical coordinates. 5. The method of claim 4, further comprising selecting centroids to be equidistance in the volume of the contents of the storage bin in each of z, r, and ϕ dimensions. 6. The method of claim 1, further comprising updating at least a portion of the contrast source inversion technique utilizing a non-linear conjugate gradient technique. 7. The method of claim 1, further comprising: causing the one or more graphical representations of depicting moisture content within at least a portion of the content within the storage bin to be displayed on a client device.

8. A system for monitoring contents within a storage bin, the system comprising: at least one processor; and at least one non-transitory computer-readable storage medium storing instructions thereon that, when executed by the at least one processor, cause the system to: receive measurement data from an antenna probe of an antenna array within a container; generate calibrated scattered-field data based at least partially on the received measurement data; apply a contrast source inversion technique to the calibrated scattered-field data to determine variations of permittivity within a volume of the contents; and based at least partially on the determined variations of the permittivity within a volume of the contents, generate one or more graphical representations depicting moisture content within at least a portion of the contents within the storage bin. 9. The system of claim 8, wherein applying the contrast source inversion technique to the calibrated scattered-field data comprises incrementally increasing a number of basis functions during iterations of the contrast source inversion technique. 10. The system of claim 9, wherein the number of basis functions are increased based at least partially on about a 2.0% change in a relative norm of basis function coefficients. 11. The system of claim 8, wherein applying the contrast source inversion technique to the calibrated scattered-field data comprises selecting and utilizing Gaussian radial basis functions in cylindrical coordinates. 12. The system of claim 11, further comprising instructions that, when executed by the at least one processor, cause the system to: select centroids to be equidistance in the volume of the contents of the storage bin in each of z, r, and ϕ dimensions.

13. The system of claim 8, further comprising instructions that, when executed by the at least one processor, cause the system to: update at least a portion of the contrast source inversion technique utilizing a non-linear conjugate gradient technique. 14. The system of claim 8, further comprising instructions that, when executed by the at least one processor, cause the system to: cause the one or more graphical representations of depicting moisture content within at least a portion of the content within the storage bin to be displayed on a client device.

15. A system comprising: a container housing a commodity; an antenna array having a plurality of antenna probes within the container; an antenna controller operably coupled to and in communication with the antenna array; and a commodity monitoring system in communication with the antenna controller and comprising: at least one processor; and at least one non-transitory computer-readable storage medium storing instructions thereon that, when executed by the at least one processor, cause the commodity monitoring system to: receive measurement data from an antenna probe of an antenna array within a container; generate calibrated scattered-field data based at least partially on the received measurement data; apply a contrast source inversion technique to the calibrated scattered-field data to determine variations of permittivity within a volume of the contents; and based at least partially on the determined variations of the permittivity within a volume of the contents, generate one or more graphical representations depicting moisture content within at least a portion of the contents within the storage bin. 16. The system of claim 15, wherein applying the contrast source inversion technique to the calibrated scattered-field data comprises incrementally increasing a number of basis functions during iterations of the contrast source inversion technique. 17. The system of claim 16, wherein the number of basis functions are increased based at least partially on about a 2.0% change in a relative norm of basis function coefficients.

18. The system of claim 15, wherein applying the contrast source inversion technique to the calibrated scattered-field data comprises selecting and utilizing Gaussian radial basis functions in cylindrical coordinates. 19. The system of claim 18, further comprising instructions that, when executed by the at least one processor, cause the system to: select centroids to be equidistance in the volume of the contents of the storage bin in each of z, r, and ϕ dimensions. 20. The system of claim 15, further comprising instructions that, when executed by the at least one processor, cause the system to: update at least a portion of the contrast source inversion technique utilizing a non-linear conjugate gradient technique.

Description:
MODIFYING THE CONTRAST BASIS WHEN USING CONTRAST SOURCE INVERSION METHOD TO IMAGE A STORED COMMODITY IN A GRAIN BIN TECHNICAL FIELD [0001] The present disclosure is generally related to electromagnetic imaging of containers. BACKGROUND [0002] The safe storage of grains is crucial to securing the world’s food supply. Estimates of storage losses vary from 2 to 30%, depending on geographic location. Grains are usually stored in large containers, referred to as grain silos or grain bins, after harvest, and can be left there for days to years. Because of non-ideal storage conditions, spoilage and grain loss are inevitable. Consequently, continuous monitoring of the stored grain is an essential part of the post-harvest stage for the agricultural industry. Recently, electromagnetic inverse imaging (EMI) using radio frequency (RF) excitation has been proposed to monitor the moisture content of stored grain. The possibility of using electromagnetic waves to quantitatively image grains, and the motivation to do so, derives from the well-known fact that the dielectric properties of agricultural products (e.g., the complex-valued permittivity) vary with their physical attributes, such as the moisture content and the temperature, which in turn, indicates their physiological state. [0003] Part of existing grain imaging products involves the creation of a coarse parametric model of the stored grain that is subsequently used as prior information for full grain moisture imaging (FGMI). The coarse parametric model is also used to calibrate scattered field data used by the FGMI algorithm. Currently, the coarse parametric model used in some grain imaging technology consists of only four (4) parameters: grain height at the storage bin wall, cone angle, and real and imaginary parts of the complex-valued permittivity (Ɛr and Ɛi). These parameters are obtained using uncalibrated, magnitude-only, total field measurements between the antennas of the storage bin, a step sometimes referred to as retrieval of the bulk average moisture content (BAMC). After the BAMC step, which provides an average moisture content (AMC) throughout the stored grain as well as an inventory of the amount of stored grain (estimated from the height and