Vectorized Hankel Lift: A Convex Approach for Blind Super-Resolution of Point Sources

Jinchi Chen; Weiguo Gao; Sihan MaoKe Wei

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Vectorized Hankel Lift: A Convex Approach for Blind Super-Resolution of Point Sources

机译：Vectorized Hankel Lift: A Convex Approach for Blind Super-Resolution of Point Sources

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摘要

We consider the problem of resolving $r$ point sources from $n$ samples at the low end of the spectrum when point spread functions (PSFs) are not known. Assuming that the spectrum samples of the PSFs lie in low dimensional subspace (let $s$ denote the dimension), we can formulate it as a matrix recovery problem, followed by location estimation. By exploiting the low rank structure of the vectorized Hankel matrix associated with the target matrix, a convex approach called Vectorized Hankel Lift is proposed for the matrix recovery. It is shown that $ngtrsim rslog ^{4} n$ samples are sufficient for Vectorized Hankel Lift to achieve the exact recovery. For the location retrieval from the matrix, applying the single snapshot MUSIC method within the vectorized Hankel lift framework corresponds to the spatial smoothing technique proposed to improve the performance of the MMV MUSIC for the direction-of-arrival (DOA) estimation.

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来源
《IEEE Transactions on Information Theory》 |2022年第12期|8280-8309|共30页
作者
Jinchi Chen; Weiguo Gao; Sihan MaoKe Wei;
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作者单位

School of Data Science, Fudan University, Shanghai, China;

School of Mathematical Sciences and School of Data Science, Fudan University, Shanghai, China;

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原文格式 PDF
正文语种英语
中图分类通信;
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Superresolution; Sparse matrices; Multiple signal classification; TV; Matrix decomposition; Estimation; Atomic measurements;

Vectorized Hankel Lift: A Convex Approach for Blind Super-Resolution of Point Sources

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