Lossless image compression using wavelet decomposition

Research advances in wavelet theory and subband coding have created a surge of interest in wavelet based applications during the past decade. Image coding (or compression) is an important application that has benefited significantly from the wavelet theory. Lossless image coding using wavelet decomposition is the main focus of this dissertation. Specific contributions involve design of algorithms, the development of criteria for selection of appropriate wavelets and new context models for entropy coding of wavelet coefficients. A wavelet decomposed image has intraband and interband correlations which can be exploited to obtain higher compression. In order to exploit the intraband correlation, four lossless image compression schemes based on prediction are proposed. The schemes combine wavelet decomposition and variable block size segmentation (VBSS) entropy encoding. The proposed schemes are evaluated and compared with other schemes in the literature.; In order to exploit the interband correlation, a need arises to incorporate an appropriate data structure, like the embedded zerotree proposed by Shapiro (23). The embedded zerotree wavelet (EZW) framework for image coding system consists of three stages: (i) wavelet transform, (ii) an embedded zerotree encoding, and (iii) adaptive arithmetic entropy encoding. In this framework, the selection of appropriate wavelet filter plays an important role for obtaining good compression efficiency. Two new criteria are proposed for evaluating the performance of wavelets in lossless image compression applications: zerotree count and monotone spectral ordering of subbands produced after wavelet transform. Several wavelet filters are evaluated to test the criteria and experimental results are presented to justify the proposed performance criteria.; It is shown that by replacing the regular raster scan approach performed in most EZW algorithms with the z-scan algorithm, better compression efficiency can be achieved. The z-scan ordering exploits the correlation among the transformed coefficients in a 2 x 2 local neighborhood. In the three stage framework, the zerotree coding in the second stage and the context modeling based arithmetic coding in the third stage play an important role in obtaining good compression efficiency apart from the proper choice of wavelet filter. In the rest of the dissertation, several approaches for grouping and context modeling are investigated. In the proposed approaches, the set partitioning based zerotree coding (42) is used to split the wavelet coefficients into (i) a significance map and (ii) a residue map. The significance information in the significance map can be either coded bitwise (without any modeling) or can be coded as a 4-bit symbol. The residue map and the symbols corresponding to the significance map are then encoded using context based arithmetic coding. Several experiments that were conducted on context modeling of significance and residue maps in order to maximize the compression efficiency of the EZW-based lossless image coding scheme are discussed. It was observed that while context modeling of residue improves compression, the context modeling of significance map does not yield better compression.