Reliable Recovery of Hierarchically Sparse Signals for Gaussian and Kronecker Product Measurements

Roth, Ingo; Kliesch, Martin; Flinth, Axel; Wunder, Gerhard; Eisert, Jens

doi:10.1109/tsp.2020.3003453

Cited by 14 publications

(16 citation statements)

References 41 publications

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“…As a direct consequence, we establish that the condition (1) is sufficient to ensure that, with probability of at least 1 − ǫ, the HiHTP algorithm 1 succesfully recovers each (s, σ)-sparse ground truth h ⊗ b by Ref. [26,Thm. 1].…”

Section: Resultsmentioning

confidence: 89%

“…multiple convoluted signals are linearly superimposed. Hierarchical compressed sensing naturally extends to deeper hierarchies of sparsity levels [5], [26]. For instance, we say that a block vector (X 1 , .…”

Section: Multiuser Casementioning

confidence: 99%

“…The HiHTP algorithm can still be employed for the recovery of such signals when using the equally efficient projection onto (S, s, σ)-sparse vectors in line 4. Recovery can again be guaranteed with the help of a hierarchically restricted isometry property [26].…”

Section: Multiuser Casementioning

confidence: 99%

“…In Refs. [26], [27], it has been shown that such vectors can be efficiently reconstructed from linear measurements A(h⊗b) with the HiHTP algorithm, the hierarchical hard-thresholding pursuit, Algorithm 1. The HiHTP is guaranteed to converge to the ground truth signal if the linear map A exhibits the hierarchical restricted isometry property (HiRIP).…”

Section: Introductionmentioning

confidence: 99%

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Guaranteed blind deconvolution and demixing via hierarchically sparse reconstruction

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Section: Resultsmentioning

confidence: 89%

Section: Multiuser Casementioning

confidence: 99%

Section: Multiuser Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Guaranteed blind deconvolution and demixing via hierarchically sparse reconstruction

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Roth²,

Groß³

et al. 2021

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“…The signals occupy only a small fraction of the entire transformed signal space, which can be represented sparsely by a few elementary components out of a given collection. Consequently, sparsity can also be observed in other classes of natural signals [28]. When the length of the original signal is N, there exist W=2 N possible forms of the transmitted signal x ϵR N×1 in the entire signal space X.…”

Section: A Tdvc Signalsmentioning

confidence: 99%

Maintaining the Status Quo: Simultaneous Estimation and Elimination for Multiple Interference in Transform Domain Vehicular Communication

Wang

Han

Wang

et al. 2022

IEEE Trans. Veh. Technol.

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Wireless communication in vehicular networks is highly vulnerable to electromagnetic interference, which seriously undermines the communication effectiveness. Thus, interference estimation and elimination are essential in vehicular communications. To solve the multitasking problem of interference estimation and cancelation within the transformation domain of vehicular communications where they are divided into the consistency and inconsistency based on the different conditions of spectrum sensing, the present study proposes an iterative Bayesian sparse learning approach for simultaneous interference recovery and elimination which applies multiple Bayesian learning for measured signals, and the structured sparse learning method for simultaneous interference mitigation with signal recovery. Furthermore, the updating optimization based on Bayesian estimation framework is performed to facilitate the learning process and improve the performance of interference estimation and signal reconstruction. Simulation results show that the proposed algorithms achieved more rapid convergence and more accurate recovery (31.84% and 27.88% higher in spectrum sensing with consistency and inconsistency, respectively) than conventional algorithms. During all iterations, the proposed algorithms, because of updating optimization, were more robust than conventional ones, but the computational complexity remained largely the same. To explore the correlation between the parameters and the interference recovery performance, we performed experiments, which revealed linear, logarithmic, and exponential regression correlations for particular forms of interference. We also compared the demodulation performance of the proposed algorithm with existing methods, and it turned out the proposed algorithm also obtained higher gains on average in the bit error rate.

show abstract

Hierarchical Compressed Sensing

Eisert

Flinth

Groß

et al. 2022

Compressed Sensing in Information Processing

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Reliable Recovery of Hierarchically Sparse Signals for Gaussian and Kronecker Product Measurements

Cited by 14 publications

References 41 publications

Guaranteed blind deconvolution and demixing via hierarchically sparse reconstruction

Guaranteed blind deconvolution and demixing via hierarchically sparse reconstruction

Maintaining the Status Quo: Simultaneous Estimation and Elimination for Multiple Interference in Transform Domain Vehicular Communication

Hierarchical Compressed Sensing

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