Study On Wavelet Frame Based Poisson Image Denoising Methods

In recent years, image denoising from Poisson noisy data has drawn much atten-tion in the research field of image processing as well as in application areas such as astronomical image processing and medical image restoration. Multi-resolution analy-sis (MRA) has become a landmark in the literature of wavelet had play an important role in signal processing. The denoising model based on MRA is different from those base on total variation model in regularization term where the former use the wavelet decomposition operator while the latter use the gradient operator.Based on Bayesian theory, KL divergence is used as the fidelity term for Poisson noisy data.Several numerical algorithms are compared for solving based on (?){(?){[(Hx+ b)i]-yi log (Hx+b)i}+β|Wx|1}, it is the so-called analysis based approach. Popular existent analysis based approach include EM-framelet method, reweighted l2 method and KL+Split Bregman method. Moreover, the preconditioned alternating proximal algorithm is adapted to tight frame based analysis model where the gradient operator in the regularity term were substituted by framelet decomposition operator.The goal of this paper is to improve the image denoising from Poisson noise data by proposing modification of the regularity term and fidelity term in existent algo-rithms. The proposed methods improve the speed and efficiency of noise processing to guarantee the output of the original image. The convergence of the different algorithms are compared in term of decreasing of objective function and PSNR values, for which measures the improvement of image quality.