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 frame-
works 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