DCT based weighted adaptive multi-linear data completion and denoising

This paper emphasises on formulating a weighted adaptive transform based solution for multi-linear signal completion and denoising problems based on the fact that the real-valued DCT based tensor algebra provides better low-rank representation compared with the existing Fourier transform based framework. Using an m-mode DCT based tensor SVD, complementary information existing in all modes of the tensor is effectively employed to achieve better performance. Further improvement in the tensor recovery is accomplished by adaptive low-rank regularization via measuring the degree of the low-rank structure existing in each mode. The proposed method follows adaptive low rank regularization strategy which provides more gravitas to the better low-rank representation. The proposed algorithm built by combining the three aspects of tensor processing such as, DCT based tensor SVD, utilization of complementary information from all the modes of the tensor and adaptive low-rank regularization to attain greater signal recovery. The performance of the proposed method is evaluated by applying to video completion and denoising problems.