This webpage presents the paper "Separating Signal from Noise using Patch Recurrence Across Scale" (CVPR 2013).
Paper [PDF]
Abstract
Recurrence of small clean image patches across different
scales of a natural image has been successfully used
for solving ill-posed problems in clean images (e.g., superresolution
from a single image). In this paper we show how
this multi-scale property can be extended to solve ill-posed
problems under noisy conditions, such as image denoising.
While clean patches are obscured by severe noise in the
original scale of a noisy image, noise levels drop dramatically
at coarser image scales. This allows for the unknown
hidden clean patches to “naturally emerge” in some coarser
scale of the noisy image. We further show that patch recurrence
across scales is strengthened when using directional
pyramids (that blur and subsample only in one direction).
Our statistical experiments show that for almost any noisy
image patch (more than 99%), there exists a “good” clean
version of itself at the same relative image coordinates in
some coarser scale of the image. This is a strong phenomenon
of noise-contaminated natural images, which can
serve as a strong prior for separating the signal from the
noise. Finally, incorporating this multi-scale prior into a
simple denoising algorithm yields state-of-the-art denoising
results.
Results shown on a few example images (mostly for high noise levels, where the visual differences between the methods are more visible).
All images are presented in the original size.
Results are compared to the following methods (using the implementatios on their websites):
EPLL-GMM [D. Zoran and Y. Weiss. From learning models of natural
image patches to whole image restoration. In ICCV, 2011]. LSSC [J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman.
Non-local sparse models for image restoration. In ICCV,2009]. BM3D [K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian. Image
denoising by sparse 3d transform-domain collaborative filtering. IEEE T-IP, 16(8), 2007].
To switch between images please use the colored buttons on the right.
Please note that the images are initialized to Noisy Images.
In order to see our results, please click the red button.
σ=35
[PSNR values (in dB): Ours=27.91, EPLL=27.82, LSSC=27.81, BM3D=27.87]
σ=55
[PSNR values (in dB): Ours=26.02, EPLL=25.9, LSSC=25.82, BM3D=25.9]
σ=45
[PSNR values (in dB): Ours=30.04, EPLL=29.16, LSSC=29.8, BM3D=30.19]
σ=45
[PSNR values (in dB): Ours=27.31, EPLL=27.15, LSSC=27.13, BM3D=27]
σ=45
[PSNR values (in dB): Ours=27.44, EPLL= 27.12, LSSC=27.25, BM3D=27.45]
σ=45
[PSNR values (in dB): Ours=26.38, EPLL= 26.24, LSSC=26.14, BM3D=26.09]
σ=45
[PSNR values (in dB): Ours=28.42, EPLL= 28.02, LSSC=28.23, BM3D=27.99]
σ=55
[PSNR values (in dB): Ours=24.52, EPLL= 24.51, LSSC=24.36, BM3D=24.5]
σ=45
[PSNR values (in dB): Ours=21.69, EPLL= 21.72, LSSC=21.68, BM3D=21.29]
σ=35
[PSNR values (in dB): Ours=26.86, EPLL= 26.59, LSSC=26.88, BM3D=26.86]
