Academic reports:Low-Rank Hankel Matrix Completion for Spectrally Sparse Signal Reconstruction with Super Resolution

Speaker: Cai Jianfeng (Jianfeng Cai), Associate Professor of Hong Kong University of Science and Technology

Time: (Thursday) afternoon, May 18th 4: 00-5: 00

Location: Mathematics and Information Science Lecture Hall 201

Contact: Professor Zhang Na

Abstract：A spectrally sparse signal of order r is a mixture of r damped or undamped complex sinusoids. In this talk, we consider the problem of reconstructing spectrally sparse signals from a random subset of n regular time domain samples, which can be reformulated as a low rank Hankel matrix completion problem. We introduce a fast iterative hard thresholding (FIHT) algorithm for efficient reconstruction of spectrally sparse signals via low rank Hankel matrix completion. Theoretical recovery guarantees have been established for FIHT, showing that O(r^2log^2(n)) number of samples are sufficient for exact recovery with high probability. Empirical performance comparisons establish significant computational advantages for FIHT. In particular, numerical simulations on 3D arrays demonstrate the capability of FIHT on handling large and high-dimensional real data.

Speaker Profile:

    Cai Jianfeng joined the Hong Kong University of Science and Technology in 2015, currently Associate Professor number. He graduated from the Department of Mathematics, Fudan University undergraduate in 2000, and received a doctorate in mathematics at the Chinese University of Hong Kong in 2007. Prior to joining HKUST, Cai Jianfeng worked in the National University of Singapore, University of California, Los Angeles, and the University of Iowa to work. Cai Jianfeng in harmonic analysis and application of the calculation, the field of image processing and data analysis done a lot of good research. J. is now in the top mathematics journals international Amer. Math. Soc., And internationally renowned journals such as Appl. Comput. Harmon. Anal., IEEE Trans. Image Process., IEEE Trans. Signal Process., SIAM J. Optimiz., SIAM J. Imaging Sci. and other published nearly 50 papers, Google Scholar papers total number of citations is 5357 times.