Color Image Restoration Using Sub-Image Based Low-Rank Tensor Completion

Many restoration methods use the low-rank constraint of high-dimensional image signals to recover corrupted images. These signals are usually represented by tensors, which can maintain their inherent relevance. The image of this simple tensor presentation has a certain low-rank property, but does not have a strong low-rank property. In order to enhance the low-rank property, we propose a novel method called sub-image based low-rank tensor completion (SLRTC) for image restoration. We first sample a color image to obtain sub-images, and adopt these sub-images instead of the original single image to form a tensor. Then we conduct the mode permutation on this tensor. Next, we exploit the tensor nuclear norm defined based on the tensor-singular value decomposition (t-SVD) to build the low-rank completion model. Finally, we perform the tensor-singular value thresholding (t-SVT) based the standard alternating direction method of multipliers (ADMM) algorithm to solve the aforementioned model. Experimental results have shown that compared with the state-of-the-art tensor completion techniques, the proposed method can provide superior results in terms of objective and subjective assessment.