Hierarchical Bayesian approach for jointly-sparse solution of multiple-measurement vectors

2015 IEEE Signal Processing and Signal Processing Education Workshop (SP/SPE)

2015

Self Cite

Based on the compressive sensing (CS) theory, it is possible to recover signals, which are either compressible or sparse under some suitable basis, via a small number of non-adaptive linear measurements. In this paper, we investigate recovering of block-sparse signals via multiple measurement vectors (MMVs) in the presence of noise. In this case, we consider one of the existing algorithms which provides a satisfactory estimate in terms of minimum mean-squared error but a non-sparse solution. Here, the algorithm is first modified to result in sparse solutions. Then, further modification is performed to account for the unknown block sparsity structure in the solution, as well. The performance of the proposed algorithm is demonstrated by experimental simulations and comparisons with some other algorithms for the sparse recovery problem.

Section: Stopping Rulementioning

confidence: 99%

Section: Stopping Rulementioning

confidence: 99%

Section: Stopping Rulementioning

confidence: 99%

Section: Stopping Rulementioning

confidence: 99%

Section: New Algorithm For Block-sparse Mmvsmentioning

confidence: 99%

See 3 more Smart Citations

On the block-sparsity of multiple-measurement vectors

2015 IEEE Signal Processing and Signal Processing Education Workshop (SP/SPE)

2015

Self Cite

On the block-sparse solution of single measurement vectors

2015 49th Asilomar Conference on Signals, Systems and Computers

2015

Finding the solution of single measurement vector (SMV) problem with an unknown block-sparsity structure is considered. Here, we propose a sparse Bayesian learning (SBL) algorithm simplified via the approximate message passing (AMP) framework. In order to encourage the block-sparsity structure, we incorporate a parameter called Sigma-Delta as a measure of clumpiness in the supports of the solution. Using the AMP framework reduces the computational load of the proposed SBL algorithm and as a result makes it faster. Furthermore, in terms of the mean-squared error between the true and the reconstructed solution, the algorithm demonstrates an encouraging improvement compared to the other algorithms.

Sparse Bayesian learning using variational Bayes inference based on a greedy criterion

2017 51st Asilomar Conference on Signals, Systems, and Computers

2017

Self Cite

Compressive sensing (CS) is an evolving area in signal acquisition and reconstruction with many applications [1][2][3]. In CS the goal is to efficiently measure and then reconstruct the signal under the assumption that such signal is sparse but the number and location of nonzeros are unknown. A linear CS problem is modeled as y=Ax s +e, where y ∈ ℝ M contains measurements, x s ∈ ℝ N is the sparse solution, and e is the noise with M ≪ N [4][5][6]. A = ΦΨ, where Φ is the sensing matrix and Ψ is a proper basis in which x s is sparse. There are three approaches to solve for x s i.e, greedy-based, convex-based, and sparse Bayesian learning (SBL) algorithms. Here, we consider the SBL approach. Specifically, we consider Gaussian-Bernoulli prior to promote sparsity in the solution and then use variational Bayes (VB) inference to estimate the variables and parameters of the model. In the Gaussian-Bernoulli model, the sparse solution is defined as x s =(s∘x), where s is a binary support learning vector, x accounts for the values of the solution, and "∘" is the element-wise product [7,8].It turns out that using VB inference for CS problem has the over fitting issue mainly when the number of measurements are low. For example, for the CluSS-VB algorithm, Yu et al.[8] pointed out that the solution may tend to become non-sparse. In this work, we propose a VB-based SBL algorithm which uses a simple criterion to remove such effect and forces the solution to become sparse. We also discuss and compare the update rules obtained from the SBL using fully hierarchical Bayesian approach via Markov chain Monte Carlo (MCMC) [7], expectation-maximization (EM) algorithm, and the VB inference. As expected, there exist a very close relationship between all these algorithms and we provide some intuition on how to turn equations of one approach to another approach. Also, we will provide some simulation results to compare the performance of such algorithms for the CS problems. G-OSBL (VB): An SBL algorithm using VBSuppose there is a model with parameters Θ, hidden variables collected in x, and a set of observations denoted by y. Then, the approximation to the joint density p(x,Θ|y) can be represented by p(x,Θ|y) ≈ q x (x)q θ (Θ). Then, the lower bound on the model log marginal likelihood can be iteratively optimized by the following updates [9]