论文标题
Bisparse通过层次稀疏恢复通过盲目反卷积
Bisparse Blind Deconvolution through Hierarchical Sparse Recovery
论文作者
论文摘要
层次稀疏框架，尤其是HIHTP算法，最近已成功地应用于许多相关的通信工程问题，尤其是当信号空间层次结构结构时。在本文中，研究了HIHTP算法在解决BI-SPARSE盲目反卷积问题上的适用性。这里的Bi-Sparse盲卷积设置包括从$ h*（qb）$的知识中恢复$ h $和$ b $，其中$ q $是一些线性操作员，$ b $和$ h $都被认为是稀疏的。该方法基于将问题提升到线性的方法，然后通过\ emph {层次稀疏框架}应用HIHTP。特别是，提出了有效的HIHTP算法来执行恢复。 然后，对于高斯绘制随机矩阵$ q $，理论上表明，$ s $ -sparse $ h \ in \ mathbb {k}^μ$和$σ$ -sparse $ b \ in \ mathbb {K} s \ log（s）^2 \ log（μ）\ log（μn） +sσ\ log（n）$。
The hierarchical sparsity framework, and in particular the HiHTP algorithm, has been successfully applied to many relevant communication engineering problems recently, particularly when the signal space is hierarchically structured. In this paper, the applicability of the HiHTP algorithm for solving the bi-sparse blind deconvolution problem is studied. The bi-sparse blind deconvolution setting here consists of recovering $h$ and $b$ from the knowledge of $h*(Qb)$, where $Q$ is some linear operator, and both $b$ and $h$ are both assumed to be sparse. The approach rests upon lifting the problem to a linear one, and then applying HiHTP, through the \emph{hierarchical sparsity framework}. %In particular, the efficient HiHTP algorithm is proposed for performing the recovery. Then, for a Gaussian draw of the random matrix $Q$, it is theoretically shown that an $s$-sparse $h \in \mathbb{K}^μ$ and $σ$-sparse $b \in \mathbb{K}^n$ with high probability can be recovered when $μ\succcurlyeq s\log(s)^2\log(μ)\log(μn) + sσ\log(n)$.
