Related papers: Regularization for Matrix Completion
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 regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…
We consider the problem of estimating a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method depends crucially on the choice of loss function. In this paper, we use a family of weighted loss…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
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),…
Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…
Gradient descent algorithms on Riemannian manifolds have been used recently for the optimization of quantum channels. In this contribution, we investigate the influence of various regularization terms added to the cost function of these…
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…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
Crucial information barely visible to the human eye is often embedded in a series of low-resolution images taken of the same scene. Super-resolution enables the extraction of this information by reconstructing a single image, at a high…
We propose a new framework -- Square Root Principal Component Pursuit -- for low-rank matrix recovery from observations corrupted with noise and outliers. Inspired by the square root Lasso, this new formulation does not require prior…