Search Results for author: Jian-Feng Cai

Found 20 papers, 7 papers with code

Computationally Efficient and Statistically Optimal Robust Low-rank Matrix and Tensor Estimation

no code implementations2 Mar 2022 Yinan Shen, Jingyang Li, Jian-Feng Cai, Dong Xia

Lastly, RsGrad is applicable for low-rank tensor estimation under heavy-tailed noise where a statistically optimal rate is attainable with the same phenomenon of dual-phase convergence, and a novel shrinkage-based second-order moment method is guaranteed to deliver a warm initialization.

Provable Tensor-Train Format Tensor Completion by Riemannian Optimization

no code implementations27 Aug 2021 Jian-Feng Cai, Jingyang Li, Dong Xia

In this paper, we provide, to our best knowledge, the first theoretical guarantees of the convergence of RGrad algorithm for TT-format tensor completion, under a nearly optimal sample size condition.

Matrix Completion Riemannian optimization

Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery

2 code implementations13 Oct 2019 HanQin Cai, Jian-Feng Cai, Tianming Wang, Guojian Yin

We study the robust recovery problem for the spectrally sparse signal under the fully observed setting, which is about recovering $\boldsymbol{x}$ and a sparse corruption vector $\boldsymbol{s}$ from their sum $\boldsymbol{z}=\boldsymbol{x}+\boldsymbol{s}$.

A stochastic alternating minimizing method for sparse phase retrieval

no code implementations14 Jun 2019 Jian-Feng Cai, Yuling Jiao, Xiliang Lu, Juntao You

Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention.

Optimal low rank tensor recovery

no code implementations12 Jun 2019 Jian-Feng Cai, Lizhang Miao, Yang Wang, Yin Xian

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries.

Riemannian optimization

Fast Single Image Reflection Suppression via Convex Optimization

1 code implementation CVPR 2019 Yang Yang, Wenye Ma, Yin Zheng, Jian-Feng Cai, Weiyu Xu

Removing undesired reflections from images taken through the glass is of great importance in computer vision.

BIG-bench Machine Learning

Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections

1 code implementation22 Nov 2018 Jian-Feng Cai, Dong Li, Jiaze Sun, Ke Wang

The key in our proof is that random projections embed stably the set of sparse vectors or a low-dimensional smooth manifold into a low-dimensional subspace.

Dimensionality Reduction

Data-Driven Tight Frame for Cryo-EM Image Denoising and Conformational Classification

1 code implementation20 Oct 2018 Yin Xian, Hanlin Gu, Wei Wang, Xuhui Huang, Yuan YAO, Yang Wang, Jian-Feng Cai

We introduce the use of data-driven tight frame (DDTF) algorithm for cryo-EM image denoising.

Computation Image and Video Processing

Accelerated Alternating Projections for Robust Principal Component Analysis

1 code implementation15 Nov 2017 HanQin Cai, Jian-Feng Cai, Ke Wei

We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$.

Separation-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach

no code implementations4 Nov 2017 Weiyu Xu, Jirong Yi, Soura Dasgupta, Jian-Feng Cai, Mathews Jacob, Myung Cho

However, it is known that in order for TV minimization and atomic norm minimization to recover the missing data or the frequencies, the underlying $R$ frequencies are required to be well-separated, even when the measurements are noiseless.

Super-Resolution

Hankel Matrix Nuclear Norm Regularized Tensor Completion for $N$-dimensional Exponential Signals

no code implementations6 Apr 2016 Jiaxi Ying, Hengfa Lu, Qingtao Wei, Jian-Feng Cai, Di Guo, Jihui Wu, Zhong Chen, Xiaobo Qu

Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging.

Precise Phase Transition of Total Variation Minimization

no code implementations15 Sep 2015 Bingwen Zhang, Weiyu Xu, Jian-Feng Cai, Lifeng Lai

Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics.

Denoising

Projected Wirtinger Gradient Descent for Low-Rank Hankel Matrix Completion in Spectral Compressed Sensing

no code implementations14 Jul 2015 Jian-Feng Cai, Suhui Liu, Weiyu Xu

This paper considers reconstructing a spectrally sparse signal from a small number of randomly observed time-domain samples.

Matrix Completion

Robust recovery of complex exponential signals from random Gaussian projections via low rank Hankel matrix reconstruction

no code implementations10 Mar 2015 Jian-Feng Cai, Xiaobo Qu, Weiyu Xu, Gui-Bo Ye

Our method can be applied to spectral compressed sensing where the signal of interest is a superposition of $R$ complex sinusoids.

Precise Semidefinite Programming Formulation of Atomic Norm Minimization for Recovering d-Dimensional ($d\geq 2$) Off-the-Grid Frequencies

no code implementations2 Dec 2013 Weiyu Xu, Jian-Feng Cai, Kumar Vijay Mishra, Myung Cho, Anton Kruger

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous.

Guarantees of Total Variation Minimization for Signal Recovery

no code implementations28 Jan 2013 Jian-Feng Cai, Weiyu Xu

In this paper, we consider using total variation minimization to recover signals whose gradients have a sparse support, from a small number of measurements.

A Singular Value Thresholding Algorithm for Matrix Completion

4 code implementations18 Oct 2008 Jian-Feng Cai, Emmanuel J. Candes, Zuowei Shen

Off-the-shelf algorithms such as interior point methods are not directly amenable to large problems of this kind with over a million unknown entries.

Optimization and Control

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