arXiv subjects

Lingxiao Wang

Publications and source records attributed to Lingxiao Wang.

95 records · Page 6Linked to original sources

arXiv2018

Robust Wirtinger Flow for Phase Retrieval with Arbitrary Corruption

We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow to jointly estimate the unknown signal and the sparse corruption. We show that our proposed algorithm is guaranteed to converge linearly to the unknown true signal up to a minimax optimal statistical precision in such a challenging setting. Compared with existing robust phase retrieval methods, we achieve an optimal sample complexity of $O(n)$ in both noisy and noise-free settings. Thorough experiments on both synthetic and real datasets corroborate our theory.

stat.ML↗

arXiv2017

DeepDeblur: Fast one-step blurry face images restoration

We propose a very fast and effective one-step restoring method for blurry face images. In the last decades, many blind deblurring algorithms have been proposed to restore latent sharp images. However, these algorithms run slowly because of involving two steps: kernel estimation and following non-blind deconvolution or latent image estimation. Also they cannot handle face images in small size. Our proposed method restores sharp face images directly in one step using Convolutional Neural Network. Unlike previous deep learning involved methods that can only handle a single blur kernel at one time, our network is trained on totally random and numerous training sample pairs to deal with the variances due to different blur kernels in practice. A smoothness regularization as well as a facial regularization are added to keep facial identity information which is the key to face image applications. Comprehensive experiments demonstrate that our proposed method can handle various blur kenels and achieve state-of-the-art results for small size blurry face images restoration. Moreover, the proposed method shows significant improvement in face recognition accuracy along with increasing running speed by more than 100 times.

cs.CV↗

arXiv2017

A Universal Variance Reduction-Based Catalyst for Nonconvex Low-Rank Matrix Recovery

We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs projected gradient descent based on a novel semi-stochastic gradient specifically designed for low-rank matrix recovery. Based upon the mild restricted strong convexity and smoothness conditions, we derive a projected notion of the restricted Lipschitz continuous gradient property, and prove that our algorithm enjoys linear convergence rate to the unknown low-rank matrix with an improved computational complexity. Moreover, our algorithm can be employed to both noiseless and noisy observations, where the optimal sample complexity and the minimax optimal statistical rate can be attained respectively. We further illustrate the superiority of our generic framework through several specific examples, both theoretically and experimentally.

stat.ML↗

arXiv2017

Stochastic Variance-reduced Gradient Descent for Low-rank Matrix Recovery from Linear Measurements

We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex optimization problem of matrix sensing. Our algorithm is applicable to both noisy and noiseless settings. In the case with noisy observations, we prove that our algorithm converges to the unknown low-rank matrix at a linear rate up to the minimax optimal statistical error. And in the noiseless setting, our algorithm is guaranteed to linearly converge to the unknown low-rank matrix and achieves exact recovery with optimal sample complexity. Most notably, the overall computational complexity of our proposed algorithm, which is defined as the iteration complexity times per iteration time complexity, is lower than the state-of-the-art algorithms based on gradient descent. Experiments on synthetic data corroborate the superiority of the proposed algorithm over the state-of-the-art algorithms.

stat.ML↗

arXiv2016

A Unified Computational and Statistical Framework for Nonconvex Low-Rank Matrix Estimation

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general case with noisy observations, we show that our algorithm is guaranteed to linearly converge to the unknown low-rank matrix up to minimax optimal statistical error, provided an appropriate initial estimator. While in the generic noiseless setting, our algorithm converges to the unknown low-rank matrix at a linear rate and enables exact recovery with optimal sample complexity. In addition, we develop a new initialization algorithm to provide a desired initial estimator, which outperforms existing initialization algorithms for nonconvex low-rank matrix estimation. We illustrate the superiority of our framework through three examples: matrix regression, matrix completion, and one-bit matrix completion. We also corroborate our theory through extensive experiments on synthetic data.

stat.ML↗