Title:

M i crowave Si ogle Pixel Imager (MSPI)

Inventors:

Justin Bobak. Hath» Aiqadah, Scott M. Rudolph, and Michael W. Nurnberger

Citizenship: OS

Citizenship: US

Citizenship; US

Citizenship; US

Suresh Koshy - 42,761

US N AVAL RESEARCH LABORATORY

4555 Overlook Ave, SW

Code 1008.2

Washington, DC 20375

(202) 767-0302 Mlerowave Single Pixel Imager (MSP!)

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This Application claims the benefit of U.S. Provisional Application Serial No,

62/867,431. filed on 27 June 2019, the entirety of which i incorporated herein by reference.

FEDERALLY-SPONSORED RESEARCH AMD DEVELOPMENT

[0002] The United States Government has ownership rights in this invention. Licensing inquiries ma be directed to Office of Technology Transfer, IIS Naval Research Laboratory, Code 1004, Washington, DC 20375, USA; +1,202,767,7230; techtran@nrinavy.mih referencing NC 1 11393-1182.

BACKGROUND OF THE INVENTION

Field of the Invention

[0003] This invention relates m general to a microwave single pixel radiometric system, and in particular to a microwave single pixel radiometric system having a reconfigurable reilectarray antenna.

Description of the Related Ait

[0004] Radio frequency systems used for remote sensing have relativel large apertures to achieve desired beam directivity, which drives angular resolution. The increasing use of' smaller platforms in space, air, and on the ground/sea, requires smal ler sensor systems. Receivers, including radiometer receivers, can and have been miniaturized, hut the aperture physical dimensions have not

1 been reduced, except when tile mission allows the resolution to be proportionately reduced, in turn allowing the beamwidth to be relatively large. The frequency of operation can be increased, leading to smaller physical apertures that have the same electrical size, but there are mission that must be performed with specific microwave frequency bands due to the wavelength-dependent sensitivity of environmental parameters.

[0(105] For scenes that are sufficiently compressible, compressive sensing recovery techniques can be used. This means 1) a scene can be represented by a limited number (often substantially fewer than the n umber of pixels in an image) of representa tion basis elements. Further , 2} A set of sampling basis functions that are not unique and do not need to be known priori, so that any set of sampling bases, or sampling basis functions, that meet the proper criteria, can be used to sample the scene and retrieve a representative image. AlSaafin, W, et al,“Compressive sensing super resolution from multiple observations with application to passive millimeter wave images," Digital Signal Processing, 2015, pp J 80-190* Vol.50, Elsevier, Amsterdam, Netherlands, incorporated herein by reference, showed that super-resolution, meaning resolution greater than that achievable by a dif eiion-limited system, can be incorporated with compressive sensing,

[0006] The single pixel camera is a specific hardware implementation of compressive sensing principles. The technique was originally demonstrated optically, in which an image Is focused on an array of digital micromirrors, as discussed in Barauiuk, R,“A lecture on compressive sensing,” IEEE

Signal Processing Magazine, June 2007, pp.1-9, Issue 24, Mo. 4, IEEE, Piseataway, NJ, incorporated herein by reference. The reflection from the array was then focused into a single photodetector. The mirrors were turned‘fen" or“off ^, (i.e., direction of reflection directed towards or away fro the photodetector) according to a randomly-generated set of sequences, forming the sampling bases mentioned above). A photodetector measurement was taken for each sequence of mirror setings,

2 The output .measurements and the associated sequences were combined in an algorithm that generated an image. A simi lar technique was used at millimeter wave frequencies at Northwestern University and Argqune National Labs, as discussed in ITS, Patent No. 8941061 to Gopaisami, et ah, incorporated herein by reference, A traditional architecture millimeter wave receiver was used as the single sensor. An image was formed on a lithographically-produced, oversized mask that allowed radiation through some“pixels” and blocked radiation incident upon other“pixels”. This mask was carefully positione and -translated in a plane perpendicular to the radiometer boresight in order to form the sampling bases mentioned above.

BRIEF SUMMARY OF THE INVENTION

[0007] An embodiment of the invention includes a method A targeted scene is sampled.