cone angle), the acquired scattered field measurements may be calibrated to provide both magnitude and phase of the measurements to the FGMI algorithm. Some examples of imaging methods for grain bins are commonly assigned U.S. Patent No. 11,125,796 entitled “Electromagnetic Imaging and Inversion of Simple Parameters in Storage Bins” and U.S. Provisional Application No.63/163,959, filed March 22, 2021 entitled “Ray-Based Imaging in Grain Bins.” [0004] Quantitative electromagnetic imaging algorithms attempt to solve an ill-posed and non-linear optimization problem by minimizing the error between measured data and data obtained using a numerical model for the imaging target and imaging system. These optimization problems are typically solved iteratively, where estimates of the target function are updated at each iteration of the algorithm. They also generally use regularization, either as additional penalty terms or by limiting the types of reconstructions that are possible, in an attempt to uncover physically meaningful solutions. It is common for these regularized iterative algorithms to produce images with artifacts that are not representative of the physical target, and these artifacts can persist or worsen as iterations progress. While such problems exist for any application field of imaging (e.g., biomedical imaging and monitoring, sub-surface imaging) and any iterative algorithm (e.g., contrast source inversion, Gauss Newton inversion, the Born Iterative Method), they are especially challenging when the imaging system consists of a resonant or semi-resonant enclosure such as those encountered in the grain bin imaging problem. Most imaging algorithms represent the contrast (unknown moisture profile) as a pulse (or polynomial) basis on each mesh element. The flexibility of such a finely-resolved basis aggravates imaging artifacts, especially (though not exclusively) in (quasi-) resonant imaging systems. BRIEF SUMMARY [0005] Some embodiments of the disclosure include methods of imaging contents of a storage bin. The methods may include receiving radio frequency data from one or more antenna probes of an antenna array mounting within the storage bin, applying a parametric inversion to at least one or more portions of the radio frequency data to estimate a height of the contents, a cone-angle of the contents, or a bulk permittivity of the contents, setting an imaging domain to reflect the estimated height of the contents and the cone-angle of the contents, generating calibrated scattered-field data based at least partially on the estimated bulk permittivity of the contents and utilizing a one-shot calibration technique, applying a contrast source inversion technique to the calibrated scattered-field data to determine variations of permittivity within a volume of the contents, and based at least partially on the estimated bulk permittivity of the contents and the determined variations of the permittivity within a volume of the contents, generating one or more graphical representations depicting moisture content within at least a portion of the contents within the storage bin. [0006] Applying the contrast source inversion technique to the calibrated scattered-field data may include incrementally increasing a number of basis functions during iterations of the contrast source inversion technique. [0007] The number of basis functions may be increased based at least partially on about a 2.0% change in a relative norm of basis function coefficients. [0008] Applying the contrast source inversion technique to the calibrated scattered-field data may include selecting and utilizing Gaussian radial basis functions in cylindrical coordinates. [0009] The methods may further include selecting centroids to be equidistance in the volume of the contents of the storage bin in each of z, r, and ϕ dimensions. [0010] The methods may further include updating at least a portion of the contrast source inversion technique utilizing a non-linear conjugate gradient technique. The methods may further include causing the one or more graphical representations of depicting moisture content within at least a portion of the content within the storage bin to be displayed on a client device. [0011] One or more embodiments of the disclosure includes systems for monitoring contents within a storage bin. The system may include at least one processor and at least one non-transitory computer-readable storage medium storing instructions thereon that, when executed by the at least one processor, cause the system to: receive measurement data from an antenna probe of an antenna array within a container, generate calibrated scattered-field data based at least partially on the received measurement data, apply a contrast source inversion technique to the calibrated scattered-field data to determine variations of permittivity within a volume of the contents, and based at least partially on the determined variations of the permittivity within a volume of the contents, generate one or more graphical representations depicting moisture content within at least a portion of the contents within the storage bin. [0012] Applying the contrast source inversion technique to the calibrated scattered-field data may include incrementally increasing a number of basis functions during iterations of the contrast source inversion technique. [0013] The number of basis functions may be increased based at least partially on about a 2.0% change in a relative norm of basis function coefficients. [0014] Applying the contrast source inversion technique to the calibrated scattered-field data may include selecting and utilizing Gaussian radial basis functions in cylindrical coordinates. [0015] The system may further include instructions that, when executed by the at least one processor, cause the system to: select centroids to be equidistance in the volume of the contents of the storage bin in each of z, r, and ϕ dimensions. [0016] The system may further include instructions that, when executed by the at least one processor, cause the system to: update at least a portion of the contrast source inversion technique utilizing a non-linear conjugate gradient technique. [0017] The system may further include instructions that, when executed by the at least one processor, cause the system to: cause the one or more graphical representations of depicting moisture content within at least a portion of the content within the storage bin to be displayed on a client device. [0018] One or more embodiments of the disclosure include systems including a container housing a commodity, an antenna array having a plurality of antenna probes within the container, an antenna controller operably coupled to and in communication with the antenna array; and a commodity monitoring system in communication with the antenna controller. The commodity monitoring system may include at least one processor and at least one non-transitory computer- readable storage medium storing instructions thereon that, when executed by the at least one processor, cause the commodity monitoring system to: receive measurement data from an antenna probe of an antenna array within a container; generate calibrated scattered-field data based at least partially on the received measurement data; apply a contrast source inversion technique to the calibrated scattered-field data to determine variations of permittivity within a volume