G. Maino and G.L. Foresti (Eds.): ICIAP 2011, Part I, LNCS 6978, pp. 534–543, 2011. © Springer-Verlag Berlin Heidelberg 2011 Optimal Choice of Regularization Parameter in Image Denoising Mirko Lucchese, Iuri Frosio, and N. Alberto Borghese Applied Intelligent System Laboratory Computer Science Dept., University of Milan Via Comelico 39/41 – 20135 Milan Italy {mirko.lucchese,iuri.frosio,alberto.borghese}@unimi.it Abstract. The Bayesian approach applied to image denoising gives rise to a regularization problem. Total variation regularizers have been introduced with the motivation of being edge preserving. However we show here that this may not always be the best choice in images with low/medium frequency content like digital radiographs. We also draw the attention on the metric used to evaluate the distance between two images and how this can influence the choice of the regularization parameter. Lastly, we show that hyper-surface regularization parameter has little effect on the filtering quality. Keywords: Denoising, Total Variation Regularization, Bayesian Filtering, Digital Radiography. 1 Introduction Poisson data-noise models naturally arise in image processing where CCD cameras are often used to measure image luminance counting the number of incident photons. Photon counting process is known to have a measurement error that is modeled by a Poisson distribution [1]. Radiographic imaging, where the number of counted photons is low (e.g. a maximum count of about 10,000 photons per pixel in panoramic radiographies [2]) is one of the domains in which Poisson noise model has been largely adopted. The characteristics of this kind of noise can be taken into account inside the Bayesian filtering framework, developing an adequate likelihood function which is, apart from a constant term, equivalent to the Kullback–Leibler (KL) divergence [3, 4]. Assuming the a-priori distribution of the solution image of Gibbs type and considering the negative logarithm of the a-posteriori distribution, the estimate problem is equivalent to a regularization problem [5, 6]. The resulting cost function, J(.), is a weighted sum of a negative log-likelihood (data-fit, J L (.)) and a regularization term (associated to the a-priori knowledge on the solution, J R (.)). Tikhonov-like (quadratic) regularization often leads to over-smoothed images and Total Variation (TV) regularizers, proposed by [7] to better preserve edges, are nowadays widely adopted. As the resulting cost-function is non-linear, iterative optimization algorithms have been developed to determine the solution [3, 8]. To get