Vectorized Hankel Lift：一种点源盲超分辨的凸方法
Vectorized Hankel Lift: A Convex Approach for Blind Super-Resolution of Point Sources
摘要：
我们考虑的问题，解决$ r$点源时，在频谱的低端$n$样本点扩展函数（PSF）是未知的。假设PSF的频谱样本位于低维子空间中（让$s$表示维数），则该问题可以重新表示为矩阵恢复问题，然后进行位置估计。通过利用目标矩阵的向量化Hankel矩阵的低秩结构，提出了一种称为向量化Hankel提升的凸矩阵恢复方法。结果表明，$n\gtrsim rs\log^4 n$样品是足够的矢量汉克尔提升，以实现准确的恢复。对于从矩阵的位置检索，应用单快照MUSIC方法在矢量化汉克尔提升框架内对应于空间平滑技术，提出了提高性能的MMV MUSIC的到达方向（DOA）估计。
英文摘要：
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), 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.
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