To provide an image coding apparatus and an image decoding apparatus, in which an image coding data is generated by converting a high-frequency conversion factor spatially corresponding to a conversion factor as a first wave when image data is encoded, and the image is decoded by converting again the already converted conversion factor when the image coded data is decoded.

Discrete wavelet transform is given to each input picture data and is divided into two sub bands of L and H (S1202). A target wave in the L sub band is detected (S1203). When the target wave is detected, the substituted wave in the part spatially corresponding to the target wave on the H sub band is converted to a form wave (S1204). After the substituted wave is converted to the form wave, ten sub bands in total are made (S1205). Then, entropy encoding data is generated (S1206), and image coding data are generated (S1207).