相关论文: A Laplacian Approach to $\ell_1$-Norm Minimization

It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…

In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions (e.g., coordinate descent), or expensive iterates in…

Recently, the worse-case analysis, probabilistic analysis and empirical justification have been employed to address the fundamental question: When does $\ell_1$-minimization find the sparsest solution to an underdetermined linear system? In…

Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic…

One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…

In this paper, we propose and analyze an accelerated linearized Bregman (ALB) method for solving the basis pursuit and related sparse optimization problems. This accelerated algorithm is based on the fact that the linearized Bregman (LB)…

Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution…

Finding the sparsest solution $\alpha$ for an under-determined linear system of equations $D\alpha=s$ is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of $\alpha$…

We propose an efficient and robust iterative solution to the multi-object matching problem. We first clarify serious limitations of current methods as well as the inappropriateness of the standard iteratively reweighted least squares…

This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…

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…

The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…

The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…

In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…

We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve $L_1$/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our…

In this paper we propose a primal-dual homotopy method for $\ell_1$-minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints…

We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…

Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…

In this paper, the recursive least squares (RLS) algorithm is considered in the sparse system identification setting. The cost function of RLS algorithm is regularized by a $p$-norm-like ($0 \leq p \leq 1$) constraint of the estimated…

We consider the general nonlinear optimization problem where the objective function has an additional term defined by the $ \ell_0 $-quasi-norm in order to promote sparsity of a solution. This problem is highly difficult due to its…