Non-local Image Denoising by Using Bayesian Low-rank Tensor Factorization on High-order Patches

Removing the noise from an image is vitally important in many real-world computer vision applications. One of the most effective method is block matching collaborative filtering, which employs low-rank approximation to the group of similar patches gathered by searching from the noisy image. However, the main drawback of this method is that the standard deviation of noises within the image is assumed to be known in advance, which is impossible for many real applications. In this paper, we propose a non-local filtering method by using the low-rank tensor decomposition method. For tensor decomposition, we choose CP model as the underlying low-rank approximation. Since we assume the noise variance is unknown and need to be learned from data itself, we employ the Bayesian CP factorization that can learn CP-rank as well as noise variance solely from the observed noisy tensor data, The experimental results on image and MRI denoising demonstrate the superiorities of our method in terms of flexibility and performance, as compared to other tensor-based denoising methods