Sampling a targeted scene includes the following. A plurality of modulated antenna patterns is generated using a refleetarray and a plurality of antenna temperatures respectively corresponding to the plurality of modulated antenna patterns is measured A retrieved scene corresponding to the sample targeted scene is generated. Generating a retrieved scene corresponding to the sampled targeted scene includes the following. The plurality of modulated antenna patterns and the corresponding plurality of antenna temperatures are fed. into a compressive sensing imaging algorithm.

[0008] Another embodiment of the invention includes a microwave single pixel imager apparatus. The apparatus includes a refleetarray, The refleetarray includes a plurality of independently controllable reflector elements. Each reflector element of the plurality of

3 independently controllable reflector elements produces a corresponding independently controllable reflection coefficient.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] FIG, 1 is a flowchart of a m ethod according to a embodimen t: of the invention.

10 10] FIG.2 is a block diagram of microwave single pixel Imager apparatus according to an embodiment of the in vention.

[001 3 ] FIG. 3 is a perspective view of a fefleetarray according to an embodiment of the invention.

[0032] FIG, 4 is a block diagra of a reileetarray according to an embodiment of the invention, the refleetarray including reflector elements.

[0013] FIG. 5A is a perspective view of an illustrative, single reflector element of a reileetarray, according to an embodiment of the invention, the reflector element being in a coupled state.

[0034] FIG. SB is a cross-sectional, perspective view of the illustrative reflector element, according to an embodiment of the invention, the reflector element being in a coupled state

[0015] FIG. 5C is a cross-sectional, perspective view of the illustrative reflector element, according to an embodiment of the invention, the reflector element being in a decoupled state.

[0016] FIG. b is a block diagram of a reileetarray according to an embodiment of the invention, the reileetarray including tri-state surfaces.

4 DETAILED DESCRIPTION OF THE INVENTION

[0017 ] An embodiment of th invention includes a method and is described as follows with reference to, by way of example, FIG, 1. A targeted scene is sampled, as in Step Si 00. Sampling a targeted scene includes the following. A plurality of modulated antenna paterns is generated using a refleetarray, as in Step SH 0. I an embodiment of the invention, the reilectarray is a receive-only refleetarray. fn another embodiment of the invention, the refiectarray is a recontlgurable refiectarray, that is, a refiectarray capable of being configurable as a transmitter or as a receiver. A plurality of antenna temperatures respectively corresponding to the plurality of modulate antenna patterns is measured, as in Step SI 20 A retrieve scene corresponding to the sampled targeted scene is generated, as in Ste S200, Generating a retrieved scene corresponding to the sampled targete scene includes the following. The plurality of modulated antenna patterns and the corresponding plurality of antenna tempe tures are fed into a compressive sensing imag ng algorithm, as in Step S220.

[0018] Optionally, the generating a plurality of modulated antenna patterns using a eceive' only refiectarray using a pre-characterked plurality of diverse masks, as in Step S210. The pre- eharaeierized plurality of diverse masks are pair-wise mutually incoherent and collectively comprehensive of the targeted scene.

[00.19] For the purpose of this patent application, pair-wise mutuall incoherent is a term of art and is defined as follows. Let Iscene he a brightness temperature image consisting of n pixels, fsceae is defined as its finite approximation, when

CD

.for some tolerance v > 0, and when T'wsms satisfies

5

where Y is a » x » orfhoraorraal basis and c is a n dimensional vector of coefficients.

The further said to be a sparse approximation to ¾ene when only k « n coefficients of care non-zero. Such a vector c satisfying this property i s said to be fc-sparse. Let F be a m x n matrix comprising m different antenna patterns that measures the n pixel scene /scene- There are two characterizations of mutually incoherent antenna patterns. The first is based on a restricted isometry principle (“RIP* ⁵ ) and the second is based on mutual coherence. Define the matrix /I FY ^G , For some appropriate scaling of zl, A satisfies a RIP condition of order k, if there i a constant <¾ satisfying