of the contents; and based at least partially on the determined variations of the permittivity within a volume of the contents, generate one or more graphical representations depicting moisture content within at least a portion of the contents within the storage bin. [0019] Applying the contrast source inversion technique to the calibrated scattered-field data may include incrementally increasing a number of basis functions during iterations of the contrast source inversion technique. [0020] The number of basis functions may be increased based at least partially on about a 2.0% change in a relative norm of basis function coefficients. [0021] Applying the contrast source inversion technique to the calibrated scattered-field data may include selecting and utilizing Gaussian radial basis functions in cylindrical coordinates. [0022] The system may further include instructions that, when executed by the at least one processor, cause the system to: select centroids to be equidistance in the volume of the contents of the storage bin in each of z, r, and ϕ dimensions. [0023] The system may further include instructions that, when executed by the at least one processor, cause the system to: update at least a portion of the contrast source inversion technique utilizing a non-linear conjugate gradient technique. [0024] The system may further include instructions that, when executed by the at least one processor, cause the system to: cause the one or more graphical representations of depicting moisture content within at least a portion of the content within the storage bin to be displayed on a client device. [0025] Other technical features may be readily apparent to one skilled in the art from the following figures, descriptions, and claims. [0026] Within the scope of this application it should be understood that the various aspects, embodiments, examples and alternatives set out herein, and individual features thereof may be taken independently or in any possible and compatible combination. Where features are described with reference to a single aspect or embodiment, it should be understood that such features are applicable to all aspects and embodiments unless otherwise stated or where such features are incompatible. BRIEF DESCRIPTION OF THE DRAWINGS [0027] While the specification concludes with claims particularly pointing out and distinctly claiming what are regarded as embodiments of the present disclosure, various features and advantages may be more readily ascertained from the following description of example embodiments when read in conjunction with the accompanying drawings, in which: [0028] FIG.1 is a schematic diagram that illustrates an example environment in which an embodiment of an electromagnetic imaging system may be implemented; [0029] FIG. 2 is a flow diagram that illustrates an embodiment of an example contrast source inversion method modifying the contrast basis; [0030] FIG. 3 is a flow diagram that illustrates an embodiment of an example imaging method; [0031] FIGS 4-9 show example results of moisture content in containers obtained using one or more methods of the present disclosure; [0032] FIG. 10 depicts a tetrahedral defining vectors utilized in the methods described herein according to one or more embodiments of the disclosure; and [0033] FIG.11 is a schematic view of a computer device according to embodiments of the disclosure. DETAILED DESCRIPTION [0034] Illustrations presented herein are not meant to be actual views of any particular storage container, commodity monitoring device component, or system, but are merely idealized representations that are employed to describe embodiments of the disclosure. Additionally, elements common between figures may retain the same numerical designation for convenience and clarity. [0035] The following description provides specific details of embodiments. However, a person of ordinary skill in the art will understand that the embodiments of the disclosure may be practiced without employing many such specific details. Indeed, the embodiments of the disclosure may be practiced in conjunction with conventional techniques employed in the industry. In addition, the description provided below does not include all the elements that form a complete structure or assembly. Only those process acts and structures necessary to understand the embodiments of the disclosure are described in detail below. Additional conventional acts and structures may be used. The drawings accompanying the application are for illustrative purposes only, and are thus not drawn to scale. [0036] As used herein, the terms “comprising,” “including,” “containing,” “characterized by,” and grammatical equivalents thereof are inclusive or open-ended terms that do not exclude additional, unrecited elements or method steps, but also include the more restrictive terms “consisting of” and “consisting essentially of” and grammatical equivalents thereof. [0037] As used herein, the singular forms following “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. [0038] As used herein, the term “may” with respect to a material, structure, feature, or method act indicates that such is contemplated for use in implementation of an embodiment of the disclosure, and such term is used in preference to the more restrictive term “is” so as to avoid any implication that other compatible materials, structures, features, and methods usable in combination therewith should or must be excluded. [0039] As used herein, the term “configured” refers to a size, shape, material composition, and arrangement of one or more of at least one structure and at least one apparatus facilitating operation of one or more of the structure and the apparatus in a predetermined way. [0040] As used herein, any relational term, such as “first,” “second,” etc., is used for clarity and convenience in understanding the disclosure and accompanying drawings, and does not connote or depend on any specific preference or order, except where the context clearly indicates otherwise. [0041] As used herein, the term “substantially” in reference to a given parameter, property, or condition means and includes to a degree that one skilled in the art would understand that the given parameter, property, or condition is met with a small degree of variance, such as within acceptable manufacturing tolerances. By way of example, depending on the particular parameter, property, or condition that is substantially met, the parameter, property, or condition may be at least 90.0% met, at least 95.0% met, at least 99.0% met, or even at least 99.9% met. [0042] As used herein, the term “about” used in reference to a given parameter is inclusive of the stated value and has the meaning dictated by the context (e.g., it includes the degree of error associated with measurement of the given parameter, as well as variations resulting from manufacturing tolerances, etc.). [0043] As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. [0044] In one aspect the invention is directed to an electromagnetic imaging method comprising using a reduced set of whole domain basis functions that is chosen in an informed manner from prior information about the imaging problem, using prior information to tailor the choice of 'alternative' basis functions, e.g., first seeking layered structure in a grain storage bin, then providing support for hot-spots. In one embodiment, the