Automatic hard thresholding for sparse signal reconstruction from NDE measurements

Date
2009-07-01
Authors
Dogandžić, Aleksandar
Qiu, Kun
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Abstract

We propose an automatic hard thresholding (AHT) method for sparse‐signal reconstruction. The measurements follow an underdetermined linear model, where the regression‐coefficient vector is modeled as a superposition of an unknown deterministic sparse‐signal component and a zero‐mean white Gaussian component with unknown variance. Our method demands no prior knowledge about signal sparsity. Our AHT scheme approximately maximizes a generalized maximum likelihood (GML) criterion, providing an approximate GML estimate of the signal sparsity level and an empirical Bayesian estimate of the regression coefficients. We apply the proposed method to reconstruct images from sparse computerized tomography projections and compare it with existing approaches.

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Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

This article appeared in AIP Conference Proceedings 1211 (2010): 806–813 and may be found at http://dx.doi.org/10.1063/1.3362486.

Keywords
nondestructive testing, numerical analysis, matrix algebra, nondestructive evaluation, QNDE
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