4 . ¾ ⁾ MI < \\L*\\ί £ C ^{5 ·} +- 4} I IK (3) for all n dimensional vectors that are A-sparse. A matrix that satisfies this can be thought of as nearly orthononnal when restricted to only A-sparse vectors. For retrieval of a ^-sparse image we aim to minimize a RIP condition of order 2k for the matrix A, For example, DAVENPORT ET AL. _S Constrained Adaptive Sensing, IEEE Transactions of Signal Processing, 16 October 2016, pp. 5437- 5449, VoL 64, No. 20, IEEE, Piscataway, NI, USA,, Incorporated herein by reference, shows that when A satisfies a RIP condition of order 2k with ^’ ^ ^ for a measurement vector b corrupted with independent white Gaussian noise with variance a ² the expected quality of the z' k# ft, k>g n

reconstruction is bounded by . where C is some constant that depends on S _k . Which basically tells us if the patterns a incoherent enough we can reduce our error by either aking smaller or maybe by finding a basis for which k is smaller. The mutual coherence of a matrix A is a little bit easier to understand and it is defined as

6

which isthe largest pairwise correlation between any two columns of matrix . Mutual coherence could be linked to the RIP. For example, as discussed in ELDAR ET AL , Compressive Sensing Theory and Applications, 2012, pp 1-68, Cambridge University Press, Cambridge, UK , incorporated herein by reference, matrix ,4 satisfies the RIP of order k with constant <¾ ~ (k - 1)p, for all k < \/m. Thus, as the mutual coherence of A goes down so does its RIP constant. So, again, more sparsity is favorable. In summary, either definition of“incoherence ^* is acceptable as a guiding principle in antenna pattern design according to an embodimen of the instant invention. The RIP gives a more precise characterization in terms of mathematical guarantees for retrieval of the image coefficients c for compressive sensing algorithms:. However, it is difficult to compute and/or verify. Mutuafeoherence is easy to compute, however, it is not an absolute requirement. In other words, the compressive sensing algorithm may still be able to perform satisfactorily even if it does not meet the mutual coherence conditions. Nevertheless, the aim is to reduce the mutual coherence as much as possible.

[0020] Optionally, the pre-eharacterized plurality of diverse masks include a plurality of precharacterized randomly genera ted masks. For the purpose of this patent application, the phrase randomly generated masks i a term of art and is defined herein as masks exhibiting a random distribution of electromagnetic reflection coefficients reconfigured through controllable reflector elements. The reflection coefficients encompass randoml generated amplitude and phase characteristics draw from a discrete categorical distribution with predefined probabilities.

[0021] Optionally, a number of the plurality of modulated antenna patterns and a number of the plurality of antenna temperatures depend on an expected sparsity level, as discussed above.

7 [0022] Optionally, the comprehensive sensing imaging algorithm includes comprehensive sensing imaging algorithm based on convex optimization, a comprehensive sensing imaging algorithm based on greedy methods, or a comprehensive sensing imaging algorithm based on non- eon vex optimization

[0023] Optionally, the compressive sensing imaging algorith includes a plurality of algorithm parameters. Examples of such algorithm parameters include penalty term weights. The generating a retrieved scene corresponding to the sampled targeted scene includes the following. The comprehensive sensing imaging algorithm is calibrated. Calibrating the comprehensive sensing imaging algorithm includes optimizing the plurality of algorithm parameters. Feeding the plurality of modulated antenna patterns and the corresponding plurality of antenna temperatures into a compressive sensing imaging algorithm includes the following. The optimized plurality of algori thm parameters is fed into the compressive sensing imaging algorithm.

[0024] Optionally, generating a retrieved scene corresponding to the sampled targeted scene includes estimating a brightness temperature scene from the plurality of modulated antenna paterns and the plurality of antenna temperatures using the compressive sensing algorithm, as in Ste S230.

[0025] Optionally, the reflectarray includes a plurality of independently controllable reflector elements. Each reflector element of the plurality of independently controllable reflector elements includes, or produces, a corresponding, independently controllable, standard reflection coefficient.

