Iterative algorithm using decoupling method for third-order tensor deblurring

Karima EL Qate, Souad Mohaoui, Abdelilah Hakim, Said Raghay

Abstract


The present paper is concerned with exploiting an iterative decoupling algorithm to address the problem of third-order tensor deblurring. The regularized deblurring problem, which is mathematically given by the sum of a fidelity term and a regularization term, is decoupled into an observation fidelity and a denoiser model steps. One basic advantage of the iterative decoupling algorithm is that the deblurring problem is supervised by the efficiency of the denoiser model. Thus, we consider a patch-based weighted low-rank tensor with sparsity prior. Numerical tests to image deblurring are given to demonstrate the efficiency of the proposed decoupling based algorithm.

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M.S. Asif, J. Romberg, Fast and accurate algorithms for re-weighted l1-norm minimization, IEEE Transactions on Signal Processing 61 (2013), no. 23, 5905-5916.

O. Banouar, S. Mohaoui, S. Raghay, Collaborating filtering using unsupervised learning for image reconstruction from missing data. EURASIP Journal on Advances in Signal Processing 2018 (2018), no. 1, 1-12.

A. Beck, M. Teboulle, Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE transactions on image processing 18 (2009), no. 11, 2419-2434.

Y. Chang, L. Yan, X.-L. Zhao, H. Fang, Z. Zhang, S. Zhong, Weighted low-rank tensor recovery for hyperspectral image restoration, IEEE transactions on cybernetics 50 (2020), no. 11, 4558-4572.

Y. Chen, W. He, N. Yokoya, T.-Z. Huang, X.-L. Zhao, Nonlocal tensor-ring decomposition for hyperspectral image denoising. IEEE Transactions on Geoscience and Remote Sensing 58 (2019), no. 2, 1348-1362.

A. Cichocki, R. Zdunek, A. H. Phan, S.-I. Amari, Nonnegative matrix and tensor factorizations: applications to exploratory multi-way data analysis and blind source separation, John Wiley & Sons, 2009.

W. Dong, G. Shi, X. Li, Image deblurring with low-rank approximation structured sparse representation, In: Proceedings of the 2012 Asia Pacific Signal and Information Processing Association Annual Summit and Conference (2012), IEEE, pp. 1-5.

E.M. Eksioglu, Decoupled algorithm for mri reconstruction using nonlocal block matching model: Bm3d-mri, Journal of Mathematical Imaging and Vision 56 (2016), no. 3, 430-440.

K. El Qate, M. El Rhabi, A. Hakim, E. Moreau, N. Thirion-Moreau, Hyperspectral image completion via tensor factorization with a bi-regularization term, Journal of Signal Processing Systems (2022), 1-11.

K. El Qate, M. El Rhabi, A. Hakim, E. Moreau, N. Thirion-Moreau, N. A primal-dual algorithm for nonnegative n-th order cp tensor decomposition: application to fluorescence spectroscopy data analysis, Multidimensional Systems and Signal Processing 33 (2022), no. 2, 665-682.

K. EL Qate, S. Mohaoui, A. Hakim, S. Raghay, Color image completion using tensor truncated nuclear norm with l0 total variation, Annals of the University of Craiova-Mathematics and Computer Science Series 49 (2022), no. 2, 250-259.

H. Fang, C. Luo, G. Zhou, X. Wang, Hyperspectral image deconvolution with a spectral-spatial total variation regularization, Canadian Journal of Remote Sensing 43 (2017), no. 4, 384-395.

S. Gu, L. Zhang, W. Zuo, X. Feng, Weighted nuclear norm minimization with application to image denoising, In: Proceedings of the IEEE conference on computer vision and pattern recognition (2014), 2862-2869.

R. Hao, Z. Su, A patch-based low-rank tensor approximation model for multiframe image denoising, Journal of Computational and Applied Mathematics 329 (2018), 125-133.

W. He, H. Zhang, L. Zhang, H. Shen, Hyperspectral image denoising via noise-adjusted iterative low-rank matrix approximation, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 8 (2015), no. 6, 3050-3061.

S. Henrot, C. Soussen, D. Brie, Fast positive deconvolution of hyperspectral images, IEEE Transactions on Image Processing 22 (2012), no. 2, 828-833.

T. Korah, C. Rasmussen, Spatiotemporal inpainting for recovering texture maps of occluded building facades, IEEE Transactions on Image Processing 16 (2007), no. 9, 2262-2271.

N. Kreimer, M.D. Sacchi, A tensor higher-order singular value decomposition for prestack seismic data noise reduction and interpolation, Geophysics 77 (2012), no. 3, V113-V122.

N. Li, B. Li, Tensor completion for on-board compression of hyperspectral images, In: 2010 IEEE International Conference on Image Processing (2010), IEEE, 517-520.

S. Mohaoui, A. Hakim, S. Raghay, Tensor completion via bilevel minimization with fixed-point constraint to estimate missing elements in noisy data, Advances in Computational Mathematics 47 (2021), no. 1, 1-27.

T. Poggio, V. Torre, Ill-posed problems and regularization analysis in early vision, Technical report, MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB, 1984.

W. Ren, X. Cao, J. Pan, X. Guo, W. Zuo, M.-H. Yang, Image deblurring via enhanced low-rank prior, IEEE Transactions on Image Processing 25 (2016), no. 7, 3426-3437.

Y. Tang, Y. Xue, Y. Chen, L. Zhou, Blind deblurring with sparse representation via external patch priors, Digital Signal Processing 78 (2018), 322-331.

X. Tao, H. Gao, X. Shen, J. Wang, J. Jia, Scale-recurrent network for deep image deblurring, In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2018), 8174-8182.

Z. Wang, A.C. Bovik, H.R. Sheikh, E.P. Simoncelli, Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing 13 (2004), no. 4, 600-612.

Y.-W. Wen, M.K. Ng, W.-K. Ching, Iterative algorithms based on decoupling of deblurring and denoising for image restoration. SIAM Journal on Scientific Computing 30 (2008), no. 5, 2655-2674.

Q. Xie, Q. Zhao, D. Meng, Z. Xu, S. Gu, W. Zuo, L. Zhang, Multispectral images denoising by intrinsic tensor sparsity regularization, In: Proceedings of the IEEE conference on computer vision and pattern recognition (2016), pp. 1692-1700.

Y. Xie, Y. Qu, D. Tao, W. Wu, Q. Yuan, W. Zhang, Hyperspectral image restoration via iteratively regularized weighted schatten p-norm minimization, IEEE Transactions on Geoscience and Remote Sensing 54, (2016), no. 8, 4642-4659.

J. Xu, L. Zhang, W. Zuo, D. Zhang, X. Feng, Patch group based nonlocal self-similarity prior learning for image denoising, In: Proceedings of the IEEE international conference on computer vision (2015), 244-252.

H. Zhang, Y. Dai, H. Li, P. Koniusz, Deep stacked hierarchical multi-patch network for image deblurring, In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (2019), 5978-5986.

H. Zhou, Y. Su, Z. Li, Hyperspectral mixed noise removal via subspace representation and weighted low-rank tensor regularization, arXiv preprint arXiv:2111.07044 (2021).




DOI: https://doi.org/10.52846/ami.v51i1.1753