Image restoration by sparse 3D transform-domain collaborative filtering

We propose an image restoration technique exploiting regularized inversion and the recent block-matching and 3D filtering (BM3D) denoising filter. The BM3D employs a non-local modeling of images by collecting similar image patches in 3D arrays. The so-called collaborative filtering applied on such a 3D array is realized by transform- domain shrinkage. In this work, we propose an extension of the BM3D filter for colored noise, which we use in a two-step deblurring algorithm to improve the regularization after inversion in discrete Fourier domain. The first step of the algorithm is a regularized inversion using BM3D with collaborative hard-thresholding and the seconds step is a regularized Wiener inversion using BM3D with collaborative Wiener filtering. The experimental results show that the proposed technique is competitive with and in most cases outperforms the current best image restoration methods in terms of improvement in signal-to-noise ratio.