Image Denoising Using Modified Cumulative Distribution Function in the Wavelet Domain

In this paper, we have presented two modified Cumulative Distribution Functions (CDFs) for de-noising various types of images such as MRI and hyperspectral remote sensing. The proposed techniques have been derived from standard CDF. In the first approach, we have introduced a nonlinear modified CDF in the interval of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$[- t,t]$</tex> and an identity function behind the interval. In the second method, we utilized an improved version of modified CDF in the interval combined with a nonlinear function to generate a smooth transition from 0 to 1, creating gradual converges to the identity function right behind the interval of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$[- t,t]$</tex>. These threshold functions have been introduced to improve the results of conventional noise removal methods. Although previous de-noising approaches provide good results, they fail to preserve edges and may blur parts of the images. We have compared the performance analysis of proposed methods with some other approaches such as soft threshold, NeighShrink, and Bayes in terms of Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE). Our results have shown that the proposed improved CDF achieves up to 2.01 dB improvement over adaptive differential evolution (JADE) algorithm for removing Additive White Gaussian Noise (AWGN) for standard deviation of 10.