Sparse signal/image recovery is a challenging topic that has captured a great interest during the last decades. To address the ill-posedness of the related inverse problem, regularization is often essential by using appropriate priors that promote the sparsity of the target signal/image. In this context, `0 + `1 regularization has been widely investigated. In this paper, we introduce a new prio...

Predictive modeling of functional neuroimaging data has become an important tool for analyzing cognitive structures in the brain. Brain images are high-dimensional and exhibit large correlations, and imaging experiments provide a limited number of samples. Therefore, capturing the inherent statistical properties of the imaging data is critical for robust inference. Previous methods tackle this ...

This paper studies a non-convexly constrained, sparse inverse problem in time-varying environments from a set theoretic estimation perspective. A new theory is developed that allows for the incorporation, in a unifying way, of different thresholding rules to promote sparsity, that may be even related to non-convex penalty functions. The resulted generalized thresholding operator is embodied in ...

We study recoverability in fan-beam computed tomography (CT) with sparsity and total variation priors: how many underdetermined linear measurements suffice for recovering images of given sparsity? Results from compressed sensing (CS) establish such conditions for, e.g., random measurements, but not for CT. Recoverability is typically tested by checking whether a computed solution recovers the o...

The literature on sparse recovery often adopts the `p “norm” (p ∈ [0, 1]) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding `p minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of ...

In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the corresponding inference problem amenable to Expectation Maximization (EM). We present an explicit, algebraic EM-update rule for the models, yielding two fast an...

The literature on sparse recovery often adopts the “norm” ( ) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of minimization. I...

Recent advances in stochastic optimization and regularized dual averaging approaches revealed a substantial interest for a simple and scalable stochastic method which is tailored to some more specific needs. Among the latest one can find sparse signal recovery and l0-based sparsity inducing approaches. These methods in particular can force many components of the solution shrink to zero thus cla...

Compressive sampling is an emerging technique that promises to effectively recover a sparse signal from far fewer measurements than its dimension. The compressive sampling theory assures almost an exact recovery of a sparse signal if the signal is sensed randomly where the number of the measurements taken is proportional to the sparsity level and a log factor of the signal dimension. Encouraged...