Research On Image Despeckling Models Based On Diffusion Equations And Deep Learning

Coherent imaging systems are widely used in the fields of environmental monitoring,military reconnaissance and digital medicine,among which typical representatives include SAR imaging system and the ultrasound imaging system.However,due to the special imaging mechanism,coherent imaging systems are easily contaminated by speckle noise.Therefore,removing speckle noise and improving image quality are of important research and application value.We use nonlinear diffusion equations and deep learning methods to establish image despeckling models,the main contents are as follows:To deal with the complex cause of speckle noise,we first investigate the characteristics of speckle noise from statistical information and simulation experiments.On this basis,we establish a nonlinear diffusion equation based despeckling framework,whose diffusion coefficients and source terms are constructed by theories of nonlinear diffusion equations and image processing.In order to remove speckle noise in SAR images,we propose a family of doubly degenerate diffusion equation based models,whose diffusion coefficient are composed of gray level indicator and structure detection operator,leading the diffusion behavior influenced by the gray value and gradient information.Furthermore,speckle noise in high gray value regions is suppressed and image features in low gray value regions are protected.To deal with the speckle noise removal problem in ultrasound images,we propose a variable exponential diffusion equation based model.In this model,the region indicator is introduced into the diffusion coefficient of the model,which can change diffusion types in different regions,and then effectively remove speckle noise in high gray value regions while protect or even enhance low contrast image features.For the theoretical properties of the doubly degenerate diffusion equation in the model,we prove the existence and the extremum principle of weak solutions.Since the equation may degenerate,we transform the original equation by an invertible transformation and obtain the regularization equation.Then we conduct a priori estimates of the weak solution and prove the existence by passing to the limit in the regularization equation.For the theoretical properties of variable exponent diffusion equation in the model,we prove the existence and uniqueness and the extreme value principle of the weak solution.Because of the variable exponent in the equation,we first reduce the nonlinearity of the original equation by replacing the function in the variable exponent.Then the Schauder fixed point theorem and the Gronwall inequality are used twice to obtain the existence and uniqueness of the weak solution to the original equation.For the numerical schemes and algorithm implementations of the models,we first design the traditional finite difference schemes by using partial differential equation numerical methods.Aiming at the low efficiency problem,we introduce the fast explicit diffusion scheme to accelerate original algorithms.In simulation experiments,we carry out despeckling experiments on different synthetic and real images.The synthetic image experiments give the qualitative and quantitative performance analysis of the proposed model while the real image experiments demonstrate the practical application value of the proposed model.Then we use the synthetic image experiments to discuss the effect of the gray level indicator and the region indicator,and further give the parameter selection methods.At last,we compare and analyze the denoising results of the proposed models and other classical models,and demonstrate that the proposed models outperform other models visually,quantitatively and efficiently.Despite of outstanding experimental perfermance,CNN based models in recent deep learning methods are generally lack of robustness and interpretability,while the denoised resluts of diffusion equation can be theoretically analyzed.By using the advantages with both,we propose a ultrasound image despeckling model based on diffusion equations and CNNs.From image decomposition theories and speckle noise characteristics,we first modify two deep CNN denoising models to estimate the noise and structure of the image,furthermore we propose a hybrid denoising model based on the deep CNN.To deal with the dependence on the noise variance,a hyperparameter of the above model,we analyze the properties of local mean values of diffusion equation model and propose a noise variance estimation algorithm,which is not sensitive to the noise variance.Finally,combining with the above two methods,we propose a CNN based despeckling model without the noise variance parameter,whose practical application value is enhanced.