IEEE Trans Image Process - Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization.

Tópicos

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Resumo

This paper presents a general framework for solving the low-rank and/or sparse matrix minimization problems, which may involve multiple nonsmooth terms. The iteratively reweighted least squares (IRLSs) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This paper generalizes IRLS to solve joint/mixed low-rank and sparse minimization problems, which are essential formulations for many tasks. As a concrete example, we solve the Schatten-p norm and l2,q-norm regularized low-rank representation problem by IRLS, and theoretically prove that the derived solution is a stationary point (globally optimal if p,q = 1). Our convergence proof of IRLS is more general than previous one that depends on the special properties of the Schatten-p norm and l2,q-norm. Extensive experiments on both synthetic and real data sets demonstrate that our IRLS is much more efficient.

Resumo Limpo

paper present general framework solv lowrank andor spars matrix minim problem may involv multipl nonsmooth term iter reweight least squar irlss method fast solver smooth object function minim altern updat variabl weight howev tradit irl can solv spars low rank minim problem squar loss affin constraint paper general irl solv jointmix lowrank spars minim problem essenti formul mani task concret exampl solv schattenp norm lqnorm regular lowrank represent problem irl theoret prove deriv solut stationari point global optim pq converg proof irl general previous one depend special properti schattenp norm lqnorm extens experi synthet real data set demonstr irl much effici

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