Abstract: A union of DCT (discrete cosine transform) and wavelet transform can generate a much sparser representation of the digital image signal than either of them alone. After the block-based DCT, the coefficients are rearranged into a number of frequency groups such that the coefficients locating at the same coordinate in all transform blocks are in one group. Then, one or more such groups are further decomposed by wavelet transform. After quantization, each frequency group is divided into squares. The squares are identified and encoded as either all-zero or not-all-zero. Inside those not-all-zero squares, the coefficients are encoded bit-plane by bit-plane in a 2-dimensional quaternary reaching pattern. Compared to existing peer systems, the compression performance is improved up to 30%, especially in high quality cases. For lossless compression, the image data is decomposed by a union of a reversible DCT approximant and a reversible wavelet transform.

Abstract: In wavelet-based image compression schemes, a very sparse representation of the image signal may be obtained after quantization to transform coefficients. In addition, the nonzero coefficients 2-dimensionally cluster around the edge or texture areas. In existing systems, for example JPEG2000, in the bit-plane coding process, coefficients are repeatedly scanned and encoded in a 1-dimensional pattern within code-blocks. A large number of zeros have to be encoded to record the distribution of significant coefficients. It inevitably causes a big loss of compression performance. Quaternary reaching method emphasizes reaching and encoding the significant coefficients in 2-dimensional pattern. It fully adapts to the 2-dimensional character of the significance distribution of quantized coefficients. Besides, it admits very economical implementation. The recording of redundant information is drastically reduced.