Abstract
We consider the sparse recovery problem of signals with an unknown clustering pattern in the context of multiple measurement vectors (MMVs) using the compressive sensing (CS) technique. For many MMVs in practice, the solution matrix exhibits some sort of clustered sparsity pattern, or clumpy behavior, along each column, as well as joint sparsity across the columns. In this paper, we propose a new sparse Bayesian learning (SBL) method that incorporates a total variation-like prior as a measure of the overall clustering pattern in the solution. We further incorporate a parameter in this prior to account for the emphasis on the amount of clumpiness in the supports of the solution to improve the recovery performance of sparse signals with an unknown clustering pattern. This parameter does not exist in the other existing algorithms and is learned via our hierarchical SBL algorithm. While the proposed algorithm is constructed for the MMVs, it can also be applied to the single measurement vector (SMV) problems. Simulation results show the effectiveness of our algorithm compared to other algorithms for both SMV and MMVs.
Highlights
Background and IntroductionSingle and multiple measurement vector (SMV and measurement vectors (MMVs)) problems are computational inverse problems in the compressive sensing (CS) area
The problem we address in this paper is for the recovery of sparse signals with an unknown clustering pattern via either single measurement vector (SMV) or MMVs
The support-learning component s in (1) is a binary vector, and we model the elements of s as Bernoulli random variables, whose probabilities are governed by the prior γ = [γ1, γ2, . . . , γP ] T ; that is, s p ∼ Bernoulli(γ p ), γ p ∼ Beta(α0, β 0 ), p = 1, . . . , P
Summary
Single and multiple measurement vector (SMV and MMV) problems are computational inverse problems in the compressive sensing (CS) area. CS provides the possibility of representing a sparse or compressible signal using a small set of non-adaptive linear measurements [1,2]. In linear CS, the P-dimensional signal x ∈ RP is modeled by the linear equation y = Φx, where y ∈ R M is the measurement vector (with M P) and Φ ∈ R M× P is a wide sensing matrix. The sensing matrix Φ is usually constructed from a Gaussian or Bernoulli random operator. In [3], it was shown that Φ can be constructed from a class of circulant matrices based on deterministic sequences such as the. A sparse vector contains few non-zero components
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