Algoritmos para a redução de ruído Poisson e estimativa de parâmetros utilizando distâncias estocásticas

Abstract

Noise is present in all applications of digital imaging. Due to its stochastic nature, it is impossible to determine exact procedures to completely remove noise from the image. Thus, the target signal may be affected during the noise attenuation process due to the smoothing of fine details and image structures or by the introduction of visual artifacts. State-of-the-art denoising algorithms are effective in removing noise, however, they can cause image artifacts. Furthermore, most of these algorithms are formulated under the assumption of the additive noise model. The problem of denoising Poisson-corrupted images is still an open issue and represents a great challenge, since the noise in this model is signal dependent. This property implies that the parameter of the underlying stochastic model are also dependent of the noise-free image, which is unknown in practice. The objective of this research was to propose novel approaches to address the problem of parameter estimation and noise reduction of Poisson-corrupted images, based on the use of stochastic distances as measures of similarity between distributions of random variables, capable of preserving small details and fine image structures, while avoiding the introduction of visual artifacts. Two novel approaches were proposed: (1) Poisson Wiener filtering with non-local weighted parameter estimation in the spatial domain; and (2) Wiener filtering with non-local estimates in the Haar wavelet transform domain, using stochastic distances as similarity measures between patches of wavelet coefficients. In the spatial domain, stochastic distances between distributions of Poisson variables can be used to define weighted estimators of the first and second statistical moments of the signal and noise in order to compute the Wiener filter for Poisson-corrupted data. In the Haar wavelet domain, the wavelet coefficients can be modeled as Skellam variables. Closed-form solutions for the stochastic distances between Skellam distributions could not be obtained, therefore, the Gaussian distribution was proposed as an approximation. The detail sub-bands can be denoised in the Haar wavelet domain using a non-local algorithm based on stochastic distances as similarity measures between wavelet coefficients. Experimental results demonstrated that the proposed methods are competitive with related state-of-the-art algorithms. In general, among the proposed approaches, the technique based on the use of wavelets demonstrated a greater efficiency in the reduction of noise and preservation of details.