Related papers: Improving compressed sensing with the diamond norm

Compressed sensing is an image reconstruction technique to achieve high-quality results from limited amount of data. In order to achieve this, it utilizes prior knowledge about the samples that shall be reconstructed. Focusing on image…

Since the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used in various image processing studies. Nonetheless, nuclear norm based convex surrogate of the…

This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm…

In this paper we develop a general theory of compressed sensing for analog signals, in close similarity to prior results for vectors in finite dimensional spaces that are sparse in a given orthonormal basis. The signals are modeled by…

To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…

Noiseless compressive sensing is a two-steps setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on $\lone$ regularization, provides an efficient and…

In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the…

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…

A tensor nuclear norm (TNN) based method for solving the tensor recovery problem was recently proposed, and it has achieved state-of-the-art performance. However, it may fail to produce a highly accurate solution since it tends to treats…

The main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third-order tensor completion. In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

Low-rank matrix recovery addresses the problem of recovering an unknown low-rank matrix from few linear measurements. Nuclear-norm minimization is a tractible approach with a recent surge of strong theoretical backing. Analagous to the…

Low-rank tensor recovery has attracted much attention among various tensor recovery approaches. A tensor rank has several definitions, unlike the matrix rank--e.g. the CP rank and the Tucker rank. Many low-rank tensor recovery methods are…

Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…

We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems. The setting we consider involves rank-one sensing matrices: In particular, given a set of rank-one…

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…

Gradient descent (GD) is crucial for generalization in machine learning models, as it induces implicit regularization, promoting compact representations. In this work, we examine the role of GD in inducing implicit regularization for tensor…

This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…