TAMPERE UNIVERSITY OF TECHNOLOGY Department of Signal Processing

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 2D image fragments (e.g. blocks) into 3D data arrays which we call "groups".

Collaborative filtering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of 3D group, shrinkage of transform spectrum, and inverse 3D transformation. The result is a 3D 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.

We develop algorithms based on this novel denoising strategy. The experimental results presented here demonstrate that the developed methods achieve state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

Software

Results

¹ The noisy images/videos were created by adding zero-mean white Gaussian noise with the following MATLAB commands:

randn('seed', 0);
noisy = original + sigma*randn(size(original));

People

Aram Danielyan
Kostadin Dabov
Alessandro Foi
Vladimir Katkovnik
Karen Egiazarian

Related work

Compressed Sensing Image Reconstruction, Image Upsampling, and Image/Video Super-Resolution via Recursive Spatially Adaptive Filtering

A preliminary version of BM3D using exclusively the DFT

Shape-Adaptive Transforms Filtering (Pointwise SA-DCT algorithm).

Publications

Katkovnik, V., A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising”, Int. J. Computer Vision, vol. 86, no. 1, pp. 1-32, January 2010. doi:10.1007/s11263-009-0272-7

V. Katkovnik and K. Egiazarian, “Nonlocal image deblurring: variational formulation with nonlocal collaborative l₀-norm imaging”, Proc. Int. Workshop on Local and Non-Local Approx. in Image Process., LNLA 2009, pp. 46-55, Tuusula, Finland, August 2009.

A. Danielyan and A. Foi, “Noise variance estimation in nonlocal transform domain”, Proc. Int. Workshop on Local and Non-Local Approx. in Image Process., LNLA 2009, Tuusula, Finland, pp. 41-45, August 2009.

A. Danielyan, M. Vehviläinen, A. Foi, V. Katkovnik, and K. Egiazarian, “Cross-color BM3D filtering of noisy raw data”, Proc. Int. Workshop on Local and Non-Local Approx. in Image Process., LNLA 2009, Tuusula, Finland, pp. 125-129, August 2009.

V. Katkovnik “Nonlocal collaborative l₀-norm prior for image denoising”, in Festschrift in Honor of Jaakko Astola on the Occasion of his 60th Birthday, TICSP Series 47, pp. 305-319, 2009.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “BM3D Image Denoising with Shape-Adaptive Principal Component Analysis”, Proc. Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS'09), Saint-Malo, France, April 2009. Poster

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “A nonlocal and shape-adaptive transform-domain collaborative filtering”, Proc. Int. Workshop on Local and Non-Local Approx. in Image Process., LNLA 2008, Lausanne, Switzerland, August 2008.

V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “Nonparametric regression in imaging: from local kernel to multiple-model nonlocal collaborative filtering”, Proc. Int. Workshop on Local and Non-Local Approx. in Image Process., LNLA 2008, Lausanne, Switzerland, August 2008.

G. Boracchi and A. Foi, “Multiframe raw-data denoising based on block-matching and 3-D filtering for low-light imaging and stabilization”, Proc. Int. Workshop on Local and Non-Local Approx. in Image Process., LNLA 2008, Lausanne, Switzerland, August 2008.

A. Danielyan, A. Foi, V. Katkovnik, and K. Egiazarian, “Image and video super-resolution via spatially adaptive block-matching filtering”, Proc. Int. Workshop on Local and Non-Local Approx. in Image Process., LNLA 2008, Lausanne, Switzerland, August 2008.

A. Danielyan, A. Foi, V. Katkovnik, and K. Egiazarian, “Image Upsampling Via Spatially Adaptive Block-Matching Filtering”, Proc. 16th European Signal Process. Conf., EUSIPCO 2008, Lausanne, Switzerland, August 2008.

K. Dabov, A. Foi, and K. Egiazarian, “Image restoration by sparse 3D transform-domain collaborative filtering,” Proc. SPIE Electronic Imaging '08, no. 6812-07, San Jose, California, USA, January 2008.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Joint image sharpening and denoising by 3D transform-domain collaborative filtering,” Proc. 2007 Int. TICSP Workshop Spectral Meth. Multirate Signal Process., SMMSP 2007, Moscow, Russia, September 2007.

K. Dabov, A. Foi, and K. Egiazarian, “Video denoising by sparse 3D transform-domain collaborative filtering,” Proc. 15th European Signal Processing Conference, EUSIPCO 2007, Poznan, Poland, September 2007.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Color image denoising via sparse 3D collaborative filtering with grouping constraint in luminance-chrominance space,” Proc. IEEE Int. Conf. Image Process., ICIP 2007, San Antonio, TX, USA, September 2007.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Trans. Image Process., vol. 16, no. 8, pp. 2080-2095, August 2007.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” Proc. SPIE Electronic Imaging '06, no. 6064A-30, San Jose, California, USA, January 2006.