Dictionary Preconditioning for Greedy Algorithms

This article introduces the concept of sensing dictionaries. It presents an alteration of greedy algorithms like thresholding or (Orthogonal) Matching Pursuit which improves their performance in finding sparse signal representations in redundant dictionaries while maintaining the same complexity. These algorithms can be split into a sensing and a reconstruction step, and the former will fail to identify correct atoms if the cumulative coherence of the dictionary is too high. We thus modify the sensing step by introducing a special sensing dictionary. The correct selection of components is then determined by the cross cumulative coherence which can be considerably lower than the cumulative coherence. We characterise the optimal sensing matrix and develop a constructive method to approximate it. Finally we compare the performance of thresholding and OMP using the original and modified algorithms.

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Karin Schnass, Pierre Vandergheynst
• Keywords: Cumulative Coherence, Sensing, Sparse Signal Representations, TSP 2008