Optionally, the corresponding independently controllable reflection coefficient includes a corresponding. Independently controllable, standard reflection coefficient phase. The corresponding independently controllable reflection coefficient includes a reflection coefficient amplitude that is approximately 1. One of ordinary skill in the ar will readily appreciate that the reflection coefficient amplitude relates to a signal-to-aoise ratio, where in this case, the noise includes all the various

S standard radiometric errors. The .higher the signaf-to-noise ratio, the further away from one the reflection coefficient amplitude is permitted to be. Optionally, the corresponding independently controllable reflection coefficient phase is limited to two states: a nominal phase state and a second state about 90° from the nominal phase state, or about 180° from the nominal phase state. Optionally, each reflector element includes a standard nmlti-state surface. Examples of such standard multi-state surfaces include a Standard binary-state surface, a standar tr -state surface, or a standard quad-state surface. Optionally, the binary-state· surface includes a standard piezoelectric actuator, a standard electromechanical actuator, a standard mechanical actuator, a standard mieroelectromechanieaS actuator, a standard fluidic actuator, or standard nonlinearactuator, and the tri-state surface includes a standard piezoelectric actuator, a standard electromechanical actuator, a standard mechanical actuator, a standard microelectm echanical actuator, a standard fluidic actuator, or a standard nonlinear actuator. One of ordinary skill in the art will readily appreciate that other types of actuators can be used in alternative embodiments of the invention.

[0026] Another embodiment of the invention includes a microwave single pixel imager apparatus 100 and is described as follows with reference to, by way of example, FJGs. 2-5. The apparatus 100 includes a refieetarra 110. The refieetarray includes a plurality of independently controllable reflector elements 120, 122. Each reflector element of the plurality of independently controllable reflector elements 120, 122 includes, or produces, a corresponding independently controllable reflection coefficient. In an embodiment of the invention, the refieetarray 1 10 is a reeeive-oiif refieetarray. In another embodiment of the invention, the refieetarray 110 is a reecmfigurable refieetarray, that is, a refieetarray capable of being configurable as a transmitter or as a receiver.

9 [0027] Optionally, the corresponding independently controllable reflectio coefficient includes a corresponding independently controllable reflection coefficient phase. The corresponding independently controllable reflection coefficient includes a reflection coefficient amplitude of about one. Optionally, the corresponding independently controllable reflection coefficient phase includesa nominal phase state, about 9( from the nominal phase state, or about 180° fro the nominal phase state

[0028] Optionally, each reflector element of the pluralit of independently controllable reflector elements 120, 122 includes a binary-sta te surface 130, as shown by way of example in FIG. 3, or a tri-state surface 140, as shown by way of example in FIG. 4. Optionally, each binary-state surface 130 includes a standard piezoelectric actuator 150, a standard electromechanical actuator 160, a standard mechanical actuator 170, a standard nneroeteetemeehamcal actuator 180, a standard fluidic actuator 185, author a standard nonlinear actuator 190, For example, as shown by wa of illustration in FlGs. 5B and SC, the electromechanical actuator 160 includes a standard dielectric piston 164 with a meta lace to change the capacitive coupling between resonant triangular patches. The dielectric piston 164 is actuated using a standard linear solenoid. The phase shift can be tuned by adjusting the travel of the dielectric piston 164, the diameter of the metal face and/or the gap between the triangular metallic patches Optionally, each tri-state surface 140 includes a standard piezoelectric actuator 152, a standard electromechanical actuator 162, a standard mechanical actuator 172, a standard icroelectromechameal actuator IS2 _> a standar fluidic actuator 187, and/or a standard nonlinear actuator 1 2,

[0029] Optionally, the apparatus 100 further includes a standard feedhorn 200 directed towar the reflectarray I K). The apparatus also includes a standard radiometer 210 receiving energy from the feedhora 200.

10 [0030] Optionally, the apparatus 100 farther includes a computer-readable medium 220 storing instructions that, when executed by a computer 230, cause the computer to cooperate with therefleetarray ! 10 to carry out a method for generating a retrieved scene from a targeted scene by generating modulated antenna patterns at the refleetarray. The method includes the following. The targeted scene is sampl ed. Sampling the targeted scene includes generating a plurality of modulated antenna patterns using the refleetarray, and measuring a plurality of antenna temperatures respectively corresponding to the plurality of modulated antenna patterns. The method further includes generating the retrieve scene corresponding to the sampled targeted scene. Generating a retrieved scene corresponding to "the sampled targeted scene includes feeding the plurality of modulated antenna patterns and the corresponding plurality of antenna temperatures into a compressive sensing imaging algorithm.

