Related papers: Risk estimation for matrix recovery with spectral …
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG) approach for solving a wide spectrum of regularized stochastic minimization problems, where the regularization term is composite with a linear function. It has been…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
The paper suggests a method of recovering missing values for sequences, including sequences with a multidimensional index, based on optimal approximation by processes featuring spectrum degeneracy. The problem is considered in the pathwise…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears…
For the first time, this paper investigates the phase retrieval problem with the assumption that the phase (of the complex signal) is sparse in contrast to the sparsity assumption on the signal itself as considered in the literature of…
Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large…
Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…
Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to…
This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
We address the problem of phase retrieval (PR) from quantized measurements. The goal is to reconstruct a signal from quadratic measurements encoded with a finite precision, which is indeed the case in many practical applications. We develop…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
Algorithms to solve variational regularization of ill-posed inverse problems usually involve operators that depend on a collection of continuous parameters. When these operators enjoy some (local) regularity, these parameters can be…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…