Multiplicative Noise Image To Restore The Variational Method

Image denoising is a key point in the fields of image Processing.Images are often corrupted in acquisition and transmission by various kind of noise.The noise can be divided into additive noise and multiplicative noise for two major categories by their effect.To multiplicative noise,a natural way to turn a multiplicative model into an additive one is to use the logarithm transform.Nevertheless,as can be seen on the numerical results,such a straightforward method does not lead satisfactory results.It is necessary for the multiplicative noise in different ways,otherwise it will be difficult to obtain satisfactory results.This paper mainly studies multiplicative noise for image denoising and enhancement of the variational method.This dissertation mainly includes the following contents:1.The recent developments and application fields of image denoise are introduced,which includes the multiplicative noise model of the world.And then the theoretical basis for image denoising is introduced,including the characteristics of digital images,the noise classification and the noise model, and image quality evaluation.2.The theory and development of nonlinear diffusion are introduced;The typical PM model is specifically introduced,and its advantages and disadvantages are analyzed.And then two improved models are introduced,which include the regularized PM model and the directional diffusion model,and their characteristics are analyzed.3.The denoise model based on TV method and the relational theory are introduced,and its advantage and disadvantage are analyzed.And then the data fidelity term of multiplicative noise is analyzed,and be compare with addivtive one.Another side,the multiplicative denoising model based on TV method is introduced.The differences and characteristics of the multiplicative data fidelity term and the additive data fidelity term are analyzed and verified by one-dimensional signals.The experimental result show that the multiplicative data fidelity term is more effective than the additive one to multiplicative noise,and the multiplicative data fidelity term is forward nonlinear diffusion,while the addative one is backward linear diffusion.4.Based on the above principle,TV method of removing multiplicative noise is improved by adding foregoing typical model.So,PM model of multiplicative noise,regularized PM model of multiplicative noise and directional diffusion model of multiplicative noise are proposed.These model of image denoising proposed are compared and analysed by experiment.The experimental results show that,for the image only contained edge and zero gradient,the PSNR of PM model of multiplicative noise is the highest;However,for the normal image the PSNR of regularized PM model of multiplicative noise is the highest and the edge of directional diffusion model of multiplicative noise is more smooth.5.The staircase effect is a main defect of TV model.This dissertation introduces the reason of staircase effect.The experimental result show that the staircase effect of TV model based on multiplicative fidelity term is different from additive one,but still exists.To avoid staircase effect,several typical Laplacian model are introduced.Especially a hybrid variational image diffusion model using gradient and Laplacian is introduced.And then the characteristics of these model are analyzed.TV method of removing multiplicative noise is improved by adding Laplacian.So the Laplacian multiplicative model are proposed.The experiment results of one-dimensional signals show that the Laplacian multiplicative model is forward diffusion in the edges and is backward diffusion in the region near edges,moreover it can avoid staircase effect.Based on these works,this thesis present a hybrid variational image diffusion model using gradient and Laplacian for multiplicative noise.To the numerical schemes,in order to avoid the shortcomings of insufficient stability of explicit scheme,a Gauss-sadder semi-implicit scheme is adopted.At last,the experimental result show that this model can avoid staircase effect during removing noise with edge preserving or enhancement,and it is more efficient than the foregoing regularized PM model of multiplicative noise.