[0031 ] Optionally, the generating a plurality of modulated antenna patterns using the refleetarray 110 includes using a pre-eharacterized plurality of diverse masks. The pre-eharaeterixe plurality of diverse masks being pair-wise mutually incoherent and collectively comprehensive of the targeted scene. Optionally, the pre-chantcierized plurality of diverse masks includes a precharacterized plurality of randomly generated masks. Optionally, a number of the plurality of modulated antenna patterns and a number of the plurality of antenna temperatures depend on an expected sparsity level

[0032] Optionally, in an embodiment of the invention employing blind image retrieval the comprehensive sensing imaging algorithm includes a standard compressive sensing imaging algorithm based on convex optimization, a standard compressive sensing imaging algorithm based on greedy methods, or a standard compressive sensing imaging algorithm based on non-convex optimization.

I ! [0033] Optionally, an embodiment of the invention incorporating additional prior knowledge of the scene improves accuracy. In such an embodiment of the invention, th compressive sensing imaging algorithm includes a standard compressive sensing imaging algorithm based on. convex optimization, a standard compressive sensing imaging algorithm based on. greedy methods, or a standard compressive sensing imaging algorithm based on non-eouvex optimization. Prior knowledge of the imag scene is used as a weighted bias which the various optimization methods leverage to improve brightnes temperature accuracy. This involves modifying the inputs into the standard compressive algorithms and the introductio of additional parameters. For example, a standar compressive sensing algorithm based on convex optimization takes the for

for retrieving an unknown sparse vector.* from measurements ty and b is a parameter controlling the amount of sparsity in the solution x. if, for example, we were given a prior estimate of the scene b we could modify the convex optimization program as follows

where we have added another parameter « to control the amount of bias towards the prior scene knowledge. Equation (6) does not appear as a convex optimization based standard compressive sensing algorithm, however it can be made to appear so by using a simple linear algebra transformation,

Then. (6) can be restated in a standard compressive sensing forma

12 The same sort of transformation would he applied for the case of standard non-eonvex compressive sensing or standard greedy methods based compressive sensing algorithms.

[0034] Optionally , an embodiment of the invention incorporating additional prior knowledge of the point-spread function (PSF) of the:refieeiarray 110 improves resolution. In such an embodiment of the invention, the compressive sensing imaging algorithm includes a compressive sensing imaging algorithm based on standard convex optimization, a compressive sensing imaging algorithm based on standard greedy methods, or a compressive sensing imaging algorithm based on standard non-eonvex optimization. Under such knowledge of the PSF, a high-resolution estimate of the scene image can be estimated by incorporating additional weighted constraints on the desired solution and is in the form of a constrained compressive sensing algorithm. For example, in this embodiment, a retrieval based on convex optimization would take the form

subject: to

F ^t o - Bx (9) for which c are the desired basis coefficients of the scene, x is the desired high-resolution image of the scene, G(x) is a penalty term that penalizes rapid spatial changes in the image and is given a parameter weight of b, and B is the convolutional matrix atributed to the PSF of the reileciarray. Such a formulation is in the form of a standard convex optimization program. Similar formulations can be used with standard non-eonve optimization solvers. Additionally, similar programs in the spirit of (9) can he recast in a form that is amenable to standard greedy methods.

[0035] Optionally, the compressive sensing imaging algorithm includes a plurality of algorithm parameters. Generating a retrieved scene corresponding to the sampled targete scene includes calibrating the comprehensive sensing imaging algorithm. Calibrating the comprehensive

13 sensing imaging algorithm comprising optimizing the pl urality of algorithm parameter. Feeding the plurality of modulated antenna patterns and the corresponding plurality of antenna temperatures into a compressive sensing imaging algorithm includes feeding the optimized plurality of algorithm parameters into the compressive sensing imaging algorithm.

[0036] Optionally, generating a retrieved scene corresponding to the sampled targeted scene includes estimating brightness temperature scene from the plurality of modulated antenna patterns and the plurality of antenna temperatures usin the compressive sensing algori thm.

