Related papers: Scalable Algorithms for Tractable Schatten Quasi-N…
We address some theoretical guarantees for Schatten-$p$ quasi-norm minimization ($p \in (0,1]$) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we…
In average consensus protocols, nodes in a network perform an iterative weighted average of their estimates and those of their neighbors. The protocol converges to the average of initial estimates of all nodes found in the network. The…
We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schatten spaces. We establish several…
This paper presents a patch-wise low-rank based image denoising method with constrained variational model involving local and nonlocal regularization. On one hand, recent patch-wise methods can be represented as a low-rank matrix…
This paper considers the problem of minimizing the sum of a smooth function and the Schatten-$p$ norm of the matrix. Our contribution involves proposing accelerated iteratively reweighted nuclear norm methods designed for solving the…
We study a non-convex low-rank promoting penalty function, the transformed Schatten-1 (TS1), and its applications in matrix completion. The TS1 penalty, as a matrix quasi-norm defined on its singular values, interpolates the rank and the…
Spectral functions of large matrices contains important structural information about the underlying data, and is thus becoming increasingly important. Many times, large matrices representing real-world data are \emph{sparse} or \emph{doubly…
Several recent randomized linear algebra algorithms rely upon fast dimension reduction methods. A popular choice is the Subsampled Randomized Hadamard Transform (SRHT). In this article, we address the efficacy, in the Frobenius and spectral…
A well-known approach in the design of efficient algorithms, called matrix sparsification, approximates a matrix $A$ with a sparse matrix $A'$. Achlioptas and McSherry [2007] initiated a long line of work on spectral-norm sparsification,…
Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm…
We study algorithms for the Schatten-$p$ Low Rank Approximation (LRA) problem. First, we show that by using fast rectangular matrix multiplication algorithms and different block sizes, we can improve the running time of the algorithms in…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while…
The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…
We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a…
We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian…