Study On Image Denoising Models Based On MAP Estimation, Variation And PDE

Digital image processing technology is widely used in scientific research, socialproduction and life. Digital image processing is a new developing cross disciplinecombined with engineering, computer science, information science, statistics,physics, chemistry, biology, medical science and social science. There are threeapproaches to study image processing at present, i.e., stochastic modeling, wavelettheory and partial differential equation method. In this thesis, denoising methodsbased on maximum a posterior estimation, variation and partial differential equationmethods are mainly studied. Three kinds of noise are discussed: additive Gauss noise,multiplicative noise and signal correlation Poisson noise.Main works of the thesis are listed as follow.1. Image denoising based on total variation (TV) model may cause staircaseeffect. The method that coupling gradient fidelity term can effectively restrainstaircase effect. However，it tends to blur edges because of the usage of gradientfidelity term. To overcome the above weakness, a method to detect smooth regions ofan image is discussed, and three denoising methods with gradient fidelity term on thedetected smoothing regions are proposed. Numerical experiments show that threenew denoising methods have better denoising results while overcoming staircaseeffect and preserving the edges.2. TV-Stokes method is a two-step model, which is based on total variationminimization and the geometric information, to recover image. A smoothed directionfield is obtained by using total variation to the noisy direction field; then thedenoised image is reconstructed by fitting the smoothed orientation field and thenoisy image. However, the derivation operation that to obtain the noise directionfield can increase the intensity of the noise. In this thesis the noised image issmoothed directly by anisotropic diffusion, and then orientation field of thesmoothed image is calculated. Numerical experimental results show that theapproach is effective. Another improved method to TV-Stokes method is considerd.The noised image is smoothed by anisotropic diffusion and then structure tensor fieldis calculated. The denoised image is reconstructed through fitting the structure tensorfield and the noised image. The proposed method overcomes shortages of theclassical anisotropic diffusion method. Numerical experiments show that the proposed method can remove noise effectively while preserving structures andrestraining staircase effect.3. A novel two-step image denosing method using wavelet iterative regularizationto residual is proposed. Firstly, a smoothed image is obtained through an anisotropicdiffusion. By using the nature of Bregman iterative regularization that structure isdirectly extracted, the wavelet iterative regularization to residual is applied. Thedenoised image is obtained by adding the result that the second step back to thesmoothed image obtained in the first step. Numerical experiments results show thatthe new method can enhance denoising result while weakening the staircase effectand pseudo-Gibbs phenomenon.4. Multiplicative noise removal is an important research topic on imageprocessing. Under the assumption that the multiplicative noise follows a Gammadistribution, an iteratively reweighted anisotropic-TV based model is proposed. Theregularization term is the weighted anisotropic-TV regularizer. The weight functionincorporated in the regularization term is derived from the expectation maximization(EM) principle. The merits of this model are the preservation of edges and therestraint of staircase effect while removing the noise. Then an iteratively reweightedHessian Frobenius norm based regularization model is proposed, which is anextension of iteratively reweighted TV model. A primal-dual algorithm is designed toiteratively reweighted TV regularization model and iteratively reweighted Hessianregularization model. Numerical experimental results show the better performance ofthe two models and algorithms.5. Poissonian image denoising is another important research subject that appearedin photon imaging. An iteratively reweighted total generalized variation (TGV) basedPoisson noise removal model is presented under the assumption that each pixel ofnoisy image follows a Poisson distribution. The weight function incorporated in theTGV regularization term is derived from the EM principle. A projection algorithm isdesigned to the new model, the correction parameters that appeared in classiciteratively reweighted method is avoided, which is an improvement of the classiciteratively reweighted algorithm. Numerical experimental results show the betterperformance of our model in removing noise while preserving edges and eliminatingstaircase efect.