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

08/12/2020

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by   Jinchi Chen, et al.

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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), this problem can be reformulated as a matrix recovery problem. 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 in this paper. It is shown that n≳ rslog^4 n samples are sufficient for Vectorized Hankel Lift to achieve the exact recovery. In addition, a new variant of the MUSIC method available for spectrum estimation in the multiple snapshots scenario arises naturally from the vectorized Hankel lift framework, which is of independent interest.