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In this paper we derive tail bounds on the norms of random submatrices withnon-uniformly distributed supports. We apply these results to sparseapproximation and conduct an analysis of the average case performance ofthresholding, Orthogonal Matching Pursuit and Basis Pursuit. As an applicationof these results we characterise sensing dictionaries to improve averageperformance in the non-uniform case and test their performance numerically.

Submatrices with non-uniformly selected random supports and insights into sparse approximation