Classifying compact convex sets with frames

نویسندگان

  • Amina Chebira
  • Matthew Fickus
  • Jelena Kovačević
چکیده

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 framebased 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.

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تاریخ انتشار 2008