Related papers: Low-Rank Inducing Norms with Optimality Interpreta…
This paper focuses on recovering an underlying matrix from its noisy partial entries, a problem commonly known as matrix completion. We delve into the investigation of a non-convex regularization, referred to as transformed $L_1$ (TL1),…
Rank-constrained optimization problems have received an increasing intensity of interest recently, because many optimization problems in communications and signal processing applications can be cast into a rank-constrained optimization…
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…
This paper concerns with a noisy structured low-rank matrix recovery problem which can be modeled as a structured rank minimization problem. We reformulate this problem as a mathematical program with a generalized complementarity constraint…
Mathematically characterizing the implicit regularization induced by gradient-based optimization is a longstanding pursuit in the theory of deep learning. A widespread hope is that a characterization based on minimization of norms may…
Recht, Fazel, and Parrilo provided an analogy between rank minimization and $\ell_0$-norm minimization. Subject to the rank-restricted isometry property, nuclear norm minimization is a guaranteed algorithm for rank minimization. The…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens…
In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation…
We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard…
Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
Low-rank matrix recovery from structured measurements has been a topic of intense study in the last decade and many important problems like matrix completion and blind deconvolution have been formulated in this framework. An important…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…
The nuclear norm (NN) has been widely explored in matrix recovery problems, such as Robust PCA and matrix completion, leveraging the inherent global low-rank structure of the data. In this study, we introduce a new modified nuclear norm…