Multidimensional Filter Banks and Multiscale Geometric Representations provides a systematic development of the theory and constructions of multidimensional filter banks. It thoroughly reviews several tools that have been shown to be particularly effective in the design and analysis of multidimensional filter banks, including sampling lattices, multidimensional bases and frames, polyphase representations, Groebner bases, mapping methods, frequency domain constructions, ladder structures and lifting schemes. It then focuses on the construction of filter banks and signal representations that can capture directional and geometric features, which are unique and key properties of many multidimensional signals.
Next, it studies the connection between iterated multidimensional filter banks in the discrete domain and the associated multiscale signal representations in the continuous domain through a directional multiresolution analysis framework. Finally, it shows several examples to demonstrate the power of multidimensional filter banks and geometric signal representations in applications.
Starting from basic concepts such as multidimensional filtering and nonseparable sampling, this book presents a systematic overview of the common notation, key tools, and main results in the characterization and design of multidimensional filter banks. In doing so, this book can serve as a starting point and helpful guide for those readers who would like to further explore this exciting topic.
Publisher: now publishers Inc
Number of pages: 124
Weight: 186 g
Dimensions: 234 x 156 x 7 mm
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