Perturbed Orthogonal Matching Pursuit

Compressive Sensing theory details how a sparsely represented signal in a known basis can be reconstructed with an underdetermined linear measurement model. However, in reality there is a mismatch between the assumed and the actual bases due to factors such as discretization of the parameter space d...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2013-12, Vol.61 (24), p.6220-6231
Main Authors: Teke, Oguzhan, Gurbuz, Ali Cafer, Arikan, Orhan
Format: Article
Language:English
Subjects:
Analog-digital conversion, digital-analog conversion, pcm coding
Applied sciences
basis mismatch
basis perturbation
Compressed sensing
Compressive sensing
Detection, estimation, filtering, equalization, prediction
Dictionaries
Exact sciences and technology
Image reconstruction
Information, signal and communications theory
Matching pursuit algorithms
Minimization
perturbed OMP
Sampling, quantization
Signal and communications theory
Signal processing algorithms
Signal, noise
Telecommunications and information theory
Vectors
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Summary:Compressive Sensing theory details how a sparsely represented signal in a known basis can be reconstructed with an underdetermined linear measurement model. However, in reality there is a mismatch between the assumed and the actual bases due to factors such as discretization of the parameter space defining basis components, sampling jitter in A/D conversion, and model errors. Due to this mismatch, a signal may not be sparse in the assumed basis, which causes significant performance degradation in sparse reconstruction algorithms. To eliminate the mismatch problem, this paper presents a novel perturbed orthogonal matching pursuit (POMP) algorithm that performs controlled perturbation of selected support vectors to decrease the orthogonal residual at each iteration. Based on detailed mathematical analysis, conditions for successful reconstruction are derived. Simulations show that robust results with much smaller reconstruction errors in the case of perturbed bases can be obtained as compared to standard sparse reconstruction techniques.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2013.2283840