[00371 Another embodiment of the invention includes a microwave single pixel imager apparatus (“MSPI”) 10(1 The MSP! includes a compressive sensing-supporting aperture (known as the Mechanically- Actuated Reconfigurable Refiectarray ARR ^' ') 110) and a compressive sensing imaging algorithm (‘*€SiA”}that ar coupled with a standard radiometer receiver. The apparatu 100 achieves high accuracy measurements of radiation from a significantly more constrained Size, Weight and Power and Cost (“SWaP”) sensor. Pixel angular resolution is significantly improved compared to a diffraction limited reflector of the same dimensions. System and component block diagrams are shown, by way of example, in PIGs, 2-4. The object of an embodiment of the invention is to make a series of measurements, TAI, of the scene:

Where T$ce»« is the scene data and R Q,f) are antenna pattern modulations used to sample the scene energy. MSP! incorporates the generation of sampling matrices into the MARK 110 of the system. An intermediate image is not formed on a mask, but rather the electromagnetic propert es change, resulting in the creation of different antenna patterns, 1¾{q,f).

14 [0038] The MARR 110 generates the sampling patterns, f _{B ,} The sampling paterns must provide proper sampli ng of the scene, meaning antenna paterns that sense e very e lement of the scene with different known weighting for each sequence, L The MARR 1 10 develops these modulated antenna patterns via binary state surfaces (“BBS”). The BSS are independently controllable metasurfaces or frequency-selective surfaces which change electromagnetic properties, in effect producing reflections wit specific electrical phases added. An embodiment of the MSPI 100 utilizes a specific distribution of two different BSS, one type switching between a reflection coefficient of near + .1/- I (ISO degree phase shift)., and a second type switching between reflection coefficients near 11 | (90 degree phase shift). In the current design, approximately 90% of the BSS are of the first type (÷ 1/4), The remaining elements serve to reduce the symmetry of the beam, impro ving the retrieval In order to avoid corrupting the antenna temperature measurements, TA*, extremely high reflectivity, low cross-polarization, and low sidelobe levels, are desirable from the MARR, which requires excellent electrical performance from the BSS elements.

[0039] An embodiment of the BSS elements reties on creation of a resonant structure that protrudes from a ground plane, such as shown by"way of illustration in FlGs. 5A-5C, For ease of understanding, FIG. 5 A. shows one reflector element. One of ordinary skill hi the art will readily appreciate that although FIG. 5.4 shows a hexagonal reflector element, other shapes are acceptable in alternative embodiments of the invention. Also, one of ordinary skill in the art will readily appreciate that although FIG 5A shows a resonant structure comprised of six triangular metallic patches, resonators of other shapes and materials are acceptable In alternative embodiments of the invention,

As shown in FIGs. SB and 5C, a standard linear actuator shifts a metallic face to alter the resonance. of the six metallic patches of the reflector element between a high position (“a coupled state ⁵ ), where the substructures resonate to produce a reflection coefficient phase close to that of a open circuit

15 (0°), and a low position f'a decoupled state”), in which proximity to the ground plane limits the coupling between the hexagons yielding a reflection coefficient phase close to that of a short circuit ( 180°). In such an embodiment of the invention, for example, the phase shift stays within 5° of desired value over 600 MHz bandwidth in such an embodiment of the invention, for example, this topology exhibit reflectivity of 98.7% or better, and maintains the desired 180° phase shift (4/- 15°) for incidence angles of up to 30* off-normal, which is important for a curved parabolic reflector. This embodiment of th e invention reaches reflec t ivity of 99,0%. S till other embodimen ts of the invention do not require mechanical elements, but the losses are significantly higher. Much effort has been devoted towards achieving reflectivity values that change as little as possible with BSS setting and incidence angle, and in ensuring cross-polarization contributions from the BSS elements are minimal. In another embodiment of the invention, triangles are used as shapes for the reflector elements of the MSFL The particular shapes for the individual mask elements are chosen to support easier tessellation to integrate into the doubly curved surface of the reflector.

[0040] T he reflector focal length and offset angle are optimized to both limit the degradation in the performance of BSS elements with increasing incidenc angle, and to minimize blockage by the feed horn. The reflector geometry is chosen such that the region of interest (“ROT’) for imaging has the proper sampling (over the -required set of patterns) while minimizing energy contributions from outside this ROi. A standard feedhom is used to intercept reflected energy and transfer it to the standard radiometer receiver

[0041] The antenna paterns, multiplied by the scene and integrated over 4H steradkms (SR), result In an antenna temperature, Ta:

16 [00421 The region of interest, designated (q,f)ϊΐa!, is, generally speaking, only a small fraction of the full 4p SR sphere,. iv- |F _Si (e,f) ^' r _s««e (9^)d^ - jF«(o )TsL(i), >)daki ite (i 2)

[0043] The reflector, whether standard or th MARR 1 10, further modifies the antenna temperature by having only finite emissiviiy an cross polarization performance. Calibration techniques for these terms are well known and ar not discussed here

[01)44] The antenna temperature is in reference to the output of the MARR terminals, and Is fed into a standard receiver, to produc a brightness temperature, TB.

