Compressive sensing (CS) has attracted considerable research from signal/image processing communities. Recent studies further show that structured or group sparsity often leads to more powerful signal reconstruction techniques in various CS taskes. Unlike the conventional sparsity-promoting convex regularization methods, this paper proposes a new approach for image compressive sensing recovery ...

This paper studies the asymptotic performance of maximum-a-posteriori estimation in the presence of prior information. The problem arises in several applications such as recovery of signals with non-uniform sparsity pattern from underdetermined measurements. With prior information, the maximum-a-posteriori estimator might have asymmetric penalty. We consider a generic form of this estimator and...

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is NP-hard in general. In this paper we consider a convex optimization formulation to splitting the specified mat...

Explicitly using the block structure of the unknown signal can achieve better recovery performance in compressive censing. An unknown signal with block structure can be accurately recovered from underdetermined linear measurements provided that it is sufficiently block sparse. However, in practice, the block sparsity level is typically unknown. In this paper, we consider a soft measure of block...

This paper presents the first theoretical results showing that stable identification of overcomplete μcoherent dictionaries Φ ∈ Rd×K is locally possible from training signals with sparsity levels S up to the order O(μ−2) and signal to noise ratios up to O( √ d). In particular the dictionary is recoverable as the local maximum of a new maximisation criterion that generalises the K-means criterio...

Frommany fewer acquired measurements than suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that, a signal can be reconstructed with high probability when it exhibits sparsity in some domain. Most of the conventional CS recovery approaches, however, exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are...

The modulated wideband converter (MWC) is a kind of sub-Nyquist sampling system which is developed from compressed sensing theory. It accomplishes highly accurate broadband sparse signal recovery by multichannel sub-Nyquist sampling sequences. However, when the number of sparse sub-bands becomes large, the amount of sampling channels increases proportionally. Besides, it is very hard to adjust ...

We address the problem of recovering a sparse n-vector within a given subspace. This problem is a subtask of some approaches to dictionary learning and sparse principal component analysis. Hence, if we can prove scaling laws for recovery of sparse vectors, it will be easier to derive and prove recovery results in these applications. In this paper, we present a scaling law for recovering the spa...