Application Of Partial Differential Equation In Image Noise Reduction And Image Quality Assessment

Images are always corrupted by noise, such as Gaussian noise, impulse noise and speckle. In this paper we study on noise reduction method based on partial differential equation. Different noise reduction models are presented according to different noise types. Furthermore, a method of image quality assessment is proposed.Firstly, a nonlinear diffusion model to remove Gaussian noise is introduced. Contextual discontinuity information and gradient information are used to distinguish noise and image feature in this model. Experiments show that the combined information is more robust than gradient information. Additive operator splitting scheme is introduced in the numerical solution of the proposed diffusion model.Secondly, a two-stage method is proposed to remove impulse noise. In the first stage, we introduce an augmentation of ordered difference detector to detect pixels, which are likely corrupted by impulse noise. This detector makes accurate impulse noise detection by augmenting the difference between the center pixel's intensity value and its neighbors'intensity value of a localized window. In the second stage, noise pixels are restored using an iterative and adaptive median-based filter. This filter is adaptive according to the number of noise pixels in the filtering window. Thus, noise-free pixels are unaltered and noise pixels are filtered by the adaptive filter. Inspired by this idea we introduce an adaptive variational method. In the variation iteration process, an adaptive scheme of selecting neighbors of a noise candidate is proposed.And then we propose a despeckling method combing image decomposition and ridgelet transformation denoising for removing speckle in ultrasound images. A speckle-contaminated image is splitted into a cartoon component and a component containing texture and noise. After that, ridgelet analysis is used to analyze the component containing texture and noise. Noise removal image is obtained by adding the cartoon component and the inverse-ridgelet transformation component. Simulation results indicate that the proposed method is better than other speckle removal filters, in terms of suppressing speckle and preserving image details. At the last several image quality indices such as image sharpness, noise deviation, energy and mean gradient are introduced to evaluate image quality. SVM classifier is used to classify images into different quality classes.