Related papers: Safe squeezing for antisparse coding
This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…
In constraint programming and related paradigms, a modeller specifies their problem in a modelling language for a solver to search and return its solution(s). Using high-level modelling languages such as Essence, a modeller may express…
We study the problem of reconstructing a block-sparse signal from compressively sampled measurements. In certain applications, in addition to the inherent block-sparse structure of the signal, some prior information about the block support,…
Compressive sensing has been successfully used for optimized operations in wireless sensor networks. However, raw data collected by sensors may be neither originally sparse nor easily transformed into a sparse data representation. This…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be…
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…
Owing to their statistical properties, non-convex sparse regularizers have attracted much interest for estimating a sparse linear model from high dimensional data. Given that the solution is sparse, for accelerating convergence, a working…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g.,…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Feature Squeezing is a recently proposed defense method which reduces the search space available to an adversary by coalescing samples that correspond to many different feature vectors in the original space into a single sample. It has been…
In this paper, we propose a procedure to accelerate the resolution of the well-known "Elastic-Net" problem. Our procedure is based on the (partial) identification of the solution support and the reformulation of the original problem into a…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
We present a new approach to solve the sparse approximation or best subset selection problem, namely find a $k$-sparse vector ${\bf x}\in\mathbb{R}^d$ that minimizes the $\ell_2$ residual $\lVert A{\bf x}-{\bf y} \rVert_2$. We consider a…
We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…
Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the $\ell_0$-norm is often used to control the sparsity level. Nevertheless,…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation…