相关论文: Depth Restoration: A fast low-rank matrix completi…

Low-rank matrix recovery is a fundamental problem in signal processing and machine learning. A recent very popular approach to recovering a low-rank matrix X is to factorize it as a product of two smaller matrices, i.e., X = UV^T, and then…

This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existing analysis for the low-rank matrix completion problem with…

This paper presents a novel factorization-based, low-rank regularization method for solving multidimensional deconvolution problems in the frequency domain. In this approach, each frequency component of the unknown wavefield is represented…

Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…

Works on implicit regularization have studied gradient trajectories during the optimization process to explain why deep networks favor certain kinds of solutions over others. In deep linear networks, it has been shown that gradient descent…

Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…

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…

In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless…

Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…

For subspace recovery, most existing low-rank representation (LRR) models performs in the original space in single-layer mode. As such, the deep hierarchical information cannot be learned, which may result in inaccurate recoveries for…

We propose an efficient pipeline for large-scale landmark image retrieval that addresses the diversity of the dataset through two-stage discriminative re-ranking. Our approach is based on embedding the images in a feature-space using a…

Graph matching or quadratic assignment, is the problem of labeling the vertices of two graphs so that they are as similar as possible. A common method for approximately solving the NP-hard graph matching problem is relaxing it to a convex…

Depth images have a wide range of applications, such as 3D reconstruction, autonomous driving, augmented reality, robot navigation, and scene understanding. Commodity-grade depth cameras are hard to sense depth for bright, glossy,…

The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…

The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…

Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Often, graph signals are corrupted in the sensing process, thus…

In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…