method first uses a pulse basis and then projects the basis onto the 'alternative' basis. This allows for more than one 'alternative' basis at each iteration. Similarities and differences between the target reconstruction in different alternative bases can be used to guide the reconstruction procedure. In an alternate embodiment the method constructs the 'alternative basis' directly and modifies the underlying inversion algorithm to accommodate the new basis. The method uses the information to parametrically describe a state of a stored commodity [0045] The proposed invention specifically addresses the need to provide a completely flexible dynamic modification of the 'alternative' basis where the user can specify and/or automate the choice of basis functions at each iteration of the inversion algorithm. [0046] Certain embodiments of an electromagnetic imaging system and method are disclosed that improve upon the aforementioned bulk average moisture content (BAMC) process by creating higher-order, and therefore more accurate, parametric models of a state of a stored commodity (e.g., grain). In one embodiment, a whole domain basis function, ray based inversion model is implemented and that is configured to extract the coefficients of a higher-order set of basis functions that are then used to parametrically describe the state of the stored grain. One algorithm uses time-of-flight determinations between each pair of antennas/sensors arranged within a container (e.g., storage bin). In such an approach, a wave speed of the stored grain is reconstructed parametrically. Another algorithm uses attenuation of a signal between each transmitter/receiver pair of sensors, which enables reconstruction of a wave attenuation coefficient of the stored grain. Both parametric reconstructions may be based on (e.g., initially) uncalibrated data, and may be used to improve calibration (e.g., more accuracy) of acquired data. [0047] In some embodiments, in addition to, or in lieu of the whole domain basis embodiment, a resonance system is used that measures resonances of the storage bin. The resonances are indications of, for instance, a fill-level of the bin, as well as other features (e.g., complex-valued permittivity of the stored grain). The resonances are extracted from wide-band (frequency-domain or time-domain) data collected between each transmitter/receiver pair of sensors. In addition to the resonances, the signals are modeled by a set of poles and zeros representing an equivalent transfer-function between the sensors. These pole/zero representations provide information about the stored grain (e.g., its geometry and/or physical properties of the grain). [0048] In some embodiments, any one of a plurality of neural network (e.g., deep learning) techniques may be used both for extraction of information in one or both of the above- mentioned algorithms as well as in fusing the data from each technique. [0049] Digressing briefly, obtaining highly accurate reconstructions of the complex- valued permittivity generally requires the use of computationally expensive iterative techniques, such as those found in contrast source inversion (CSI) techniques (e.g., Finite-Element (FEM) forward model CSI). This is especially true when trying to image highly inhomogeneous scatterers with high contrast values. Despite the advances made during the last twenty years, images containing reconstruction artifacts still remain an issue. As for reconstruction time, the traditional CSI technique, with its iterative approach, may consume hours of processing time and require extensive computational resources. In contrast, certain embodiments of an electromagnetic imaging system replace in whole or in part forward solves and, in general, the CSI approach, improving computation speed and reducing imaging artifacts, as well as, in some embodiments, improving accuracy of an initial guess/prior information and calibration of data. [0050] Having summarized certain features of an electromagnetic imaging system of the present disclosure, reference will now be made in detail to the description of an electromagnetic imaging system as illustrated in the drawings. While an electromagnetic imaging system will be described in connection with these drawings, there is no intent to limit it to the embodiment or embodiments disclosed herein. For instance, in the description that follows, one focus is on grain bin monitoring, and in particular, the imaging of grain as a stored commodity. However, certain embodiments of an electromagnetic imaging system may be used to determine the features of other contents/commodities of a container, including one or any combination of other materials or solids, fluids, or gases, as long as such contents reflect electromagnetic waves. Additionally, certain embodiments of an electromagnetic imaging system may be used in other industries, including the medical industry, among others. Further, although the description identifies or describes specifics of one or more embodiments, such specifics are not necessarily part of every embodiment, nor are all various stated advantages necessarily associated with a single embodiment or all embodiments. On the contrary, the intent is to cover all alternatives, modifications and equivalents included within the spirit and scope of the disclosure as defined by the appended claims. Further, it should be appreciated in the context of the present disclosure that the claims are not necessarily limited to the particular embodiments set out in the description. [0051] Some embodiments of the disclosure may utilize a one-shot calibration system to provide for a single data set calibration for an electromagnetic inverse imaging system. For example, embodiments of the disclosure may utilize any of the one-shot calibration systems and methods described in International Application PCT/IB2022/052392, to Asefi et al., filed March 16, 2022, and published as WO 2022/200932 A1. [0052] FIG.1 is a schematic diagram that illustrates an example environment 10 in which an embodiment of an electromagnetic imaging system (e.g., a commodity monitoring system) may be implemented. It should be appreciated by one having ordinary skill in the art in the context of the present disclosure that the environment 10 is one example among many, and that some embodiments of an electromagnetic imaging system may be used in environments with fewer, greater, and/or different components than those depicted in FIG.1. The environment 10 comprises a plurality of devices that enable communication of information throughout one or more networks. The depicted environment 10 comprises an antenna array 12 comprising a plurality of antenna probes 14 and an antenna acquisition system 16 (e.g., an antenna controller) that is used to monitor contents, or as equivalently used herein, a commodity, within a container 18 and uplink with other devices to communicate and/or receive information. The container 18 is depicted as one type of grain storage bin (or simply, grain or storage bin), though it should be appreciated that containers of other geometries, for the same (e.g., grain) or other contents, with a different arrangement (side ports, etc.) and/or quantity of inlet and outlet ports, may be used in some embodiments. As is known, electromagnetic imaging uses active transmitters and receivers of electromagnetic radiation to obtain quantitative