Reliable recovery of hierarchically sparse signals and application in machine-type communications

We examine and propose a solution to the problem of recovering a block sparse signal with sparse blocks from linear measurements. Such problems naturally emerge in the context of mobile communication, in settings motivated by desiderata of a 5G framework. We introduce a new variant of the Hard Thresholding Pursuit (HTP) algorithm referred to as HiHTP. For the specific class of sparsity structures, HiHTP performs significantly better in numerical experiments compared to HTP. 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.

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