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We propose a compressed sensing algorithm termed variance state propagation (VSP) for block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. The VSP algorithm is developed under the Bayesian framework. A hierarchical Gaussian prior is introduced to depict the clustered patterns in the sparse signal. Markov random field (MRF) is introduced to characterize the state of the variances of the Gaussian priors. Such a hierarchical prior has the potential to encourage clustered patterns and suppress isolated coefficients whose patterns are different from their respective neighbors. The core idea of our algorithm is to iteratively update the variances in the prior Gaussian distribution. The message passing technique is employed in the design of the algorithm. For messages that are difficult to calculate, we correspondingly design reasonable methods to achieve approximate calculations. The hyperparameters can be updated within the iteration process. Simulation results demonstrate that the VSP algorithm is able to handle a variety of block-sparse signal recovery tasks and presents a significant advantage over the existing methods.

This letter concentrates on the problem of spectral compressed sensing in impulsive noise, which aims to recover a spectrally sparse signal from its contaminated and undersampled measurements. We propose a robust formulation for joint sparse signal and frequency recovery, which includes the generalized $\ell _p$ -norm $(0 data-fidelity fitting term added to a log-sum sparsity-promoting regularizer. To handle this intractable issue, we develop an iteratively reweighted $\ell _2$ approach via majorizing the original objective function by a quadratic surrogate function. Simulation results illustrate that the proposed approach attains a significant performance improvement over the existing methods under impulsive noise.

This paper reformulates the problem of direction-of-arrival (DOA) estimation for unknown nonuniform noise by exploiting a sparse representation of the array covariance vectors. In the proposed covariance sparsity-aware DOA estimator, the unknown noise variances can be eliminated by a linear transformation, and DOA estimation is reduced to a sparse reconstruction problem with nonnegativity constraint. The proposed method not only obtains an extended-aperture array with increased degrees of freedom which enables us to handle more sources than sensors, but also provides superiority in performance and robustness against nonuniform noise. Numerical examples under different conditions demonstrate the effectiveness of the proposed method.

This paper considers the sparse recovery problem of multiple measurement vector (MMV) model corrupted in impulsive noise. To ensure outlier-robust sparse recovery, we formulate an MMV problem that includes the generalized lp-norm (1 < p < 2) divergence data-fidelity term added to the l2,0 joint sparsity-promoting regularizer. The joint sparse penalty, however, is non-continuous and hence non-differentiable, which inevitably raises difficulty in optimization when using a gradient-based method. To address this, we build a smooth approximation for the l2,0-based sparse metric via the log-sum based sparse-encouraging surrogate function. Then, we propose a block successive upper-bound minimization algorithm for the smooth MMV problem by solving a series of subproblems based on the block coordinate descent (BCD) method. Furthermore, local convergence of the proposed algorithm to a stationary point of the smooth problem is proved. Experiments demonstrate its efficiency and robust recovery performance for suppressing impulsive noise.

Most of the existing sparse recovery methods are based on the squared error criterion, i.e., l 2 -norm metric, by appropriately adding to a sparsity-promoting regularizer. This criterion is, however, statistically optimal only when the noise are Gaussian distributed. In fact, non-Gaussian impulsive noise with heavy tailed distribution has been reported in a variety of practical applications. To guarantee outlier-resistant sparse reconstruction for impulsive noise, in this paper we instead employ the generalized l p -norm (1 ≤ p p − l 0 sparse recovery problem, where the reweighted matrices constructed from the previous iterative solution are considered both for l p and l 0 metrics. Simulation results demonstrate the efficiency and robustness of the proposed algorithms.