and qualitative images of one or more features (e.g., the complex dielectric profile) of an object of interest (e.g., here, the contents or grain). Thus, the transmitters illuminate the target with electromagnetic signals and data is collected by several receivers on the measurement surface S. The target lies in the imaging domain D formed by the container 18. [0053] As shown in FIG. 1, multiple antenna probes 14 of the antenna array 12 are mounted along the interior of the container 18 in a manner that surrounds the contents to effectively collect the scattered signal. For instance, each transmitting antenna probe is polarized to excite/collect the signals scattered by the contents. That is, each antenna probe 14 illuminates the contents while the receiving antenna probes or sensors collect the signals scattered by the contents. The antenna probes 14 are connected (via cabling, such as coaxial cabling) to a radio frequency (RF) switch matrix or RF multiplexor (MUX) of the antenna acquisition system 16, the switch/mux switching between the transmitter/receiver pairs. That is, the RF switch/mux enables each antenna probe 14 to either deliver RF energy to the container 18 or collect the RF energy from the other antenna probes 14. The switch/mux is followed by an electromagnetic transceiver (TCVR) system of the antenna acquisition system 16 (e.g., an antenna controller including a vector network analyzer or VNA). The electromagnetic transceiver system generates the RF wave for illumination of the contents of the container 18 as well as receiving the measured fields by the antenna probes 14 of the antenna array 12. As the arrangement and operations of the antenna array 12 and antenna acquisition system 16 are known, further description is omitted here for brevity. Additional information may be found in the publications “Industrial scale electromagnetic grain bin monitoring”, Computers and Electronics in Agriculture, 136, 210-220, Gilmore, C., Asefi, M., Paliwal, J., & LoVetri, J., (2017), “Surface-current measurements as data for electromagnetic imaging within metallic enclosures”, IEEE Transactions on Microwave Theory and Techniques, 64, 4039, Asefi, M., Faucher, G., & LoVetri, J. (2016), and “A 3-d dual-polarized near-field microwave imaging system”, IEEE Trans. Microw. Theory Tech., Asefi, M., OstadRahimi, M., Zakaria, A., LoVetri, J. (2014). [0054] Note that in some embodiments, the antenna acquisition system 16 may include additional circuitry, including a global navigation satellite systems (GNSS) device or triangulation- based devices, which may be used to provide location information to another device or devices within the environment 10 that remotely monitors the container 18 and associated data. The antenna acquisition system 16 may include suitable communication functionality to communicate with other devices of the environment. [0055] The uncalibrated, raw data collected from the antenna acquisition system 16 is communicated (e.g., via uplink functionality of the antenna acquisition system 16) to one or more devices of the environment 10, including devices 20A and/or 20B and/or servers 26A through 26N. Communication by the antenna acquisition system 16 may be achieved using near field communications (NFC) functionality, Blue-tooth functionality, 802.11-based technology, satellite technology, streaming technology, including LoRa, and/or broadband technology including 3G, 4G, 5G, etc., and/or via wired communications (e.g., hybrid-fiber coaxial, optical fiber, copper, Ethernet, etc.) using TCP/IP, UDP, HTTP, DSL, among others. The devices 20A and 20B communicate with each other and/or with other devices of the environment 10 via a wireless/cellular network 22 and/or wide area network (WAN) 24, including the Internet. The wide area network 24 may include additional networks, including an Internet of Things (IoT) network, among others. Connected to the wide area network 24 is a computing system comprising one or more servers 26 (e.g., 26A...26N). [0056] The devices 20 may be embodied as a smartphone, mobile phone, cellular phone, pager, stand-alone image capture device (e.g., camera), laptop, tablet, personal computer, workstation, among other handheld, portable, or other computing/communication devices, including communication devices having wireless communication capability, including telephony functionality. In the depicted embodiment of FIG.1, the device 20A is illustrated as a smartphone and the device 20B is illustrated as a laptop for convenience in illustration and description, though it should be appreciated that the devices 20A, 20B may take the form of other types of devices as explained above, and as described in further detail below in regard to FIG.11. [0057] The devices 20A, 20B provide (e.g., relay) the (uncalibrated, raw) data sent by the antenna acquisition system 16 to one or more servers 26 via one or more networks. The wireless/cellular network 22 may include the necessary infrastructure to enable wireless and/or cellular communications between the devices 20A, 20B (also referred to herein collectively as “20”) and the one or more servers 26A through 26N (referred to herein collectively as “26”). There are a number of different digital cellular technologies suitable for use in the wireless/cellular network 22, including: 3G, 4G, 5G, GSM, GPRS, CDMAOne, CDMA2000, Evolution-Data Optimized (EV-DO), EDGE, Universal Mobile Telecommunications System (UMTS), Digital Enhanced Cordless Telecommunications (DECT), Digital AMPS (IS-136/TDMA), and Integrated Digital Enhanced Network (iDEN), among others, as well as Wireless-Fidelity (Wi-Fi), IEEE 802.11, streaming, etc., for some example wireless technologies. [0058] The wide area network 24 may comprise one or a plurality of networks that in whole or in part comprise the Internet. The devices 20 may access the one or more servers 26 via the wireless/cellular network 22, as explained above, and/or the Internet 24, which may be further enabled through access to one or more networks including PSTN (Public Switched Telephone Networks), POTS, Integrated Services Digital Network (ISDN), Ethernet, Fiber, DSL/ADSL, Wi-Fi, among others. For wireless implementations, the wireless/cellular network 22 may use wireless fidelity (Wi-Fi) to receive data converted by the devices 20 to a radio format and process (e.g., format) for communication over the Internet 24. The wireless/cellular network 22 may comprise suitable equipment that includes a modem, router, switching circuits, etc. [0059] The servers 26 are coupled to the wide area network 24, and in one embodiment may comprise one or more computing devices networked together, including an application server(s) and data storage. In one embodiment, the servers 26 may serve as a cloud computing environment (or other server network) configured to perform processing required to implement an embodiment of an electromagnetic imaging system. When embodied as a cloud service or services, the server 26 may comprise an internal cloud, an external cloud, a private cloud, a public cloud (e.g., commercial cloud), or a hybrid cloud, which includes both on-premises and public cloud resources. For instance, a private cloud may be implemented using a variety of cloud systems including, for example, Eucalyptus Systems, VMWare vSphere®, or Microsoft® HyperV. A public cloud may include, for example, Amazon