In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In the important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as sparsity measure an...

We address the problem of signal denoising and pattern recognition in processing batch-mode time-series data by combining linear time-invariant filters, orthogonal multiresolution representations, sparsity-based methods. propose a novel approach to designing higher-order zero-phase low-pass, high-pass, band-pass infinite impulse response filters as matrices, using spectral transformation state-...

We consider the problem of recovering a signal x∗ ∈ R, from magnitude-only measurements, yi = |〈ai,x〉| for i = {1, 2, . . . ,m}. This is a stylized version of the classical phase retrieval problem, and is a fundamental challenge in nanoand bio-imaging systems, astronomical imaging, and speech processing. It is well known that the above problem is ill-posed, and therefore some additional assumpt...

The use of convex optimization for the recovery of sparse signals from incomplete or compressed data is now common practice. Motivated by the success of basis pursuit in recovering sparse vectors, new formulations have been proposed that take advantage of different types of sparsity. In this paper we propose an efficient algorithm for solving a general class of sparsifying formulations. For sev...

Abstract In this paper, we show the important roles of sharp minima and strong for robust recovery. We also obtain several characterizations convex regularized optimization problems. Our are quantitative verifiable especially case decomposable norm problems including sparsity, group-sparsity low-rank For problems, that a unique solution is obtains uniqueness.

Sparse signal recoveries from multiple measurement vectors (MMV) with joint sparsity property have many applications in signal, image, and video processing. The problem becomes much more involved when snapshots of the matrix are temporally correlated. With signal's temporal correlation mind, we provide a framework iterative MMV algorithms based on thresholding, functional feedback null space tu...

We propose a new estimator of high-dimensional spectral density matrices, called ALgebraic Spectral Estimator (ALSE), under the assumption an underlying low rank plus sparse structure, as typically assumed in dynamic factor models. The ALSE is computed by minimizing quadratic loss nuclear norm l1 constraint to control latent and residual sparsity pattern. function requires input classical smoot...

The theory of compressive sensing (CS) asserts that an unknown signal x ∈ CN can be accurately recovered from m measurements with m N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ‖x‖0 as an input. However, generally s is unknown, and directly estimating the sparsity has been an open problem. In this study, an estimator of sparsity is proposed by using Bayesia...

We extend ideas from compressive sensing to a structured sparsity model related to fusion frames. We present theoretical results concerning the recovery of sparse signals in a fusion frame from undersampled measurements. We provide both nonuniform and uniform recovery guarantees. The novelty of our work is to exploit an incoherence property of the fusion frame which allows us to reduce the numb...