论文标题
在本地行动的好处：重建算法稀疏信号的稀疏信号具有稳定且稳健的恢复保证
The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees
论文作者
论文摘要
水平模型的稀疏性最近激发了新一代的有效采集和重建方式，以进行压缩成像。此外，它自然出现在信号处理的各个领域，例如并行获取，雷达和稀疏腐败问题。稀疏信号的重建策略通常依赖于合适的凸优化程序。值得注意的是，尽管迭代和贪婪的算法可以在计算效率方面胜过凸的优化，并且在标准稀疏性的情况下进行了广泛的研究，但对它们对稀疏设置的概括知之甚少。在本文中，我们通过显示新的稳定且稳健的均匀恢复来保证迭代硬阈值和COSAMP算法的水平变体稀疏。我们的理论分析概括了在标准稀疏性情况下目前可用的恢复保证，并且相比之下，与加权$ \ ell^1 $最小化的稀疏级别相比。此外，我们还提出和数字测试正交匹配的追踪算法的扩展，以稀疏信号。
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel acquisition, radar, and the sparse corruptions problem. Reconstruction strategies for sparse in levels signals usually rely on a suitable convex optimization program. Notably, although iterative and greedy algorithms can outperform convex optimization in terms of computational efficiency and have been studied extensively in the case of standard sparsity, little is known about their generalizations to the sparse in levels setting. In this paper, we bridge this gap by showing new stable and robust uniform recovery guarantees for sparse in level variants of the iterative hard thresholding and the CoSaMP algorithms. Our theoretical analysis generalizes recovery guarantees currently available in the case of standard sparsity and favorably compare to sparse in levels guarantees for weighted $\ell^1$ minimization. In addition, we also propose and numerically test an extension of the orthogonal matching pursuit algorithm for sparse in levels signals.
