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Reversible interger-to-interger wavelet transforms for image coding Adams, Michael David

Abstract

Reversible integer-to-integer (ITI) wavelet transforms are studied in the context of image coding. Considered are matters such as transform frameworks, transform design techniques, the utility of transforms for image coding, and numerous practical issues related to transforms. The generalized reversible ITI transform (GRITIT) framework, a single unified framework for reversible ITI wavelet/block transforms, is proposed. This new framework is then used to study several previously proposed frameworks and their interrelationships. For example, the framework based on the overlapping rounding transform is shown to be a special case of the lifting framework with only trivial extensions. The applicability of the GRITIT framework for block transforms is also demonstrated. Throughout all of this work, particularly close attention is paid to rounding operators and their characteristics. Strategies for handling the transformation of arbitrary-length signals in a nonexpansive manner are considered (e.g., symmetric extension, per-displace-step extension). Two families of symmetry-preserving transforms (which are compatible with symmetric extension) are introduced and studied. We characterize transforms belonging to these families. Some new reversible ITI structures that are useful for constructing symmetry-preserving transforms are also proposed. A simple search-based design technique is explored as means for finding effective low-complexity transforms in the above-mentioned families. In the context of image coding, a number of reversible ITI wavelet transforms are compared on the basis of their lossy compression performance, lossless compression performance, and computational complexity. Of the transforms considered, several were found to perform particularly well, with the best choice for a given application depending on the relative importance of the preceding criteria. Reversible ITI versions of numerous transforms are also compared to their conventional (i.e., non-reversible real-to-real) counterparts for lossy compression. At low bit rates, reversible ITI and conventional versions of transforms were found to often yield results of comparable quality. Factors affecting the compression performance of reversible ITI wavelet transforms are also presented, supported by both experimental data and theoretical arguments. In addition to this work, the JPEG-2000 image compression standard is discussed. In particular, the JPEG-2000 Part-1 codec is described, analyzed, and evaluated.

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