Generalized notions of sparsity and restricted isometry property. Part I: a unified framework
Generalized notions of sparsity and restricted isometry property. Part I: a unified framework
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DOI：
10.1093/imaiai/iay018
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发表时间：
2020-03-01
影响因子：
1.6
通讯作者：
Lee, Kiryung
中科院分区：
文献类型：
--
作者：
Junge, Marius;Lee, Kiryung
限制等距性（RIP）是分析稀疏模型下各种反问题的重要工具。受压缩感知和降维的低秩张量的应用，我们提出了广义的稀疏性的概念，并提供了一个统一的框架，相应的RIP，特别是当结合各向同性组动作。我们的结果扩展了一种方法，由Rudelson和Vershynin更广泛的范围内，包括交换和非交换函数空间。此外，我们的Banach空间的稀疏性概念适用于仿射群作用。广义方法特别适用于高阶张量积。
The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose generalized notions of sparsity and provide a unified framework for the corresponding RIP, in particular when combined with isotropic group actions. Our results extend an approach by Rudelson and Vershynin to a much broader context including commutative and non-commutative function spaces. Moreover, our Banach space notion of sparsity applies to affine group actions. The generalized approach in particular applies to high-order tensor products.