134 citations · 644 across the 51 of their papers we have counts for
14 papers · 1 filter
Near-Optimal Nonconvex Matrix Completion
Jian-Feng Cai, Xiliang Lu, Juntao You
We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries. Convex methods achieve sample complexity linear in the m…
The global landscape of phase retrieval II: quotient intensity models
Jian-Feng Cai, Meng Huang, Dong Li +1
A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only measurements. In this work we introduce three novel quotient intensity-bas…
The global landscape of phase retrieval I: perturbed amplitude models
Jian-Feng Cai, Meng Huang, Dong Li +1
A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this pa…
Sample-Efficient Sparse Phase Retrieval via Stochastic Alternating Minimization
Jian-Feng Cai, Yuling Jiao, Xiliang Lu +1
In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm…
Image Restoration: Structured Low Rank Matrix Framework for Piecewise Smooth Functions and Beyond
Jian-Feng Cai, Jae Kyu Choi, Jingyang Li +1
Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate…
Provable Near-Optimal Low-Multilinear-Rank Tensor Recovery
Jian-Feng Cai, Lizhang Miao, Yang Wang +1
We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one st…