Merge Coding of Atoms for Wavelet/Matching Pursuits Image Compression

Improved coding of atoms in image compression by matching pursuits (MP) after a wavelet decomposition is achieved. The positions of atoms in the wavelet sub-bands are communicated by run length coding. The MERGE coding scheme replaces individual coding of any alphabet of symbols by dividing the symbols into groups and run length coding their positions. It is shown theoretically that the use of MERGE with an efficient run length coder approaches the theoretical entropy of an alphabet of symbols. The embedded nature of MERGE makes it a near-ideal coding scheme for the amplitudes of atoms. An additional layer of MERGE coding for the basis indices of atoms approaches the theoretical optimum and is superior to either separable or combined Huffman coding.