Related papers: Subspace Recovery from Structured Union of Subspac…
We investigate non-negative least squares (NNLS) for the recovery of sparse non-negative vectors from noisy linear and biased measurements. We build upon recent results from [1] showing that for matrices whose row-span intersects the…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few…
This paper studies the problem of support recovery of sparse signals based on multiple measurement vectors (MMV). The MMV support recovery problem is connected to the problem of decoding messages in a Single-Input Multiple-Output (SIMO)…
In this paper, we consider recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given observations, including thresholding,…
Compressive Sensing (CS) theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. Most of conventional CS recovery approaches, however,…
Periodic signals composed of periodic mixtures admit sparse representations in nested periodic dictionaries (NPDs). Therefore, their underlying hidden periods can be estimated by recovering the exact support of said representations. In this…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…
This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse…
Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…
The recovery of signals that are sparse not in a basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard…
This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…
Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…
In this paper, we consider the block-sparse signals recovery problem in the context of multiple measurement vectors (MMV) with common row sparsity patterns. We develop a new method for recovery of common row sparsity MMV signals, where a…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
Many practical sensing applications involve multiple sensors simultaneously acquiring measurements of a single object. Conversely, most existing sparse recovery guarantees in compressed sensing concern only single-sensor acquisition…