The Mathematical Institute, University of Oxford, Eprints Archive

Performance Comparisons of Greedy Algorithms in Compressed Sensing

Blanchard, Jeffrey D. and Tanner, Jared (2013) Performance Comparisons of Greedy Algorithms in Compressed Sensing. Technical Report. Wiley. (Submitted)

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Abstract

Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. In the compressed sensing setting, greedy sparse approximation algorithms have been observed to be both able to recovery the sparsest solution for similar problem sizes as other algorithms and to be computationally efficient; however, little theory is known for their average case behavior. We conduct a large scale empirical investigation into the behavior of three of the state of the art greedy algorithms: NIHT, HTP, and CSMPSP. The investigation considers a variety of random classes of linear systems. The regions of the problem size in which each algorithm is able to reliably recovery the sparsest solution is accurately determined, and throughout this region additional performance characteristics are presented. Contrasting the recovery regions and average computational time for each algorithm we present algorithm selection maps which indicate, for each problem size, which algorithm is able to reliably recovery the sparsest vector in the least amount of time. Though no one algorithm is observed to be uniformly superior, NIHT is observed to have an advantageous balance of large recovery region, absolute recovery time, and robustness of these properties to additive noise and for a variety of problem classes. The algorithm selection maps presented here are the first of their kind for compressed sensing.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1695
Deposited By: Lotti Ekert
Deposited On:16 Apr 2013 07:03
Last Modified:29 May 2015 19:23

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