Related papers: A Convergence Analysis on URV Refinement
In this paper, we revisit the class of iterative shrinkage-thresholding algorithms (ISTA) for solving the linear inverse problem with sparse representation, which arises in signal and image processing. It is shown in the numerical…
The random reshuffling Kaczmarz (RRK) method enjoys the simplicity and efficiency in solving linear systems as a Kaczmarz-type method, whereas it also inherits the practical improvements of the stochastic gradient descent (SGD) with random…
Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…
The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
In this paper, the quaternion matrix UTV (QUTV) decomposition and quaternion tensor UTV (QTUTV) decomposition are proposed. To begin, the terms QUTV and QTUTV are defined, followed by the algorithms. Subsequently, by employing random…
This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…
This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…
Iterative sketching and sketch-and-precondition are well-established randomized algorithms for solving large-scale, over-determined linear least-squares problems. In this paper, we introduce a new perspective that interprets Iterative…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real or complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
In this work, we address the problem of outlier detection for robust motion estimation by using modern sparse-low-rank decompositions, i.e., Robust PCA-like methods, to impose global rank constraints. Robust decompositions have shown to be…
In this paper, we propose a lower rank quaternion decomposition algorithm and apply it to color image inpainting. We introduce a concise form for the gradient of a real function in quaternion matrix variables. The optimality conditions of…