Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering

Abstract

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 2-D image fragments (e.g., blocks) into 3-D data arrays which we call "groups." Collaborative filtering is a special procedure developed to deal with these 3-D groups. We realize it using the three successive steps: 3-D transformation of a group, shrinkage of the transform spectrum, and inverse 3-D transformation. The result is a 3-D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered 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 significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient 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.

The Noise Clinic: a Blind Image Denoising Algorithm

“…Classic denoising algorithms such as BM3D (Dabov et al [7]), NL-means (Buades et al [2]), K-SVD (Mairal et al [17], [18]), Wiener filters applied on DCT (Yaroslavsky et al [26], [25]) or on wavelet transform (Donoho et al [24]) and the total variation minimization (Rudin et al [23]) achieve good results for moderate noise (σ ≤ 20). Yet for larger noise artifacts inherent to each method (and different for each method) start appearing.…”

Data Adaptive Dual Domain Denoising: a Method to

“…Current state-of-the-art denoising methods such as BM3D [5] and NL-Bayes [17] take advantage of both space-and transform-domain approaches. They group similar image patches and jointly denoise them by collaborative filtering on a transformed domain.…”

“…Among them, the most famous is BM3D [5], that denoises blocks of similar patches in the DCT domain. Since the patches are denoised together, this effectively allows to take into account their similarity.…”

Accelerating Monte Carlo Renderers by Ray Histogram Fusion

“…This is a very classic procedure in patch based image denoising [3,5,20]. Given a noisy patch P x centered at pixel x its denoised version V x is first computed by averaging all the patches being at a Chi-square distance smaller than κ:…”

“…Taking the mean as done in the preceding formula is the simplest possible aggregation method as proposed in other denoising algorithms [3,5].…”