## Stable Recovery of Sparse Signals With Non-convex Weighted $r$-Norm Minus $1$-Norm

Given the measurement matrix $A$ and the observation signal $y$, the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system $y=Ax+z$, where $x$ is the $s$-sparse signal to be recovered and $z$ is the noise vector. Zhou and Yu \cite{Zhou and Yu 2019} recently proposed a novel … Read more

This paper studies construction of signals, which are sparse or nearly sparse with respect to a tight frame $D$ from underdetermined linear systems. In the paper, we propose a non-convex relaxed $\ell_q(0 Article Download View Analysis non-sparse recovery for non-convex relaxed$ell_q$minimization ## Sparse Recovery via Partial Regularization: Models, Theory and Algorithms In the context of sparse recovery, it is known that most of existing regularizers such as$\ell_1$suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class of models with partial regularizers for recovering a sparse solution of a linear system. We … Read more ## A Proximal-Gradient Homotopy Method for the Sparse Least-Squares Problem We consider solving the$\ell_1$-regularized least-squares ($\ell_1$-LS) problem in the context of sparse recovery, for applications such as compressed sensing. The standard proximal gradient method, also known as iterative soft-thresholding when applied to this problem, has low computational cost per iteration but a rather slow convergence rate. Nevertheless, when the solution is sparse, it often … Read more ## On partially sparse recovery In this paper we consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the l1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to the classical problem in Compressed Sensing where the l1-norm of the … Read more ## Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations … Read more ## On partially sparse recovery In this paper we consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the l1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to the classical problem in Compressed Sensing where the l1-norm of the … Read more ## Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations … Read more ## Accuracy guarantees for ℓ1-recovery We discuss two new methods of recovery of sparse signals from noisy observation based on ℓ1- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with efficiently verifiable guaranties of performance. By optimizing these bounds with respect to the method parameters we are able to … Read more ## Verifiable conditions of$\ell_1hBcrecovery for sparse signals with sign restrictions

We propose necessary and sufficient conditions for a sensing matrix to be “$s$-semigood” — to allow for exact $\ell_1$-recovery of sparse signals with at most $s$ nonzero entries under sign restrictions on part of the entries. We express error bounds for imperfect $\ell_1$-recovery in terms of the characteristics underlying these conditions. These characteristics, although difficult … Read more