compendium

A. Chebira, M. C. Fickus and J. Kovačević. Classifying compact sets with frames. Appl. Comput. Harmon. Anal., 27(1):73-86, July 2009.

[ pdf | @ @ ScienceDirect | bibtex]

Classification is a fundamental image processing task. Recent empirical evidence suggests that classification algorithms which make use of redundant linear transforms will regularly outperform their nonredundant counterparts. We provide a rigorous explanation of this phenomenon in the single-class case. We begin by developing a measure-theoretic analysis of the set of points at which a given decision rule will have an intolerable chance of making a classification error. We then apply this general theory to the special case where the class is compact and convex, showing that such a class may be arbitrarily well-approximated by frame sets, namely, preimages of hyperrectangles under frame analysis operators. This leads to a frame-based classification scheme in which frame coefficients are regarded as features. We show that, indeed, the accuracy of such a classification scheme approaches perfect accuracy as the redundancy of the frame grows large.

matlab

The zipped archive contains the code to generate the figures in the paper.

[download]

All necessary proofs are included in the paper.

MATLAB 7.0.1 on Windows XP Professional

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