Abstract: Methods for compression of two-dimensional data arrays which are piece-wise smooth in one direction and have oscillating events in the other direction. In one embodiment, a wavelet transform is applied in the piece-wise smooth direction and a local cosine transform (LCT) is applied in the direction with oscillatory events, both producing respective transform coefficients. The LCT coefficients are reordered to mimic a wavelet transform coefficient order, and both wavelet transform and reordered LCT coefficients are quantized and entropy coded to obtain a compressed 2D image. In some embodiments with oscillatory events in both directions, a LCT is applied in both directions and all the LCT coefficients in each direction are reordered before the quantization and entropy coding.