Classifying Compact Convex Sets with Frames
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.
Abstract © Elsevier
Applied and Computational Harmonic Analysis
Chebira, A., Fickus, M., & Kovačević, J. (2009). Classifying compact convex sets with frames. Applied and Computational Harmonic Analysis, 27(1), 73–86. https://doi.org/10.1016/j.acha.2008.11.002