TB - MTa+B (! 3) where both the gain, M, and offset, B, include constants and receiver pertbrmah.ce values {constant and fluctuating). For each sequence, i, (and pattern f»,0 _> a brightness temperature, TBi, i measured. The calibration of the brightness temperatures impacts the retrieval accuracy limit, so errors are corrected to the appropriate level such that the result is an image with appropriate noise for the given application. Most receiver error terms are stable over the course of the m measurements required to produce an image, leaving radiometer sensitivity (which can be reduced by either lengthening the integration time or by averaging measurements), and the variation in the antenna from different instantiations as differences between each TBi which must be considered. Thus, it is important to have emisslviiy values for the BSS as similar as possible for each setting, and to carefully measure

17 the crosspoiarizatkm and sidelobe levels for each pattern, ¾. Careful estimates of ITXPOL and TSL, the crosspolarized and sidelobe energy contributions, respectively, are also necessary.

[0045] The calibrated brightness temperatures are fe into the compressive sensing imaging algorithm, which can be remote from the sensor (e g,, being resident on a standard ground station for a spacebome application), reducing the required onboard processing needs and data transmission bandwidth. The algorithm already has knowledge of the preselected antenna pattern/sequeoee associated with each -measurement The retrieval algorithm couples a compressive reconstruction to solve the imderdetermmed aspect of the problem, with a deconvolution approach that seeks to enhance the spatial resolution of the reconstruction. The retrieval algorithm is optimized to provide the required spatial (or effectivel angular) resolution and to meet requirements on the accuracy of the retrieval in terms of brightnes temperatures compared to the scene on a pixet-by~pixei basis. Minimizing the number of measurements, m, is important to minimize image smearing from platform motion.

[01)46] Embodiments of the invention include different retrieval algorithms, such as a convex optimization program, which take into account the assumed sparsity prior, as well as computation l models of the BSS projection paterns. An Iterative first-order numerical optimization solver is, for example, employed as the underlying computational solver for the convex optimization program. In an embodiment of the invention, current retrievals do not rely on any external information such as a priori information about the scene. However, one of ordinary skill in the art will readily appreciate that in alternative embodiments of the invention, such external information can be incorporated to improve the performance.

[0047] The image i then, for example, calibrated using typical image processing techniques, such as standard flat fielding. For this purpose, calibration targets with known values and little spatial

18 variation will be used. This is also where a priori knowledge, such as known image features, can be used to good effect.

[0048] The retrieved image is a sparse representation of the true scene. There are different choices of bases that may be used to yield a sufficiently sparse approximation to the true scene. The current version represents the underlying image using a representation basis, A.

1 sparse^A I scene <14)

[0049] If the average brightness temperature of the c ne is known in advance, this average value could also be subtrac ted. The di fference between ie sparsifted representation of the image a nd the true image results in an additional error source, and the choic is made with ears.

[0050] Portions of the invention operate in a standard computing operating environment, for example, a desktop computer, a laptop computer, a mobile computer, a server computer, and the like, in which embodiments of the invention may be practiced. While the invention is described in the genera! context of program modules that ran on an operating system on a personal computer those skilled in the art will recognize that the invention may also be implemented in combination wi th other types of computer sy stems and program modules.

[0051 ] Generally, program modules include routines, programs, components, data structures, and other types of structures that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the invention may be practiced with other computer system configurations, including hand-held devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe com ters, autonomous embedded computers, and the like. The invention may also be practiced in distributed

19 computing environments where tasks are performed by remote processing devices that are linked through a eommiitrieatkms network hi a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0052] An illustrative operating environment for embodiments of the invention is described as follows. A computer comprises a genera! purpose desktop, laptop, handheld, mobile or other type of computer (computing device) capable of executing one or more application programs. The computer includes at least one central processing unit ("CPU"), a system memory, including a random access memory ("RAM”) and a read-only memory ("ROM”), and a system bus that couples the memor to the CPU. A basic input/output system containing the basic routines that help to transfer information between elements within the computer, such as during startup, is stored in the ROM. The computer further includes a mass storage device for storing an operating system, application programs, and other program modules.

