High-order tensor nuclear norm with Multiway Delay-embedding Transform for color image recovery

Recently, Multiway Delay-embedding Transform (MDT)-based low-rank tensor completion has achieved a lot of attention for color image recovery. However, existing studies mostly focus on tensor decomposition to encode the low-rankness of the Hankel tensor derived from MDT, which are sensitive to the predefined rank and limit the recovery performance. Aiming at addressing this issue, in this paper, we use the High-order Tensor Nuclear Norm (HTNN) to approximate the Hankel tensor rank, thus a new model named MDT-HTNN is proposed for low-rank tensor completion. Efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the proposed model and its convergence analysis is discussed in detail. Extensive experiments on a series of color images and MRI illustrate that our proposed algorithm significantly improve the recovery accuracy. Specifically, under multiple sampling rate settings for multiple color images, the average PSNR value increased by 14.8% and the CPU time decreased by 89.5% compared with the classical MDT-Tucker method.