to solve in general. In this paper we consider a convex optimization formulation to splitting the specified matrix into its components, by minimizing a linear combination of the ℓ1 norm and the nuclear norm of the components. We develop a notion of rank-sparsity incoherence, expressed as an uncertainty

Abstract. The problem of recovering the sparse and low-rank components of a matrix captures a broad spectrum of applications. Authors in [4] proposed the concept of ”rank-sparsity incoherence ” to characterize the fundamental identifiability of the recovery, and derived practical sufficient

and network scenaria giv-ing rise to accurate traffic estimation. Tests with real Internet data corroborate the effectiveness of the novel estimator. Index Terms — Sparsity, low rank, traffic estimation. 1.

optimization approach, where the nuclear-norm is used to enforce low-rank in L and the l1-norm to enforce sparsity in S. Feasibility of the L+S reconstruction was tested in several dynamic MRI experiments with true acceleration including cardiac perfusion, cardiac cine, time-resolved angiography, abdominal

that is not known a priori. In this paper, with incoherence condi-tion and proposed ambiguity condition we prove that Outlier Pursuit succeeds when the rank of the intrinsic matrix is of O(n / logn) and the sparsity of the corruption matrix is of O(n). We further show that the orders of both bounds are tight. Thus

matrix has remained elusive. Deviating from the models with generic measurements, in this paper we show that if the sensing vectors are chosen at random from an incoherent subspace, then the low-rank and sparse structures of the target signal can be effectively decoupled. We show that a recovery

is not known ahead of time, a very popular and successful heuristic is to search for a dictionary that minimizes an appropriate sparsity surrogate over a given set of sample data. While this idea is appealing, the behavior of these algorithms is largely a mystery; although there is a body of empirical evidence

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The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable deterministic parameter vector is to be estimated from measurements corrupted by Gaussian noise, and derive a lower bound on the mean-squared error (MSE) achievable in this setting. To this end, an appropriate definition of bias in the sparse setting is developed, and the constrained Cramér–Rao bound (CRB) is obtained. This bound is shown to equal the CRB of an estimator with knowledge of the support set, for almost all feasible parameter values. Consequently, in the unbiased case, our bound is identical to the MSE of the oracle estimator. Combined with the fact that the CRB is achieved at high signal-to-noise ratios by the maximum likelihood technique, our result provides a new interpretation for the common practice of using the oracle estimator as a gold standard against which practical approaches are compared.