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Reliable Recovery of Hierarchically Sparse Signals for Gaussian and Kronecker Product Measurements
Publikationstyp
Journal Article
Date Issued
2020
Sprache
English
Volume
68
Start Page
4002
End Page
4016
Article Number
9120242
Citation
IEEE Transactions on Signal Processing 68: 9120242 (2020)
Publisher DOI
Scopus ID
We propose and analyze a solution to the problem of recovering a block sparse signal with sparse blocks from linear measurements. Such problems naturally emerge inter alia in the context of mobile communication, in order to meet the scalability and low complexity requirements of massive antenna systems and massive machine-type communication. We introduce a new variant of the Hard Thresholding Pursuit (HTP) algorithm referred to as HiHTP. We provide both a proof of convergence and a recovery guarantee for noisy Gaussian measurements that exhibit an improved asymptotic scaling in terms of the sampling complexity in comparison with the usual HTP algorithm. Furthermore, hierarchically sparse signals and Kronecker product structured measurements naturally arise together in a variety of applications. We establish the efficient reconstruction of hierarchically sparse signals from Kronecker product measurements using the HiHTP algorithm. Additionally, we provide analytical results that connect our recovery conditions to generalized coherence measures. Again, our recovery results exhibit substantial improvement in the asymptotic sampling complexity scaling over the standard setting. Finally, we validate in numerical experiments that for hierarchically sparse signals, HiHTP performs significantly better compared to HTP.
Subjects
block sparse
channel estimation
coherence
compressed sensing
hard thresholding
hierarchical sparsity
Inverse problem
Kronecker product
machine-type communications
pursuit algorithms
recovery guarantee
restricted isometry property
sparse vectors