Total Variation Restoration of Images Corrupted by Poisson Noise with Iterated Conditional Expectations
Interpreting the celebrated Rudin-Osher-Fatemi (ROF) model in a Bayesian framework has led to interesting new variants for Total Variation image denoising in the last decade. The Posterior Mean variant avoids the so-called staircasing artifact of the ROF model but is computationally very expensive. Another recent variant, called TV-ICE (for Iterated Conditional Expectation), delivers very similar images but uses a much faster fixed-point algorithm. In the present work, we consider the TV-ICE approach in the case of a Poisson noise model. We derive an explicit form of the recursion operator, and show linear convergence of the algorithm, as well as the absence of staircasing effect. We also provide a numerical algorithm that carefully handles precision and numerical overflow issues, and show experiments that illustrate the interest of this Poisson TV-ICE variant.
KeywordsPoisson noise removal Image denoising Total variation Posterior mean Marginal conditional mean Staircasing effect Fixed-point algorithm Incomplete gamma function
Unable to display preview. Download preview PDF.
- 2.Caselles, V., Chambolle, A., Novaga, M.: Total variation in imaging. In: Handbook of Mathematical Methods in Imaging, pp. 1016–1057. Springer, New York (2011)Google Scholar
- 8.Louchet, C., Moisan, L.: Total variation denoising using posterior expectation. In: Proc, European Signal Processing Conf (2008)Google Scholar
- 10.Louchet, C., Moisan, L.: Total variation denoising using iterated conditional expectation. In: Proc, European Signal Processing Conf (2014)Google Scholar
- 12.Deledalle, C., Tupin, F., Denis, L.: Poisson NL means: Unsupervised non local means for poisson noise. In: Proc. Int. Conf. Imag. Processing, pp. 801–804 (2010)Google Scholar
- 13.Schmidt, K.D.: On the covariance of monotone functions of a random variable. Unpublished note, University of Dresden (2003)Google Scholar
- 15.NIST Digital Library of Mathematical Functions (2014). http://dlmf.nist.gov/ (release 1.0.9 of August 29, 2014)
- 17.Jones, W.B., Thron, W.J.: Continued Fractions: Analytic Theory and Applications. Encyclopedia of Mathematics and its Applications, vol. 11. Addison-Wesley Publishing Co., Reading, MA (1980)Google Scholar
- 18.Numerical recipes: The art of scientific computing, 2nd edn. Cambridge University (2007)Google Scholar
- 19.Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Courier Dover Publications no. 55 (1972)Google Scholar