Study On Variational Regularization Models And Algorithms With Application To Multichannel Image Restoration

Multichannel image restoration is a kind of ill-posed inverse problem,which is usually solved by the vectorial variational regularization methods.However,multichannel images are more complex than the gray ones.The methods directly generalized by the scale methods for gray images can not get good restoration results for multichannel images.In this paper,we analyze the characteristics of several kinds of multichannel images,and use the independent and related prior information of the multichannel images to study the vectorial variational regularization method of multichannel image restoration,including the establishment of the new vectorial variational regularization models,as well as the proof of the well-posedness;the design of the algorithm for the new models,as well as the convergence proof;and the applications to multichannel image restoration.The main works of this paper are:Firstly,a non-local vectorial total variational model for the multichannel images denoising is established,as well as the fixed point iterative algorithm and the alternating minimization algorithm designed.The classical multichannel image processing methods,such as the vectorial total variation model,can not preserve the detail characteristics of the image.In this paper,a novel non-local vectorial total variational model is proposed to conquer this weakness.The existence and uniqueness of the solution to this new model are proved in theory.Thus the well-posedness of the new model is guaranteed.For solving this model,the discrete scheme of new model is designed,and then a fixed point iterative algorithm is designed.The convergence of the fixed point iterative algorithm is proved in theory.Then an alternating minimization algorithm is designed to solve this model as well.This algorithm uses techniques of separation of variables and the penalty method.Then the original model of the minimization problem of the energy functional is decomposed into two sub-optimization problems,one of which is a simple L1 minimization problem solved by the threshold method;while the other is a simple L2 minimization problem solved by the calculus of variations,where the iterative scheme is simplified by the Taylor expansion approximation.The theoretical analysis proves that the algorithm converges faster than the fixed point iterative algorithm.A finite convergence for some variables and a q-linear convergence for the rest of the algorithm is proved in theory.Taking RGB color image denoising application as an example,the effectiveness and fast convergence of the algorithm is verified in the experiment.This non-local vectorial total variational model is applied to the multichannel SAR image restoration as well,including the multi-polarimetric SAR image and the multi-temporal SAR image.From the experimental results,the visual effect and evaluation index show that the proposed model is better than the classical vectorial total variational model.It is indicated that this kind of variational regularization method could despeckle the multichannel SAR images,which verifies there is additive noise in multichannel SAR images.Secondly,a variational regularization model for multi-polarimetric SAR image speckle reduction based on multiplicative-additive noise model is established,as well as the two level alternating minimization algorithm designed.According to the scattering matrix representation model of the multi-polarimetric SAR image,the amplitude coupling term of the arbitrarily two channels of the multi-polarimetric SAR image satisfies a multiplicativeadditive noise model.The distribution of the two kinds of noise is determined by the correlation coefficient of the two channels.This paper establishes a variational regularization model for denoising this kind of multiplicative-additive noise.The existence and uniqueness of the solution to this new model are proved in theory.A auxiliary variable is introduced into the observe model to decompose it into an additive noise model and a multiplicative noise model.Then the variational regularization model for restoring the two channel coupling term from the multiplicative-additive noise is obtained by using the MAP method.To solve this model,it is considered as a minimization model of the primal and the auxiliary variables.Then an alternating minimization algorithm is used to solve the problem.The sub-model with respect to the primal variable is non-convex,which is convexed by a variable substitution technique.Then according to the separation of variables,the penalty method,and the iterative reweighted least squares method,the convex model is transformed into a minimization model with respect to three variables,which is solved again by an alternating minimization algorithm.On the other hand,the sub-model with respect to the auxiliary variable is quadratic convex,which can be easily solved by the Newton iteration method.The convergence of this algorithm is proved in theory.In this paper,this new model is applied to the multi-polarimetric SAR image,and a fine despeckling result is obtained.Finally,a variational regularization model based on the intensity separation of the multi-temporal SAR image is established,as well as a fixed point algorithm and a differential iterative algorithm is designed.The channels of the multi-temporal SAR image have strong scattering target distribution in different positions.Focus on this,this paper propose the intensity segregation representation model for the multi-temporal SAR image.Furthermore,a variational regularization model based on the intensity separation of the multi-temporal SAR image is established.This new model is composed of two sub-models.One is a variational regularization model for the intensity component of the image,where the noise is assumed to be multiplicative,and the regularization term is the total variation.Then a fixed point iterative algorithm is used to solve the Euler-Lagrangian equation of this sub-model.The other sub-model is the vectorial variational regularization model for the vector component of the image,which is obtained by the assumption that the noise is multiplicative noise,and the vectorial total variation norm of the vector defined on the unit sphere is obtained.A partial differential equation method is used to get the differential iterative algorithm to solve the Euler-Lagrangian equation of this submodel.In this paper,this intensity separation model is applied to the multi-temporal SAR image despeckling.The strong scattering target is well preserved while the good efficient of despeckling is obtained.