Document Type

Conference Proceeding

Publication Date

2010

Journal or Book Title

Proceedings of SPIE

Volume

7798

First Page

1

Last Page

13

DOI

10.1117/12.862377

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.

Comments

This article is from Proceedings of SPIE, Applications of Digital Image Processing XXXIII 7798 (2010): 779813, doi:10.1117/12.862377. Posted with permission.

Rights

Copyright 2010 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

Copyright Owner

Society of Photo-Optical Instrumentation Engineers

Language

en

File Format

application/pdf

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