Likelihood Estimation and Wavelet Transformation Based Optimization for Minimization of Noisy Pixels

Abstract

In recent times the statistical computation techniques are gaining a lot of interest for analyzing the behavior of various mathematical distributions. This paper derives the likelihood distribution of image priors which has been further used to denoise the image. This paper aims to maximize the likelihood estimation of the parameters of interest i.e. prior and posterior estimation. We have proposed a prior-based distribution model which has been applied to additive, multiplicative and mixed noise cases. The various estimation parameters such as statistical variance and mean parameters have been used to evaluate the maximum likelihood of image priors for these noise models. Later, we have used an optimization technique based on the likelihood to reconstruct noise-free images efficiently. This paper uses conditional likelihood and wavelet transformation-based minimization techniques to minimize the noise in the pixels and a final denoised image is recovered. The conditional likelihood of the image has been optimized using pixel-based minimization w.r.t. the wavelet transformation coefficients. The simulation and analytical results have also been presented for the different noise cases.

Keywords

• Gamma
• Gaussian and Poisson distributions
• image priors
• log-likelihood estimator
• normalization and minimization
• noise models