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Arbitrary Block-Sparse Signal Reconstruction Based on Incomplete Single Measurement Vector

机译：基于不完整单个测量向量的任意块稀疏信号重构

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摘要

Within the compressive sensing framework, reconstruction algorithms of block-sparse signal (BSS) often have special requirements on sparsity patterns. As a result, only some particular BSSs can be reconstructed. In this paper, we present a new universal greedy iteration algorithm, named block-matching pursuit (BMP), for BSS with an arbitrary sparsity pattern. The BMP can reconstruct the target signal without prior information of the signal's sparsity pattern and achieves an outstanding reconstruction probability. In each iteration, the BMP first estimates a part of support set of the signal by a correlation test. Based on the estimated support and the property of nonzero blocks, coordinates of all possible nonzero entries can be obtained to form a candidate list. Then some coordinates in the list, which are deemed sufficiently reliable by a final test, are added to the current estimated support set. When iteration ends, the true sparsity level, namely true support set, can be exactly calculated by searching a support set with the smallest cardinality; once the true set is derived, the target signal can be reconstructed. Theoretical analysis indicates that BMP can reconstruct the target signal as long as the sampling matrix meets a certain condition. Simulation results show that the reconstruction performance of BMP is better than that of other greedy algorithms. In particular, if the signal with high sparsity level contains a few blocks, BMP can still reconstruct it with a high probability.
机译：在压缩感测框架内，块稀疏信号（BSS）的重建算法通常对稀疏模式有特殊要求。结果，只能重构某些特定的BSS。在本文中，我们为具有任意稀疏模式的BSS提供了一种新的通用贪婪迭代算法，称为块匹配追踪（BMP）。 BMP可以在没有信号稀疏模式的先验信息的情况下重建目标信号，并实现出色的重建概率。在每次迭代中，BMP首先通过相关性测试估计信号支持集的一部分。基于估计的支持和非零块的属性，可以获得所有可能的非零条目的坐标以形成候选列表。然后，列表中的一些坐标（被最终测试认为足够可靠）被添加到当前估计的支持集中。当迭代结束时，可以通过搜索基数最小的支持集来精确计算出真正的稀疏度，即真正的支持集；一旦导出真实集合，就可以重建目标信号。理论分析表明，只要采样矩阵满足一定条件，BMP就可以重构目标信号。仿真结果表明，BMP的重构性能优于其他贪婪算法。特别是，如果具有高稀疏度的信号包含几个块，则BMP仍然可以以较高的概率对其进行重构。

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