Multidimensional Filter Banks and Multiscale Geometric Representations

Abstract

Thanks to the explosive growth of sensing devices and capabilities, multidimensional (MD) signals — such as images, videos, multispectral images, light fields, and biomedical data volumes — have become ubiquitous. Multidimensional filter banks and the associated constructions provide a unified framework and an efficient computational tool in the formation, representation, and processing of these multidimensional data sets. In this survey we aim to provide a systematic development of the theory and constructions of multidimensional filter banks. We thoroughly review 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, Grobner bases, mapping methods, frequency domain constructions, ladder structures and lifting schemes. We then focus 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, Full text available at: http://dx.doi.org/10.1561/2000000012