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An iterative hard thresholding algorithm with improved convergence for low-rank tensor recovery

Abstract : Recovering low-rank tensors from undercomplete linear measurements is a computationally challenging problem of great practical importance. Most existing approaches circumvent the intractability of the tensor rank by considering instead the multilinear rank. Among them, the recently proposed tensor iterative hard thresholding (TIHT) algorithm is simple and has low cost per iteration, but converges quite slowly. In this work, we propose a new step size selection heuristic for accelerating its convergence, relying on a condition which (ideally) ensures monotonic decrease of its target cost function. This condition is obtained by studying TIHT from the standpoint of the majorization-minimization strategy which underlies the normalized IHT algorithm used for sparse vector recovery. Simulation results are presented for synthetic data tensor recovery and brain MRI data tensor completion, showing that the performance of TIHT is notably improved by our heuristic, with a small to moderate increase of the cost per iteration.
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Contributor : José Henrique de Morais Goulart <>
Submitted on : Tuesday, June 23, 2015 - 8:02:24 PM
Last modification on : Wednesday, October 14, 2020 - 3:02:02 PM
Long-term archiving on: : Tuesday, September 15, 2015 - 10:25:35 PM


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  • HAL Id : hal-01132367, version 2



José Henrique de Morais Goulart, Gérard Favier. An iterative hard thresholding algorithm with improved convergence for low-rank tensor recovery. 2015 European Signal Processing Conference (EUSIPCO 2015), Aug 2015, Nice, France. ⟨hal-01132367v2⟩



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