Image denoising by sparse 3D transform-domain collaborative ltering

—We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g. blocks) into 3D data arrays which we call "groups". Collaborative ltering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D estimate that consists of the jointly ltered grouped image blocks. By attenuating the noise, the collaborative ltering reveals even the nest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block. The ltered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A signi cant improvement is obtained by a specially developed collaborative Wiener ltering. An algorithm based on this novel denoising strategy and its ef cient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality. Index Terms—image denoising, sparsity, adaptive grouping, block-matching, 3D transform shrinkage.