EC2®, Amazon Web Services®, Terremark®, Savvis®, or GoGrid®. Cloud-computing resources provided by these clouds may include, for example, storage resources (e.g., Storage Area Network (SAN), Network File System (NFS), and Amazon S3®), network resources (e.g., firewall, load-balancer, and proxy server), internal private resources, external private resources, secure public resources, infrastructure-as-a-services (IaaSs), platform-as-a-services (PaaSs), or software-as-a-services (SaaSs). The cloud architecture of the servers 26 may be embodied according to one of a plurality of different configurations. For instance, if configured according to MICROSOFT AZURE™, roles are provided, which are discrete scalable components built with managed code. Worker roles are for generalized development, and may perform background processing for a web role. Web roles provide a web server and listen for and respond to web requests via an HTTP (hypertext transfer protocol) or HTTPS (HTTP secure) endpoint. VM roles are instantiated according to tenant defined configurations (e.g., resources, guest operating system). Operating system and VM updates are managed by the cloud. A web role and a worker role run in a VM role, which is a virtual machine under the control of the tenant. Storage and SQL services are available to be used by the roles. As with other cloud configurations, the hardware and software environment or platform, including scaling, load balancing, etc., are handled by the cloud. [0060] In some embodiments, the servers 26 may be configured into multiple, logically- grouped servers (run on server devices), referred to as a server farm. The servers 26 may be geographically dispersed, administered as a single entity, or distributed among a plurality of server farms. The servers 26 within each farm may be heterogeneous. One or more of the servers 26 may operate according to one type of operating system platform (e.g., WINDOWS-based O.S., manufactured by Microsoft Corp. of Redmond, Wash.), while one or more of the other servers 26 may operate according to another type of operating system platform (e.g., UNIX or Linux). The group of servers 26 may be logically grouped as a farm that may be interconnected using a wide- area network connection or medium-area network (MAN) connection. The servers 26 may each be referred to as, and operate according to, a file server device, application server device, web server device, proxy server device, or gateway server device. [0061] In one embodiment, one or more of the servers 26 may comprise a web server that provides a web site that can be used by users interested in the contents of the container 18 via browser software residing on a device (e.g., device 20). For instance, the web site may provide visualizations that reveal physical properties (e.g., moisture content, permittivity, temperature, density, etc.) and/or geometric and/or other information about the container and/or contents (e.g., the volume geometry, such as cone angle, shape, height of the grain along the container wall, etc.). [0062] The functions of the servers 26 described above are for illustrative purpose only. The present disclosure is not intended to be limiting. For instance, functionality of an electromagnetic imaging system may be implemented at a computing device that is local to the container 18 (e.g., edge computing), or in some embodiments, such functionality may be implemented at the devices 20. In some embodiments, functionality of an electromagnetic imaging system may be implemented in different devices of the environment 10 operating according to a primary-secondary configuration or peer-to-peer configuration. In some embodiments, the antenna acquisition system 16 may bypass the devices 20 and communicate with the servers 26 via the wireless/cellular network 22 and/or the wide area network 24 using suitable processing and software residing in the antenna acquisition system 16. [0063] Note that cooperation between the devices 20 (or in some embodiments, the antenna acquisition system 16) and the one or more servers 26 may be facilitated (or enabled) through the use of one or more application programming interfaces (APIs) that may define one or more parameters that are passed between a calling application and other software code such as an operating system, a library routine, and/or a function that provides a service, that provides data, or that performs an operation or a computation. The API may be implemented as one or more calls in program code that send or receive one or more parameters through a parameter list or other structure based on a call convention defined in an API specification document. A parameter may be a constant, a key, a data structure, an object, an object class, a variable, a data type, a pointer, an array, a list, or another call. API calls and parameters may be implemented in any programming language. The programming language may define the vocabulary and calling convention that a programmer employs to access functions supporting the API. In some implementations, an API call may report to an application the capabilities of a device running the application, including input capability, output capability, processing capability, power capability, and communications capability. [0064] An embodiment of an electromagnetic imaging system (e.g., the commodity monitoring system) may include any one or a combination of the components of the environment 10. For instance, in one embodiment, the electromagnetic imaging system (e.g., the commodity monitoring system) may include a single computing device (e.g., one of the servers 26 or one of the devices 20) comprising all or in part the functionality of the electromagnetic imaging system, and in some embodiments, the electromagnetic imaging system (e.g., the commodity monitoring system) may comprise the antenna array 12, the antenna acquisition system 16, and one or more of the server 26 and/or devices 20. For purposes of illustration and convenience, implementation of an embodiment of an electromagnetic imaging system (e.g., the commodity monitoring system) is described in the following as being implemented in a computing device (e.g., comprising one or a plurality of GPUs and/or CPUs) that may be one of the servers 26, with the understanding that functionality may be implemented in other and/or additional devices. [0065] In one example operation, a user (via the device 20) may request measurements of the contents of the container 18. This request is communicated to the antenna acquisition system 16. In some embodiments, the triggering of measurements may occur automatically based on a fixed time frame or based on certain conditions or based on detection of an authorized user device 20. In some embodiments, the request may trigger the communication of measurements that have already occurred. The antenna acquisition system 16 activates (e.g., excites) the antenna probes 14 of the antenna array 12, such that the acquisition system (via the transmission of signals and receipt of the scattered signals) collects a set of raw, uncalibrated electromagnetic data at a set of (a plurality of) discrete, sequential frequencies (e.g., 10-100 Mega-Hertz (MHz), though not limited to this range of frequencies nor limited to collecting the frequencies in sequence). In one embodiment, the uncalibrated data comprises total-field, S- parameter measurements. As