GPU accelerated greedy algorithms for compressed sensing

For appropriate matrix ensembles, greedy algorithms have proven to be an efficient means of solving the combinatorial optimization problem associated with compressed sensing. This paper describes an implementation for graphics processing units (GPU) of hard thresholding, iterative hard thresholding,...

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Bibliographic Details
Published in:Mathematical programming computation Vol. 5; no. 3; pp. 267 - 304
Main Authors: Blanchard, Jeffrey D., Tanner, Jared
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2013
Subjects:
Full Length Paper
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Theory of Computation
Greedy algorithms
Sparse approximation
NIHT
Secondary 90C27
HTP
CoSaMP
Graphics processing units
Combinatorial optimization
65Y05
Primary 15–04
Parallel computing
IHT
65F30
94A12
Compressed sensing
Subspace pursuit
94A20
ISSN:1867-2949, 1867-2957
Online Access:Get full text
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Summary:For appropriate matrix ensembles, greedy algorithms have proven to be an efficient means of solving the combinatorial optimization problem associated with compressed sensing. This paper describes an implementation for graphics processing units (GPU) of hard thresholding, iterative hard thresholding, normalized iterative hard thresholding, hard thresholding pursuit, and a two-stage thresholding algorithm based on compressive sampling matching pursuit and subspace pursuit. The GPU acceleration of the former bottleneck, namely the matrix–vector multiplications, transfers a significant portion of the computational burden to the identification of the support set. The software solves high-dimensional problems in fractions of a second which permits large-scale testing at dimensions currently unavailable in the literature. The GPU implementations exhibit up to 70 × acceleration over standard Matlab central processing unit implementations using automatic multi-threading.
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-013-0056-5