  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, 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 $n\gtrsim rs\log^4 n$ 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.