[0053] The mass storage device is connected to the CPU through a mass storage- controller connected to the bus. The mass storage device and its associated computer -readable media provide non-volatile storage for the computer. Although the description of computer-readable media contained herein refers to a mass storage device, such as a hard disk or CD-ROM drive, it should be appreciate by those skille in the art that computer-readable media can be any available media that can be accessed or utilized by the computer.

[0054] By way of example, and not limitation, computer-readable media comprise computer storage media and communication media. Computer storage media includes non-transitory, nonvolatile, removable and non-removable media implemented in any method or technolog for storage of information such as computer -readable instructions, data structures, program modules or other data. Such non-transitory computer storage media includes, but is not limited to, RAM, ROM,

20 EPROM, EEPROM, flash memory or other solid state memory technology. CD-ROM, digital versatile disks ("DVD"), or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other tangible non-transitory medium which can be used to store the desired information and which can be accessed by the computer.

[0055] According to various embodiments of the in vention, the computer may operate in a networked environment using logical connections to remote computers through a network, such as a local network, the internet, etc. for example. The computer may connect to the network through a network interface unit connected to the bus. It should be appreciated that the network interface unit may also be utilized to connect to other types of networks and remote computing systems.

[ 0056 ] The computer may also include an inpuEoutput controller for receiving and processing input from a number of other devices, including: a keyboard, mouse, etc,. Similarly, an input/output controller may provide output to a display screen, a printer, or other type of output device.

[00 7] As mentioned briefly above, a number of program modules and data files may be stored in the mass storage device and RAM of the computer, including an operating system suitable for controlling the operation of a networked personal computer. The mass storage device and RA may also store one or more program modules. In particular, the mass Storage device an the RAM may store application programs, such as a software application, for example, a word processing applic tion _s a spreadsheet application, a slide presentation application, a database application, etc.

[0058] It should be appreciated that various embodiments of the present invention may be implemented as a sequence of computer-implemented acts or program modules tunning on a computing system and/or as interconnected machine logic circuits or circuit modules within the computing system. The implementation is a matter of choice dependent on the performance requirements of the computing system implementing the invention. Accordingly, logical operations

21 including related algorithms can be referred to variously as operations, structural devices, acts or modules. It will be recognized by one skilled in the art that these operations, structural devices, acts and modules may be implemented in software, firmware, special purpose digital logic, and any combination thereof without deviating fro the spirit and scope of the present invention as described herein.

[0(159] Although a particular feature of the disclosure may have been illustrated and/or described with respect to only one of several implementations, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular application. Also, to tire extent that the terms "including", "includes", "having", "has", "with", or variants thereof are used in the detailed description and/or in the claims, such terms are intended to be inclusive in a manner similar to the term "comprising”.

[0060] As used herein, the singular forms“a”,“and ^* an “the" do not preclude plural referents, unless the content clearly dictates otherwise,

[0061 ] As used herein, the term“and/or” includes any and all combinations of one of more of the associated listed items,

[0062] As used herein, the term“about” when used in conjunction with a stated numerical value or range denotes somewhat more or somewhat less than the stated value or range, to within a range of ±10% of that stated,

[0063] All documents mentioned herein are hereby incorporated by reference for the purpose of disclosing and describing the particular materials and methodologies for which the document was cited,

[0064] Although the present invention has been described in connection with preferred embodiments thereof, it will he appreciated by those skilled in the art that additions, deletions,

22 modifications, and substitutions not specifically described may be made without departing from the spirit and scope of the invention Terminology used herein should not be construed as being“means- plus-function” language unless the term“means is expressly used in association therewith,

[0065] This written description sets forth the best mode of the invention an provides examples to describe the invention and to enable a person of ordinary skill in the art to make and use the invention. This written description does not limit the invention to the precise terms set forth. Thus, while the invention has been described in detail with reference to the examples set forth above, those of ordinary skill in the art may effect alterations, modifications and variations to the examples without departing from the scope of the invention.

[0066] These and other implementations are within the scope of the following claims.

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