Poisson NL-means

• Description of the filter
• Qualitative Evaluation of the Denoising Algorithms
• Quantitative Evaluation of the Denoising Algorithms
• Download the Poisson NL means filter New
• References

Description of the filter

• This work has been achieved by Charles Deledalle supervised by Florence Tupin and Loïc Denis. The aim was to adapt the Non-Local means (NL means) filter [1] to images sensed in low-light conditions. The Poisson NL means filter is based on the PPB filter [2] which ables to extend the NL means to deal with the Poisson distribution followed by the noise in such images. An efficient estimator has been designed, able to cope with the statistics and especially with the signal-dependent nature of such images.

• The Poisson NL means filter is an an extension of the non local (NL) [1] means for images damaged by Poisson noise. The proposed method is guided by the noisy image and a pre-filtered image and is adapted to the statistics of Poisson noise as recommended in [2]. The influence of both images can be tuned using two filtering parameters. These two parameters are automatically set to minimize an estimation of the mean square error (MSE). This selection uses an estimator of the MSE for NL means with Poisson noise and a Newton's method to find the optimal parameters in few iterations.

• A full description of Poisson NLmeans is available in the following report:
   

  Charles-Alban Deledalle, Florence Tupin and Loïc Denis,
  Poisson NL means: unsupervised non local means for Poisson noise,
  In the proceedings of ICIP, Hong Kong, September 2010 (pdf)

Qualitative Evaluation of the Denoising Algorithms

 

 

(a)

(b)

(c)

(a) Original images damaged by Poisson noise, denoised images obtained by (b) Poisson TV [3] and (c) the proposed Poisson NL means.

Image courtesy of Y. Tourneur for the image of a mitochondrion (Tetramethylrhodamine methyl ester, TMRM) sensed in low-light conditions by confocal fluorescence microscopy.

Quantitative Evaluation of the Denoising Algorithms

• The above table gives the signal-to-noise ratio (SNR) values obtained by different denoising methods on four 256 x 256 reference images damaged by synthetic Poisson noise with different degradation levels. A moving average filter is applied with a 9 x 9 disk kernel. We performed a Poisson based total-variation minimization (Poisson TV) as proposed in [3], the NL means and the Poisson NL means. For both NL means versions, the optimal parameters are obtained by risk minimization using a Newton's method. Poisson NL means provides the best performances.

Download the Poisson NL means filter

These pieces of Matlab softwares are based on C++ Mex-Functions compiled for Linux 32-bit, Linux 64-bit and Windows 32 bit. Matlab script exemples are given, they have been written for MATLAB with the Image Processing Toolbox (to load the images) and the Statistic Toolbox (to generate Poisson noise). Please refer to the REAME file for more details. For any comment, suggestion or question please contact Charles-Alban Deledalle at deledalle (at) telecom-paristech (dot) fr.

• Poisson NL means filter [download],

References

1. Buades, A. and Coll, B. and Morel, J.M.
   A Non-Local Algorithm for Image Denoising,
   IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, 2005
2. Charles-Alban Deledalle, Loïc Denis and Florence Tupin,
   Iterative Weighted Maximum Likelihood Denoising with Probabilistic Patch-Based Weights,
   IEEE Trans. on Image Processing, vol. 18, no. 12, pp. 2661-2672, December 2009 (download)
3. T. Le, R. Chartrand, and T. Asaki,
   A variational approach to reconstructing images corrupted by Poisson noise,
   J. of Math. Imaging and Vision, vol. 27, no. 3, pp. 257-263, 2007.