Image Denoising And Moving Object Segmentation Based On Low-rank Tensor Recovery

Recently,the model of robust principal component analysis ?RPCA?has been successfully used in the filed of image denoising , image restoration, image classification and moving object segmentation. The main idea is that a matrix/tensor constructed by a series of similar images with noise can be decomposed into a low rank matrix/tensor ?i.e., pure images that we need to recover? and a sparse matrix/tensor ?i.e., sparse noises in images?. In view of the non-convex and non-continuity of rank function and l₀ norm, the common technique is to relax the rank function and l₀ norm to the nuclear norm and l1 norm respectively, thus the original problem can be degraded as a convex optimization problem. However, to guarantee that the solution of the relaxed convex problem is close to the solution of the original problem, strong incoherence conditions should be imposed. On the other hand, the similar images should be well aligned to ensure that the tensor of the images stack to have low-rank. But precise alignments are not always guaranteed for most practical data, and even small misalignments will break the low-rank structure of the data. To address these issues, this paper proposes a non-convex approximation model to the original problem, i.e.,by using Schatten-p norm and lp norm to relax the rank function and l₀ norm respectively, which requires much weaker incoherence conditions to guarantee a successful recovery. At the same time, we adopt a set of transformations which act on the images.By solving the optimal transformations, the strict alignments of the images are achieved in the denosing process. Furthermore, we propose an efficient algorithm based on the method of Alternating Direction Method of Multipliers ?ADMM? for the non-convex optimization problem. The extensive experiments on the artificial datasets and real image datasets have shown the superiority of our algorithm in image alignment and denoising. At the same time, we apply our model to the field of moving object segmentation. The experimental results show that our model and algorithm have high efficiency and great potential in the field of moving object segmentation.