|The use of ITI transforms has other beneﬁts as well. Typically, in the case of ITI transforms, a smaller word size
can be used for storing transform coefﬁcients, leading to reduced memory requirements. Also, this smaller word size
may potentially reduce computational complexity (depending on the method of implementation).
Reversible ITI wavelet transforms approximate the behavior of their parent linear transforms, and in so doing
inherit many of the desirable properties of their parent transforms. For example, linear wavelet transforms are known
to be extremely effective for decorrelation and also have useful multiresolution properties.
For all of the reasons described above, reversible ITI wavelet transforms are an extremely useful tool for signal coding applications. Such transforms can be employed in lossless coding systems, hybrid lossy/lossless coding
systems, and even strictly lossy coding systems as well.
|Thisthesisstudiesreversible ITI wavelet transforms and their application to image coding. In short, this work examines
such matters as: transform frameworks, rounding operators and their characteristics, transform design techniques,
strategies for handling the transformation of arbitrary-length signals in a nonexpansive manner, computational and
memory complexity issues for transforms, and the utility of various transforms for image coding.
Structurally, this thesis is organized into six chapters and one appendix. The ﬁrst two chapters provide the background information necessary to place this work in context and facilitate the understanding of the research results
presented herein. The remaining four chapters present a mix of research results and additional concepts required for
the comprehension of these results. The appendix provides supplemental information about related topics of interest,
but such details are not strictly necessary for an understanding of the main thesis content.
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