相关论文: Analysis of Basis Pursuit Via Capacity Sets
Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…
The \textsc{Capacitated $d$-Hitting Set} problem involves a universe $U$ with a capacity function $\mathsf{cap}: U \rightarrow \mathbb{N}$ and a collection $\mathcal{A}$ of subsets of $U$, each of size at most $d$. The goal is to find a…
We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction.…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
Solutions to the linear complementarity problem (LCP) are naturally sparse in many applications such as bimatrix games and portfolio section problems. Despite that it gives rise to the hardness, sparsity makes optimization faster and…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Recently, many new challenges in Compressed Sensing (CS), such as block sparsity, arose. In this paper, we present a new algorithm for solving CS with block sparse constraints (BSC) in complex fields. Firstly, based on block sparsity…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by…
For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able…
In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…
We consider the classical problem of finding the sparse representation of a signal in a pair of bases. When both bases are orthogonal, it is known that the sparse representation is unique when the sparsity $K$ of the signal satisfies…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…
We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this…
Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…
Recently, finding the sparsest solution of an underdetermined linear system has become an important request in many areas such as compressed sensing, image processing, statistical learning, and data sparse approximation. In this paper, we…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…