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Proceedings Paper

ECME hard thresholding methods for image reconstruction from compressive samples
Author(s): Kun Qiu; Aleksandar Dogandžić
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Paper Abstract

We propose two hard thresholding schemes for image reconstruction from compressive samples. The measurements follow an underdetermined linear model, where the regression-coefficient vector is a sum of an unknown deterministic sparse signal component and a zero-mean white Gaussian component with an unknown variance. We derived an expectation-conditional maximization either (ECME) iteration that converges to a local maximum of the likelihood function of the unknown parameters for a given image sparsity level. Here, we present and analyze a double overrelaxation (DORE) algorithm that applies two successive overrelaxation steps after one ECME iteration step, with the goal to accelerate the ECME iteration. To analyze the reconstruction accuracy, we introduce minimum sparse subspace quotient (minimum SSQ), a more flexible measure of the sampling operator than the well-established restricted isometry property (RIP). We prove that, if the minimum SSQ is sufficiently large, the DORE algorithm achieves perfect or near-optimal recovery of the true image, provided that its transform coefficients are sparse or nearly sparse, respectively. We then describe a multiple-initialization DORE algorithm (DOREMI) that can significantly improve DORE's reconstruction performance. We present numerical examples where we compare our methods with existing compressive sampling image reconstruction approaches.

Paper Details

Date Published: 7 September 2010
PDF: 13 pages
Proc. SPIE 7798, Applications of Digital Image Processing XXXIII, 779813 (7 September 2010); doi: 10.1117/12.862377
Show Author Affiliations
Kun Qiu, Iowa State Univ. (United States)
Aleksandar Dogandžić, Iowa State Univ. (United States)

Published in SPIE Proceedings Vol. 7798:
Applications of Digital Image Processing XXXIII
Andrew G. Tescher, Editor(s)

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