BibTeX
@MISC{And_lowrank,
author = {Moody Chu And and Moodyt. Chuandrobertj. Plemmonsy},
title = {Low Rank Circulant Approximation},
year = {}
}
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Abstract
Partially due to the fact that the empirical data collected in practice by devices with finite bandwidth often neither maintain the specified structure nor induce a certain desired rank, structured low rank approximation arises in many important applications. Approximation by structured low rank matrices has particular significance in signal and image processing. This paper discusses a procedure for low rank approximation involving circulant structure. The low rank circulant real approximation problem is not as straightforward as the usual truncated singular value decomposition since a conjugate-even set of eigenvalues must be maintained to guarantee a real-valued approximation. The fast Fourier transform together with a sorting scheme are employed to compute the nearest real-valued circulant approximation with a specific rank to a given target matrix. Extensions of this work to block circulant with circulant blocks is possible which could lead to an efficient way of preconditioning image post-processing computations.
Keyphrases
low rank circulant approximation singular value decomposition target matrix conjugate-even set low rank approximation real-valued circulant approximation circulant structure image processing circulant block efficient way empirical data many important application fast fourier transform specified structure image post-processing computation finite bandwidth particular significance low rank approximation arises real-valued approximation low rank matrix sorting scheme certain desired rank specific rank
