Jaewook Kang

Bayesian Hypothesis Test Using Nonparametric Belief Propagation for Noisy Sparse Recovery

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 estimator. The support detector is designed under the criterion of the minimum detection error probability using a nonparametric belief propagation (nBP) and composite binary hypothesis tests. The nonzeros are estimated in the sense of linear MMSE, where the support detection result is utilized. BHT-BP has its strength in noise robust support detection, effectively removing quantization errors caused by the uniform sampling-based nBP. Therefore, in the NSR problems, BHT-BP has advantages over CS-BP which is an existing nBP algorithm, being comparable to other recent CS solvers, in several aspects. In addition, we examine impact of the minimum nonzero value of sparse signals via BHT-BP, on the basis of the results. Our empirical result shows that variation of xminis reflected to recovery performance in the form of SNR shift.

Bayesian hypothesis test for sparse support recovery using belief propagation

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 used in the test are obtained by aid of belief propagation (BP). Since BP provides precise posterior information using the noise statistic, BHT-BP can recover the support with robustness against the measurement noise. In addition, BHT-BP has low computational cost compared to the other algorithms by the use of BP. We show the support recovery performance of BHT-BP on the parameters (N, M, K, SNR) and compare the performance of BHT-BP to OMP and Lasso via numerical results.

Fast Signal Separation of 2-D Sparse Mixture via Approximate Message-Passing

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 MixAMP for two types of the sparsity separation: separation of the direct-and-group sparsity, and that of the direct-and-finite-difference sparsity. This case study shows that the MixAMP method offers computational advantages over the conventional first-order method, TFOCS.

One-dimensional piecewise-constant signal recovery via spike-and-slab approximate message-passing

This paper proposes a novel AMP solver for problems of 1-D piecewise-constant signals recovery under the compressed sensing framework. The proposed solver is named ssAMP-1D. The proposed solver is based on a factor graph consisting of two types of the factor nodes: one is for handling sparsity in finite differences Xi - Xi-1, and another is related to the measurement generation Y = HX + W. We construct the ssAMP-1D iteration from a sum-product rule based on the factor graph, where we use a spike-and-slab prior to encourage sparsity in the 1-D finite differences. We provide a summary of the algorithm construction, discussing the several aspects of ssAMP-1D through empirical comparison to the state-of-the-art solvers, GrAMPA, TV-AMP, EFLA and TV-CP.

Sparse or dense — Message Passing (MP) or Approximate Message Passing (AMP) for Compressed Sensing signal recovery

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 of its good performance and yet simple structure. Although Belief Propagation (BP) algorithms were previously considered to give good performance only in Sparse graphs, AMP algorithm is based on the application of BP on dense graphs. The application of BP in dense graphs asks for a re-look on the design of BP algorithms over graphs which can have a bearing on many applications including coding theory, neural networks etc. This paper aims to compare different existing variants of Message Passing algorithms on sparse and dense graphs for the CS recovery problem.