Hierarchical Isometry Properties of Hierarchical Measurements
arXiv:2005.10379 · doi:10.1016/j.acha.2021.12.006
Abstract
A new class of measurement operators, coined hierarchical measurement operators, and prove results guaranteeing the efficient, stable and robust recovery of hierarchically structured signals from such measurements. We derive bounds on their hierarchical restricted isometry properties based on the restricted isometry constants of their constituent matrices, generalizing and extending prior work on Kronecker-product measurements. As an exemplary application, we apply the theory to two communication scenarios. The fast and scalable HiHTP algorithm is shown to be suitable for solving these types of problems and its performance is evaluated numerically in terms of sparse signal recovery and block detection capability.
arXiv comment22 pages, 5 figures. v3: Significant rework of previous version. Section on incoherent blocks added, as well as more numerical experiments. v4: Revision of the manuscript. Several previous mistakes have been corrected
References in corpus (11)
- Compressed Sensing of Block-Sparse Signals: Uncertainty Relations and Efficient Recovery
- Model-Based Compressive Sensing
- The Convex Geometry of Linear Inverse Problems
- A note on the group lasso and a sparse group lasso
- Structured Variable Selection with Sparsity-Inducing Norms
- C-HiLasso: A Collaborative Hierarchical Sparse Modeling Framework
- The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees
- Reliable recovery of hierarchically sparse signals for Gaussian and Kronecker product measurements
- Semi-device-dependent blind quantum tomography
- Proceedings of the third "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'16)
- Hierarchical sparse recovery from hierarchically structured measurements with application to massive random access