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In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of an minimum mean square error (MMSE) estimator that has support knowledge beyond a certain SNR thredhold. The key idea behind(More)
This paper proposes a low-computational Bayesian algorithm for noisy sparse recovery (NSR), called BHT-BP. In this framework, we consider an LDPC-like measurement matrices which has a tree-structured property, and additive white Gaussian noise. BHT-BP has a joint detection-and-estimation structure consisting of a sparse support detector and a nonzero(More)
In this paper, we introduce a new support recovery algorithm from noisy measurements called Bayesian hypothesis test via belief propagation (BHT-BP). BHT-BP focuses on sparse support recovery rather than sparse signal estimation. The key idea behind BHT-BP is to detect the support set of a sparse vector using hypothesis test where the posterior densities(More)
—In this paper, we propose a sparse recovery algorithm called detection-directed (DD) sparse estimation using Bayesian hypothesis test (BHT) and belief propagation (BP). In this framework, we consider the use of sparse-binary sensing matrices which has the tree-like property and the sampled-message approach for the implementation of BP. The key idea behind(More)
—This paper proposes a fast AMP algorithm for solving a compressed sensing (CS) recovery problem which includes signal sparsity in finite difference (FD). The proposed AMP algorithm, named ssAMP-1D, is fully scalable, providing low-computationality and phase transition (PT) competitive to the state-of-the-art performance. The key behind the ssAMP-1D(More)
—One of the challenges in Big Data is efficient handling of high-dimensional data or signals. This paper proposes a novel AMP algorithm for solving high-dimensional linear systems Y = HX + W ∈ R M which has a piecewise-constant solution X ∈ R N , under a compressed sensing framework (M ≤ N). We refer to the proposed AMP as ssAMP. This ssAMP algorithm is(More)
Approximate message-passing (AMP) method is a simple and efficient framework for the linear inverse problems. In this letter, we propose a faster AMP to solve the L1-Split-Analysis for the 2-D sparsity separation, which is referred to as MixAMP. We develop the MixAMP based on the factor graphical modeling and the min-sum message-passing. Then, we examine(More)
Compressed Sensing (CS) is one of the hottest topics in signal processing these days and the design of efficient recovery algorithms is a key research challenge in CS. Whereas, a large number of recovery algorithms have been proposed in literature, the recently proposed Approximate Message Passing (AMP) [19] algorithm has gained a lot of attention because(More)