相关论文: Nonconvex Robust Quaternion Matrix Completion for …

Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank…

This paper concerns a class of composite image reconstruction models for impluse noise removal, which is rather general and covers existing convex and nonconvex models proposed for reconstructing images with impluse noise. For this…

Inspired by the fact that the matrix formulated by nonlocal similar patches in a natural image is of low rank, the rank approximation issue have been extensively investigated over the past decades, among which weighted nuclear norm…

A descent algorithm, "Quasi-Quadratic Minimization with Memory" (QQMM), is proposed for unconstrained minimization of the sum, $F$, of a non-negative convex function, $V$, and a quadratic form. Such problems come up in regularized…

Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…

Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…

In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…

Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…

Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…

The cubic regularization method (CR) and its adaptive version (ARC) are popular Newton-type methods in solving unconstrained non-convex optimization problems, due to its global convergence to local minima under mild conditions. The main aim…

The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for…

Accurate and efficient wave-optics simulation of partially coherent light transport systems is critical for the design of advanced optical systems, ranging from computational lithography to diffraction-limited storage rings (DLSR). However,…

Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…

We investigate the possibility of solving continuous non-convex optimization problems using a network of interacting quantum optical oscillators. We propose a native encoding of continuous variables in analog signals associated with the…

We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…

In this paper we propose the Graduated NonConvexity and Graduated Concavity Procedure (GNCGCP) as a general optimization framework to approximately solve the combinatorial optimization problems on the set of partial permutation matrices.…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle…

The current bottleneck of globally solving mixed-integer (non-convex) quadratically constrained problem (MIQCP) is still to construct strong but computationally cheap convex relaxations, especially when dense quadratic functions are…

This paper presents a randomized quaternion singular value decomposition (QSVD) algorithm for low-rank matrix approximation problems, which are widely used in color face recognition, video compression, and signal processing problems. With…