Related papers: Nonconvex Nonsmooth Low-Rank Minimization for Gene…

Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel…

In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank…

Group sparse representation has shown promising results in image debulrring and image inpainting in GSR [3] , the main reason that lead to the success is by exploiting Sparsity and Nonlocal self-similarity (NSS) between patches on natural…

Label noise is a common issue in real-world datasets that inevitably impacts the generalization of models. This study focuses on robust classification tasks where the label noise is instance-dependent. Estimating the transition matrix…

The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to…

The use of sparse representation (SR) and collaborative representation (CR) for pattern classification has been widely studied in tasks such as face recognition and object categorization. Despite the success of SR/CR based classifiers, it…

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…

Convolutional Sparse Coding (CSC) has been attracting more and more attention in recent years, for making full use of image global correlation to improve performance on various computer vision applications. However, very few studies focus…

Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and…

Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…

We present a computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS). CS theory requires solving a convex constrained minimization problem. We…

In image denoising (IDN) processing, the low-rank property is usually considered as an important image prior. As a convex relaxation approximation of low rank, nuclear norm based algorithms and their variants have attracted significant…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

Subspace clustering and feature extraction are two of the most commonly used unsupervised learning techniques in computer vision and pattern recognition. State-of-the-art techniques for subspace clustering make use of recent advances in…

Low-rank matrix recovery can be solved to statistical optimality by convex matrix optimization under the classical assumption of restricted isometry property (RIP). However, for large problems, the convex formulation is commonly replaced by…

We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of structured high-dimensional signals such…

In x-ray computed tomography (CT) it is generally acknowledged that reconstruction methods exploiting image sparsity allow reconstruction from a significantly reduced number of projections. The use of such reconstruction methods is…

Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…

This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths…

The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the…