Applications of Digital Image Processing XXXIII
San Diego, CA
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.
Society of Photo-Optical Instrumentation Engineers
Qiu, Kun and Dogandžić, Aleksandar, "ECME Hard Thresholding Methods for Image Reconstruction from Compressive Samples" (2010). Center for Nondestructive Evaluation Conference Papers, Posters and Presentations. 103.