相关论文: Sparse Recovery, Kashin Decomposition and Conic Pr…

Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…

Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and…

In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…

We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable…

We formulate a unified framework for the separation of signals that are sparse in "morphologically" different redundant dictionaries. This formulation incorporates the so-called "analysis" and "synthesis" approaches as special cases and…

We prove super-polynomial lower bounds on the size of linear programming relaxations for approximation versions of constraint satisfaction problems. We show that for these problems, polynomial-sized linear programs are exactly as powerful…

The goal of (stable) sparse recovery is to recover a $k$-sparse approximation $x*$ of a vector $x$ from linear measurements of $x$. Specifically, the goal is to recover $x*$ such that ||x-x*||_p <= C min_{k-sparse x'} ||x-x'||_q for some…

Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…

Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local…

Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing…

Consider the approximate sparse recovery problem: given Ax, where A is a known m-by-n dimensional matrix and x is an unknown (approximately) sparse n-dimensional vector, recover an approximation to x. The goal is to design the matrix A such…

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm…

We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…

The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions,…

In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…

In this note we compare two recently proposed semidefinite relaxations for the sparse linear regression problem by Pilanci, Wainwright and El Ghaoui (Sparse learning via boolean relaxations, 2015) and Dong, Chen and Linderoth (Relaxation…

In an effort to develop an alternative approach to traditional sparse reformulations, we will provide a new type of convex reformulation of a large class of stochastic quadratically constrained quadratic optimization problems that is…

Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on…

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…