Research On PDE-based And TV-based Image Denoising And Applications In The Removal Of Several Types Of Noise

Partial differential equation (PDE) based and total variation (TV) based imagedenoising techniques are very useful and powerful tool in the field of imageprocessing. Various PDE models are widely applied nowadays in medicine, remotesensing, astronomy, biology, material science and so on. PDE-based denoisingtechniques play a very important role and attract many interests from researchers withtheir unique advantage and prosperous application. As TV-based methods are muchrelated to PDE, they also attract a lot of interested people. Many PDE modelsconcentrate on the removal of non-impulse noise, such as Gaussian noise, and there isvery little work on the suppression of impulse noise with PDE-based methods. In thisdissertation, we focus mainly on the PDE-based methods for image denoising,including the removal of random-value impulse noise, pepper-and-salt noise,superimposed noise and speckle noise, with their fast numerical solution. Thecontents include the following:1. We propose a fuzzy weighted non-local means filter for improving thenon-local means algorithm, a classical mean-type filter, for the removal of the impulsenoise and the mixed Gaussian and random-valued impulse noise. We introduce a newfuzzy weighting function, which can shut off the impulsive weight effectively, to thenon-local means. According to the new weighting function, the more a pixel iscorrupted, the less it is exploited to reconstruct image information. Experiments showthat the performances of the new filter are surprisingly satisfactory in terms of bothvisual quality and quantitative measurement.2. We derive the general way to reduce impulse noise for the PDE diffusion. Thebasic idea is that we attenuate impulses and simultaneously preserve image featuressuch as edges and details by selective diffusion and selective fidelity. Especially forthe random-valued impulse noise we introduce a new notion of ENI that issignificantly different for edge pixels, noisy pixels, and interior pixels. We redefinethe controlling speed function and the controlling fidelity function to depend on ENI.According to the new controlling functions, the diffusion and fidelity process at edgepixels, noisy pixels, and interior pixels can be selectively carried out. Furthermore, aclass of second-order improved and edge-preserving PDE denoising models based onthe two new controlling functions testifies that the proposed method can deal with random-valued impulse noise reliably.3. We also introduce the noise detection process for the PDE methods to removeimpulses. To reduce random-valued impulse and other superimposed artifacts whichhave a large or long size, we derive a homogeneous amount based filter. The filteridentifies impulses without local window restriction which is very different fromother detection methods, and can recognize and remove impulses and othersuperimposed artifacts efficiently. Combining a more efficient salt-and-pepperdetector with TV inpainting method, we demonstrate the hybrid method is verysatisfactory in noise reduction and edge preservation.4. For the removal of speckle noise, we also propose an adaptive PDE model. Anew statistic is introduced to partition the noisy image into blocks based on imageedges, and then the oriented regularization is applied within the blocks which containimage details and edges, while non-oriented regularization within the blocks whichonly has smooth regions. The experiments on the synthetic aperture radar imagesshow the hybrid PDE model can smooth noise, meanwhile, preserve and enhanceimage textures and edges satisfactorily.5. We extend the model of TV regularization to accelerate the proposedPDE-based filters, and also form a unified TV-based model with its fast numericalalgorithm is proposed. The iterative reweighted norm approach can solve the extendedmodel fast. Experiments show that the extended model is feasible and the numericalsolution is faster than that of the time matching method.