A Class Of Diffusion Equations With Smooth Solution To Remove Multiplicative Noise

As an important medium,the image has become a necessary source of information.The noise of the image is often the hardest problem to cope with among the image processing.Noise often influences the signal in additive,multiplicative and mixed form.This paper considers one multiplicative noise called speckle noise,which is more difficult to remove than additive noise due to the characteristics of multiplicative noise.It usually appears in the coherent imaging system.So far,the main research methods on speckle noise removal are variational,partial differential equations methods,Fourier transforms and wavelet methods and statistical methods.This paper presents a new diffusion model to eliminate speckle noise.The main idea is to construct the diffusion coefficient based on the gray scale value and the image gradient,and select two parameters to control the influence of the gray value and the gradient respectively.In addition to,the Gaussian function is also introduced in the diffusion coefficient.It not only makes the model has a complete solution theory,but also improves the experimental results in the removal of multiplicative noise.Then,the theory of the model solution is analyzed,including the existence,uniqueness and regularity of the solution.The maximum principle,invariance of the mean and asymptotic property of the solution are also proved.Unlike the traditional variational denoising model assuming that the image belongs to BV space,we demonstrate that the proposed diffusion model is C?.The focus of this paper is that,compared to the multiplicative variational denoising model,the solution is such smooth and offers many advantages in dealing with high-level multiplicative noise.At the expense of losing some small boundary information,the tradeoff between denoising and boundary protection enables our model to have better experimental results than the existing variational denoising models.We choose panr and mae to verify the effect of the model.Four different numerical schemes are used to realize the discretization of the model.They are classical difference method and three fast algorithms,fast explicit diffusion(FED),additive operator splittings(AOS)and krylov subspace spectral method(KSS).Comparison of four kinds of discrete numerical method and the experimental results are given.The KSS method represents a new feasible numerical method between explicit and implicit computational efficiency,we demonstrate its potential in multiplicative noise removal by numerical experiments.Experimental results show that KSS is no less efficient than the other two fast algorithms in terms of efficiency and noise reduction.The experimental results of the model are compared with other multiplicative denoising variational models like AA and SO.It is proved that the new model with the smooth solution has the advantage of removing the multiplicative noise compared with the multiplicative variational model that assume image space as BV space.Comparing to other diffusion equations for the multiplicative noise removal model,the denoising level of the new model is also significantly improved.