In this article, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by using other unitary transform matrices than that by using discrete Fourier transform matrix. This would be more effective for robust tensor completion. Experimental results for hyperspectral, video and face datasets have shown that the recovery performance for the robust tensor completion problem by using transformed tensor SVD is better in peak signal-to-noise ratio than that by using Fourier transform and other robust tensor completion methods.
K E Y W O R D Slow-rank, robust tensor completion, sparsity, transformed tensor singular value decomposition, unitary transform matrix
SG-III laser facility is now the largest laser driver for inertial confinement fusion research in China. The whole laser facility can deliver 180 kJ energy and 60 TW power ultraviolet laser onto target, with power balance better than 10%. We review the laser system and introduce the SG-III laser performance here.
For the problem of image restoration of observed images corrupted by blur and impulse noise, the widely used TVL1 model may deviate from both the data-acquisition model and the prior model, especially for high noise levels. In order to seek a solution of high recovery quality beyond the reach of the TVL1 model, we propose an adaptive correction procedure for TVL1 image deblurring under impulse noise. Then, a proximal alternating direction method of multipliers (ADMM) is presented to solve the corrected TVL1 model and its convergence is also established under very mild conditions. It is verified by numerical experiments that our proposed approach outperforms the TVL1 model in terms of signal-to-noise ratio (SNR) values and visual quality, especially for high noise levels: it can handle salt-and-pepper noise as high as 90% and random-valued noise as high as 70%. In addition, a comparison with a state-of-the-art method, the two-phase method, demonstrates the superiority of the proposed approach.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.