ECME hard thresholding methods for image reconstruction from compressive samples

Kun Qiu; Aleksandar Dogandžić

doi:10.1117/12.862377

7 September 2010 ECME hard thresholding methods for image reconstruction from compressive samples

Kun Qiu, Aleksandar Dogandžić

Proceedings Volume 7798, Applications of Digital Image Processing XXXIII; 779813 (2010) https://doi.org/10.1117/12.862377
Event: SPIE Optical Engineering + Applications, 2010, San Diego, California, United States

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.

Citation Download Citation

Kun Qiu and Aleksandar Dogandžić "ECME hard thresholding methods for image reconstruction from compressive samples", Proc. SPIE 7798, Applications of Digital Image Processing XXXIII, 779813 (7 September 2010); https://doi.org/10.1117/12.862377

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available