Wen-Hao Xu

Xi-Le Zhao, Wen-Hao Xu, Tai-Xiang Jiang et al.

Multi-dimensional images, such as color images and multi-spectral images, are highly correlated and contain abundant spatial and spectral information. However, real-world multi-dimensional images are usually corrupted by missing entries. By integrating deterministic low-rankness prior to the data-driven deep prior, we suggest a novel regularized tensor completion model for multi-dimensional image completion. In the objective function, we adopt the newly emerged tensor nuclear norm (TNN) to characterize the global low-rankness prior of the multi-dimensional images. We also formulate an implicit regularizer by plugging into a denoising neural network (termed as deep denoiser), which is convinced to express the deep image prior learned from a large number of natural images. The resulting model can be solved by the alternating directional method of multipliers algorithm under the plug-and-play (PnP) framework. Experimental results on color images, videos, and multi-spectral images demonstrate that the proposed method can recover both the global structure and fine details very well and achieve superior performance over competing methods in terms of quality metrics and visual effects.

Wen-Hao Xu, Xi-Le Zhao, Michael Ng

Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on the discrete cosine transform (DCT) matrix. The advantages of using DCT are that (i) the complex arithmetic is not involved in the cosine transform based tensor singular value decomposition, so the computational cost required can be saved; (ii) the intrinsic reflexive boundary condition along the tubes in the third dimension of tensors is employed, so its performance would be better than that by using the periodic boundary condition in DFT. We demonstrate that the tensor product between two tensors by using DCT can be equivalent to the multiplication between a block Toeplitz-plus-Hankel matrix and a block vector. Numerical examples of low-rank tensor completion are further given to illustrate that the efficiency by using DCT is two times faster than that by using DFT and also the errors of video and multispectral image completion by using DCT are smaller than those by using DFT.