Truncated and smoothed schatten-p function for robust tensor recovery

In this paper, we consider the robust tensor recovery problem in which we recover the low rank and sparse tensors from an observed data that is formed by the superposition of the two tensors. Our main contribution in this paper is deriving the truncated and smoothed schatten-p function to solve the robust tensor recovery problem using the Augmented Lagrangian Multiplier (ALM) optimization algorithm. Further, we compare the performance of our proposed algorithm against state-of-the-art robust tensor recovery algorithms using a variety of corrupted image and video signals. The experimental results show that our algorithm achieves an average of 2 dB performance improvement in PSNR; and at the same time it needs less number of iterations to converge when compared to state-of-the-art algorithms that tackle this problem.