mlsanityData to 14 Oct 2026

Normalized Iterative Hard Thresholding for Tensor Recovery

arXiv 2507.04228 ↗First posted 6 Jul 2025cs.LG eess.SPcited by 0

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Abstract (arXiv)

Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized iterative hard thresholding (NIHT) method-have been widely used in compressed sensing (CS) and applied to matrix recovery tasks. In this paper, we propose a tensor extension of NIHT, referred to as TNIHT, for the recovery of low-rank tensors under two widely used tensor decomposition models. This extension enables the effective reconstruction of high-order low-rank tensors from a limited number of linear measurements by leveraging the inherent low-dimensional structure of multi-way data. Specifically, we consider both the CANDECOMP/PARAFAC (CP) rank and the Tucker rank to characterize tensor low-rankness within the TNIHT framework. At the same time, we establish a convergence theorem for the proposed TNIHT method under the tensor restricted isometry property (TRIP), providing theoretical support for its recovery guarantees. Finally, we evaluate the performance of TNIHT through numerical experiments on synthetic, image, and video data, and compare it with several state-of-the-art algorithms.

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References · 19

  1. 2016Tensor Ring Decompositioncited by 127
  2. 2016Efficient tensor completion for color image and video recovery: Low-rank tensor traincited by 61
  3. 2017Efficient Low Rank Tensor Ring Completioncited by 45
  4. 2018On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradientcited by 43
  5. 2016Barzilai-Borwein Step Size for Stochastic Gradient Descentcited by 33
  6. 2017Weighted Low-rank Tensor Recovery for Hyperspectral Image Restorationcited by 30
  7. 2020Dictionary Learning with Low-rank Coding Coefficients for Tensor Completioncited by 19
  8. 2016Low-tubal-rank Tensor Completion using Alternating Minimizationcited by 18
  9. 2015Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Datacited by 16
  10. 2014Linear Convergence of Stochastic Iterative Greedy Algorithms with Sparse Constraintscited by 13
  11. 2019Accelerating Variance-Reduced Stochastic Gradient Methodscited by 10
  12. 2019Iterative Hard Thresholding for Low CP-rank Tensor Modelscited by 9
7 more
  1. 2022Binary Iterative Hard Thresholding Converges with Optimal Number of Measurements for 1-Bit Compressed Sensingcited by 9
  2. 2023Unsupervised HDR Image and Video Tone Mapping via Contrastive Learningcited by 6
  3. 2017Stochastic Greedy Algorithms For Multiple Measurement Vectorscited by 3
  4. 2015Multichannel sparse recovery of complex-valued signals using Huber's criterioncited by 2
  5. 2019Discrete Optimization Methods for Group Model Selection in Compressed Sensingcited by 1
  6. 2022Stochastic Variance Reduced Gradient for affine rank minimization problemcited by 1
  7. 2023Iterative Singular Tube Hard Thresholding Algorithms for Tensor Recoverycited by 1

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