论文标题
矢量化Hankel Lift：一种用于点源超级分辨率的凸方法
Vectorized Hankel Lift: A Convex Approach for Blind Super-Resolution of Point Sources
论文作者
论文摘要
我们认为，当尚不清楚点传播功能（PSF）时，在频谱的低端解决$ n $样品的$ r $点源的问题。假设PSF的频谱样本位于低维子空间（令$ s $表示维度），则可以将此问题重新归类为矩阵恢复问题，然后进行位置估计。通过利用与目标矩阵关联的矢量化Hankel矩阵的低等级结构，提出了一种称为矢量化Hankel Lift的凸方法用于矩阵恢复。结果表明，$ n \ gtrsim rs \ log^4 n $样品足以用于矢量化的hankel升降机以实现精确的恢复。对于从矩阵中检索的位置检索，在矢量化的Hankel Lift框架中应用单个快照音乐方法对应于提出的空间平滑技术，以提高MMV音乐的性能以进行超越方向（DOA）估计。
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.