is known, S-parameters are ratios of voltage levels (e.g., due to the decay between the sending and receiving signal). Though S-parameter measurements are described, in some embodiments, other mechanisms for describing voltages on a line may be used. For instance, power may be measured directly (without the need for phase measurements), or various transforms may be used to convert S-parameter data into other parameters, including transmission parameters, impedance, admittance, etc. Since the uncalibrated S-parameter measurement is corrupted by the switching matrix and/or varying lengths and/or other differences (e.g., manufacturing differences) in the cables connecting the antenna probes 14 to the antenna acquisition system 16, some embodiments of an electromagnetic imaging system may use only magnitude (i.e., phaseless) data as input, which is relatively unperturbed by the measurement system. The antenna acquisition system 16 communicates (e.g., via a wired and/or wireless communications medium) the uncalibrated (S-parameter) data to the device 20, which in turn communicates the uncalibrated data to the server 26. At the server 26, data analytics are performed using an electromagnetic imaging system as described further below. [0066] In the description that follows, an embodiment of a whole-domain basis function system configured as a CSI imaging system is described. Transmitters illuminate the target within the container 18 with electromagnetic signals and data is collected by several receivers on the measurement surface S. The target lies in the imaging domain D as defined by the container 18. Optimization-based quantitatively reconstruct the target’s dielectric properties (εr) and/or magnetic properties (μr). Regions of high moisture of store grain within the container 18, called “hotspots”, can cause spoilage. The permittivity and conductivity of grain is related to its moisture content. The size of an embodiment of container 18 is on the order of meters, “hotspots” are on the order of 10s of centimeters. As one skilled in the art will understand, a container 18 such as a grain bin is a metallic, quasi-resonant, enclosure. This causes difficulty gathering calibrated datasets. [0067] Having described certain embodiments of an electromagnetic imaging system, it should be appreciated within the context of the present disclosure that one embodiment of a CSI-based imaging method, denoted as method 102 and illustrated in FIG.2, and implemented using one or more processors (e.g., of a computing device or plural computing devices), comprises [0068] Embodiments of the present disclosure include utilizing a modified contrast source inversion (CSI) method to solve these issues. For example, whole domain basis functions may be applied to a CSI contrast update. Basis functions may be chosen based on features that are expected to be present in the container 18 with a hotspot. As a result, the number of degrees of freedom of a contrast variable may be reduced. Contrast and contrast sources may be introduced as shown in Equations 1 and 2: (Eq.1) (Eq.2) [0069] Sources for the scattered fields may depend on the operator formulation as shown in Equation 3. (Eq.3) [0070] Additionally, FEM discretization supports inhomogeneous (background) media and semi-resonant enclosure via boundary conditions, as represented in Equation 4. (Eq.4) [0071] Magnetic fields at the bin walls on S may be measured and determined from [0072] Furthermore, the contrast source forward operator may be independent of the target, as shown in Equation 5. [0073] During Contrast Source Inversion (CSI) process, two variables, w and χ may be updated to minimize the cost functional represented in Equation 6. (Eq.6) [0074] where ^ indicates the background, t indicates the transmitter (source) index, and: [0075] Furthermore, in FEM-CSI, w and χ are typically discretized in FEM nodal basis on first-order tetrahedral elements. Within a given tetrahedral, Ωk, w and χ may be represented as shown in Equation 9. (Eq.9) [0076] Variables ⃗ei are vectors determined by a tetrahedral’s geometry, as shown in FIG. 10. [0077] Additionally, the CSI technique may update w and χ using a non-linear conjugate gradient method. Gradients of the CSI Cost Functional as represented in Equation 10. (Eq.10) [0078] Equation 10 may be determined and solved with respect to pulse basis function coefficients and w edge basis coefficients. Moreover, ^ may be updated by minimizing the domain error, using the current values of and , as shown in Equation 11. (Eq.11) [0079] The method and embodiments of the disclosure may reduce the degrees of freedom of ^. Embodiments include a basis function that represents characteristic features present in problem of interest, such as, for example, Grain bin imaging → “hotspots” and “layers”. A radial basis function may be chosen according to the following: “hotspot” ≈ a spherical RBF and “layers” ≈ a one dimensional RBF in the vertical direction. [0080] According to embodiments of the disclosure, in each CSI iteration, the contrast may be updated from the domain error as shown in Equation 12: [0081] The domain error may include a corresponding linear system of equations, as represented in Equation 13. (Eq.13) [0082] where E has a shape (N tx × N tet ,N tet ), w has shape (N tx × N tet , 1), and χ has shape (N tet , 1) and represents a contrast solution in pulse basis. [0083] Additionally, may be represented using a set of basis functions coefficients , as shown in Equation 14. (Eq.14) [0084] A linear basis function may be represented as Equation 15. (Eq.15) [0085] where B is a matrix of basis functions, where each column corresponds to one basis function, and each row corresponds to a tetrahedral centroid. [0086] Updating may be performed via two methods: [0087] A first method of the two methods may be referred to as a “Built-in” method, and the Built-in method may include the acts of: [0088] (1) Solving , and [0089] (2) Updating [0090] A second method of the two methods may be referred to as a “Projection of Pulse Basis” method, and the Projection of Pulse Basis method may include the acts of: [0091] (1) Solving for , [0092] (2) Solving , and [0093] (3) Updating [0094] Regardless of method utilized to update , gradients with respect to w may be performed in edge basis. [0095] Additionally, the second method (i.e., the Projection of Pulse Basis Method) may include choosing Gaussian “radial basis functions” (“RBFs) and RBFs in cylindrical coordinates as depicted in FIG.3. Furthermore, centroids may be chosen to be equidistant in a commodity (e.g., grain) volume in each of z, r, and ϕ dimensions. The composite radial basis functions may include the functions of Equation 15. [0096] where ϕi, rj , and zk are chosen, equally spaced, centroids in each dimension. A constant term and lower order terms (e.g., f(z, r), f(z, ϕ), etc.) may also be included. [0097] Gaussian widths may be determined by adjacent functions in a given dimension intercepting at a value α. Equation 16 depicts an example determination of a Gaussian width. [0098] Where Δr represents a distance between adjacent RBFs. [0099] In some embodiments, a number of the basis functions may be increased during the CSI iterations, which may effectively increase a reconstruction resolution. An example set of CSI iterations utilizing the depicted basis function orders are shown in Table 1.

