Related papers: Sparse Sampling Kaczmarz-Motzkin Method with Linea…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to…
Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation…
This paper investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavytailed impulsive noise is well modelled with stable distributions. Since there is no explicit formulation for the…
The Kaczmarz method is a popular iterative method for solving consistent, overdetermined linear system such as medical imaging in computerized tomography. The Kaczmarz's iteration repeatedly scans all equations in order, which leads to…
This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…
Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…
In this paper we analyze approximation and recovery properties with respect to systems satisfying universal sampling discretization property and a special incoherence property. We apply a powerful nonlinear approximation method -- the Weak…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
In this paper, we compare and catalog the performance of various greedy quantized compressed sensing algorithms that reconstruct sparse signals from quantized compressed measurements. We also introduce two new greedy approaches for…
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the…
With the growth of large data as well as large-scale learning tasks, the need for efficient and robust linear system solvers is greater than ever. The randomized Kaczmarz method (RK) and similar stochastic iterative methods have received…
In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth…
In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
The reconstruction of tensor-valued signals from corrupted measurements, known as tensor regression, has become essential in many multi-modal applications such as hyperspectral image reconstruction and medical imaging. In this work, we…
Randomized iterative algorithms for solving a factorized linear system, $\mathbf A\mathbf B\mathbf x=\mathbf b$ with $\mathbf A\in{\mathbb{R}}^{m\times \ell}$, $\mathbf B\in{\mathbb{R}}^{\ell\times n}$, and $\mathbf b\in{\mathbb{R}}^m$,…
To find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, such that a consistent system is asymptotically…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…