An image data processing apparatus includes a zero-value prediction compressor for compressing data by predicting a zero-value region of a high-layer from a low layer of a wavelet space and eliminating data in a space other than a meaningful space, a zero-value prediction expander for restoring data after wavelet transform from compressed data with the data in the space other than the meaningful space being eliminated, a subtracter for making a difference between sub-bands, and a differential accumulation buffer for accumulating the difference. In addition, a decoder is provided to have a zero-value prediction expander and a difference accumulation buffer. The decoder predicts a zero-value in a high frequency component to perform mask processing.