论文标题
两级广义块正交匹配追踪(TSGBOMP)算法
A Two Stage Generalized Block Orthogonal Matching Pursuit (TSGBOMP) Algorithm
论文作者
论文摘要
从其一些投影中恢复未知的稀疏信号是压缩感应的关键目标。通常,一个信号通常不是稀疏但稀疏的信号。现有的块稀疏恢复算法(例如BOMP)可以假设均匀的块大小和已知的块边界,但是,在许多应用中,这并不是很实际。本文解决了这个问题,并提出了两个步骤过程,其中第一阶段是粗块位置识别阶段,而第二阶段则在第一阶段选择的窗口中对非零群集进行更细微的定位。通过首先定义给定的广义块稀疏信号的所谓伪块间隔块,然后在相应的RIC上施加上限,对所提出的算法进行了详细的收敛分析。我们还扩展了复杂向量的分析以及矩阵条目,事实证明扩展是非平凡的,需要特殊护理。此外,假设实际高斯传感矩阵条目,我们发现满足衍生恢复边界的概率下的下限。下边界表明有一组参数,使得派生的结合与高概率满意。与BOMP相比,模拟结果证实了所提出算法的性能显着提高。
Recovery of an unknown sparse signal from a few of its projections is the key objective of compressed sensing. Often one comes across signals that are not ordinarily sparse but are sparse blockwise. Existing block sparse recovery algorithms like BOMP make the assumption of uniform block size and known block boundaries, which are, however, not very practical in many applications. This paper addresses this problem and proposes a two step procedure, where the first stage is a coarse block location identification stage while the second stage carries out finer localization of a non-zero cluster within the window selected in the first stage. A detailed convergence analysis of the proposed algorithm is carried out by first defining the so-called pseudoblock-interleaved block RIP of the given generalized block sparse signal and then imposing upper bounds on the corresponding RIC. We also extend the analysis for complex vector as well as matrix entries where it turns out that the extension is non-trivial and requires special care. Furthermore, assuming real Gaussian sensing matrix entries, we find a lower bound on the probability that the derived recovery bounds are satisfied. The lower bound suggests that there are sets of parameters such that the derived bound is satisfied with high probability. Simulation results confirm significantly improved performance of the proposed algorithm as compared to BOMP.