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We consider the problem of resolving $ r$ point sources from $n$ samples atthe 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 matrixrecovery problem, followed by location estimation. By exploiting the low rankstructure of the vectorized Hankel matrix associated with the target matrix, aconvex approach called Vectorized Hankel Lift is proposed for the matrixrecovery. It is shown that $n\gtrsim rs\log^4 n$ samples are sufficient forVectorized Hankel Lift to achieve the exact recovery. For the locationretrieval from the matrix, applying the single snapshot MUSIC method within thevectorized Hankel lift framework corresponds to the spatial smoothing techniqueproposed to improve the performance of the MMV MUSIC for thedirection-of-arrival (DOA) estimation.

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