Related papers: Sparse matrices for weighted sparse recovery
Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with…
The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…
This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary…
We study the stable recovery of complex $k$-sparse signals from as few phaseless measurements as possible. The main result is to show that one can employ $\ell_1$ minimization to stably recover complex $k$-sparse signals from $m\geq O(k\log…
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including $\ell_1$ and nuclear norm minimization as well as…
We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity"…
In this paper, we study the support recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…
Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effective under strong regularity assumptions, but…
In this paper we study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50% of the (partial) support…
Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery…
Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery…
Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant…
Sparse recovery aims to reconstruct an unknown spare or approximately sparse signal from significantly few noisy incoherent linear measurements. As a kind of computable incoherence measure of the measurement matrix, $q$-ratio constrained…