Table 1 CSI Iterations z-order r-order ϕ-order 1-4 3 0 0 5-8 5 0 0 9-12 7 0 0 13-40 7 2 2 41-47 7 3 3 [00100] Referring still to Table 1, criterion to increase the basis function order was a 2% change in a relative norm of the basis function coefficients. [00101] FIGS 4-9 show example results of moisture content in containers obtained using the above methods. [00102] Accordingly, the basis function FEM-CSI projects contrast recovered on FEM tetrahedral mesh onto lower-order basis at each iteration of CSI. Lower-order basis constructed using Gaussian RBFs in each dimension of cylindrical coordinate system. Number of basis functions used in each dimension can be increased to increase resolution. Pattern of increasing resolution can be tailored to expected properties of application, e.g., layers of grain in the stored-grain imaging application. Resolution is increased when coefficients of the BF- expansion converge [00103] Having described certain embodiments of an electromagnetic imaging system, it should be appreciated within the context of the present disclosure that one embodiment of a CSI-based imaging method, denoted as method 102 and illustrated in FIG. 2, and implemented using one or more processors (e.g., of a computing device or plural computing devices), comprises [00104] Any process descriptions or blocks in flow diagrams should be understood as representing logic (software and/or hardware) and/or steps in a process, and alternate implementations are included within the scope of the embodiments in which functions may be executed out of order from that shown or discussed, including substantially concurrently, or with additional steps (or fewer steps), depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present disclosure. [00105] Certain embodiments of an electromagnetic imaging system creates high- order parametric models that may describe shape, moisture-content, temperature, or density maps, among other information, of a stored commodity. The higher order parametric models or algorithms may in some embodiments be created by fusing information obtained from several techniques and algorithms, including the electromagnetic ray-based inversions of the relevant physical parameters of the grain and the measured electromagnetic resonances within the storage bin. In some embodiments, deep learning techniques may be used for both the extraction of information from the above-described methods as well as in the data fusion process. [00106] FIG. 11 is a schematic view of a computer device 414. In some embodiments, one or more of the antenna acquisition system 16, the devices 20A, 20B, or the servers 26 may include a computer device such as the computer device 414 of FIG. 4. The computer device 414 may include a communication interface 402, a processor 404, a memory 406, a storage device 408, an input/output device 410, and a bus 412. [00107] In some embodiments, the processor 404 includes hardware for executing instructions, such as those making up a computer program. As an example, and not by way of limitation, to execute instructions, the processor 404 may retrieve (or fetch) the instructions from an internal register, an internal cache, the memory 406, or the storage device 408 and decode and execute them. In some embodiments, the processor 404 may include one or more internal caches for data, instructions, or addresses. As an example, and not by way of limitation, the processor 404 may include one or more instruction caches, one or more data caches, and one or more translation look aside buffers (TLBs). Instructions in the instruction caches may be copies of instructions in the memory 406 or the storage device 408. [00108] The memory 406 may be coupled to the processor 404. The memory 406 may be used for storing data, metadata, and programs for execution by the processor(s). The memory 406 may include one or more of volatile and non-volatile memories, such as Random- Access Memory (“RAM”), Read-Only Memory (“ROM”), a solid state disk (“SSD”), Flash, Phase Change Memory (“PCM”), or other types of data storage. The memory 406 may be internal or distributed memory. [00109] The storage device 408 may include storage for storing data or instructions. As an example, and not by way of limitation, storage device 408 can comprise a non- transitory storage medium described above. The storage device 408 may include a hard disk drive (HDD), Flash memory, an optical disc, a magneto-optical disc, magnetic tape, or a Universal Serial Bus (USB) drive or a combination of two or more of these. The storage device 408 may include removable or non-removable (or fixed) media, where appropriate. The storage device 408 may be internal or external to the computing storage device 408. In one or more embodiments, the storage device 408 is non-volatile, solid-state memory. In other embodiments, the storage device 408 includes read-only memory (ROM). Where appropriate, this ROM may be mask programmed ROM, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), electrically alterable ROM (EAROM), or Flash memory or a combination of two or more of these. [00110] The input/output device 410 may allow an operator of the commodity monitoring system 114 to provide input to, receive output from, and otherwise transfer data to and receive data from computer device 414. The input/output device 410 may include a mouse, a keypad or a keyboard, a joystick, a touch screen, a camera, an optical scanner, network interface, modem, other known I/O devices, or a combination of such I/O interfaces. The input/output device 410 may include one or more devices for presenting output to an operator, including, but not limited to, a graphics engine, a display (e.g., a display screen), one or more output drivers (e.g., display drivers), one or more audio speakers, and one or more audio drivers. In certain embodiments, the input/output device 410 is configured to provide graphical data to a display for presentation to an operator. The graphical data may be representative of one or more graphical user interfaces and/or any other graphical content as may serve a particular implementation. As is described above, the computer device 414 and the input/output device 410 may be utilized to display data (e.g., images and/or video data) regarding the contents of the container. [00111] The communication interface 402 can include hardware, software, or both. The communication interface 402 may provide one or more interfaces for communication (such as, for example, packet-based communication) between the computer device 414 and one or more other computing devices or networks (e.g., a server). As an example, and not by way of limitation, the communication interface 402 may include a network interface controller (NIC) or network adapter for communicating with an Ethernet or other wire-based network or a wireless NIC (WNIC) or wireless adapter for communicating with a wireless network, such as a WI-FI. [00112] In some embodiments, the bus 412 (e.g., a Controller Area Network (CAN) bus) may include hardware, software, or both that couples components of computer device 414 to each other and to external components. [00113] All references cited herein are incorporated herein in their entireties. If there is a conflict between definitions herein and in an incorporated reference, the definition herein shall control. [00114] The embodiments of the disclosure described above and illustrated in the accompanying drawings do not limit the scope of the disclosure, which is encompassed by the scope of the appended claims and their legal equivalents. Any equivalent embodiments are within the scope of this disclosure. Indeed, various modifications of the disclosure, in addition to those shown and described herein, such as alternate useful combinations of the elements described, will become apparent to those skilled in the art from the description. Such modifications and embodiments also fall within the scope of the appended claims and equivalents. [00115] It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations, merely set forth for a clear understanding of the principles of the disclosure. Many variations and modifications may be made to the above-described embodiment(s) of the disclosure without departing substantially from the scope of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.