2021
DOI: 10.1007/s11228-021-00603-2
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On the Strong Convergence of Forward-Backward Splitting in Reconstructing Jointly Sparse Signals

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Cited by 2 publications
(7 citation statements)
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“…With properties ( 16)-( 17) in hand, our result is obtained in three steps: 1) Using a partitioning technique from [11], establish finite convergence x k j → x * j for every j ∈ L. 2) Establish an angular convergence result on the extended support set E. 3) Combine the known general weak convergence of the forward-backward algorithm, see, e.g., [2], with our angular convergence result to obtain convergence in norm on E, and hence strong convergence since L ∪ E = [N ]. For more details on the above approach, see [5]. The established result can then be summarized as follows.…”
Section: Forward-backward Algorithm Formentioning
confidence: 97%
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“…With properties ( 16)-( 17) in hand, our result is obtained in three steps: 1) Using a partitioning technique from [11], establish finite convergence x k j → x * j for every j ∈ L. 2) Establish an angular convergence result on the extended support set E. 3) Combine the known general weak convergence of the forward-backward algorithm, see, e.g., [2], with our angular convergence result to obtain convergence in norm on E, and hence strong convergence since L ∪ E = [N ]. For more details on the above approach, see [5]. The established result can then be summarized as follows.…”
Section: Forward-backward Algorithm Formentioning
confidence: 97%
“…Problem (5) can be related to the joint-sparse basis pursuit denoising problem as follows. Let (φ r ) r∈N be an orthonormal basis of V, then c ν ∈ V has unique representation…”
Section: Sparse Regularization For Parameterized Pdesmentioning
confidence: 99%
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