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.

翻译：水平模型的宽度最近激发了新一代有效获取和重建压缩成像的有效模式。 此外,它自然地出现在信号处理的各个领域,如平行获取、雷达和稀少的腐败问题。 级别信号稀少的重建战略通常依赖于适当的convex优化程序。 值得注意的是,虽然迭代和贪婪的算法在计算效率方面可以优于同质优化,而且对于标准的宽度问题已经进行了广泛研究,但对于其一般化到级别设置中稀少的程度却知之甚少。 在本文中,我们为迭代硬阈值和COSaMP算法等级别变异中稀少的变异物展示了新的稳定和稳健的统一恢复保证,从而弥补了这一差距。 我们的理论分析概括了标准宽度情况下现有的恢复保证,并优于将加权 $ ell $ $ $ $ $ $ 的最小化程度保障与稀少的保证值进行比较。 此外,我们还提议并用数字测试在级别信号中稀稀稀少的或可测匹配的计算算法。