Related papers: Stable Cosparse Recovery via \ell_p-analysis Optim…
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,…
In this paper, we consider nonconvex optimization problems with nonlinear equality constraints. We assume that the objective function and the functional constraints are locally smooth. To solve this problem, we introduce a linearized…
The aim of this paper is to study the stability of the $\ell_1$ minimization for the compressive phase retrieval and to extend the instance-optimality in compressed sensing to the real phase retrieval setting. We first show that 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…
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel…
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.…
In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial…
As a natural extension of compressive sensing and the requirement of some practical problems, Phaseless Compressed Sensing (PCS) has been introduced and studied recently. Many theoretical results have been obtained for PCS with the aid of…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
Underdetermined or ill-posed inverse problems require additional information for \ldd{d} sound solutions with tractable optimization algorithms. Sparsity yields consequent heuristics to that matter, with numerous applications in signal…
Finding the sparse solution of an underdetermined system of linear equations has many applications, especially, it is used in Compressed Sensing (CS), Sparse Component Analysis (SCA), and sparse decomposition of signals on overcomplete…
Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…
The $\ell_p$ linear regression problem is to minimize $f(x)=||Ax-b||_p$ over $x\in\mathbb{R}^d$, where $A\in\mathbb{R}^{n\times d}$, $b\in \mathbb{R}^n$, and $p>0$. To avoid overfitting and bound $||x||_2$, the constrained $\ell_p$…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
$\ell_1$ minimization is often used for finding the sparse solutions of an under-determined linear system. In this paper we focus on finding sharp performance bounds on recovering approximately sparse signals using $\ell_1$ minimization,…
We study the recovery results of $\ell_p$-constrained compressive sensing (CS) with $p\geq 1$ via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds…
Inspired by an interesting idea of Cai and Zhang, we formulate and prove the convex $k$-sparse decomposition of vectors which is invariant with respect to $\ell_1$ norm. This result fits well in discussing compressed sensing problems under…
Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…