Parameters Estimate Of Some Distributed Parameter Systems And Research On Image Analyses And Application

Parameters estimation of the distributed parameter system and digital image restoration are representative Mathematical and Physics inverse problem, and they are explored in the first two chapters of this paper. Chapter 1 discusses multiple parameters simultaneous estimation of a two-dimensional distributed parameter system; First, the distributed parameter system is transformed by applying a Laplace transform; Then by defining the objective function combined with the principle of optimal control, the problem of parameter estimate is converted into the problem of optimal control. The well-posedness of the objective function is proved, so discontinuous parameters can be identified effectively. This method deals with the estimating parameters as a whole, so it reduces the dimension of the problem, furthermore, since the construction and interior structure of the mathematical model are not involved, this method can be used to solve some more complicated systems; At last, numerical simulated example is offered by the paper, which shows the feasibility of the proposed approach.Because the deconvolution of the digital image restoration is usually ill-posed, the regularization methods are usually used to assure the quality of the restored image. In chapter 2, the paper considers about applying the regularized method with a variance uniformization constraint to image restoration, therefore we discusses the relation between the variance of the restored image and the singular value of the discrete matrix of the blur operator in detail, and theoretically proves the well-posedness of the regularized method with a variance uniformization constraint. The paper does experiment on the image restoration by using the regularized method with a variance uniformization constraint, and the results show that this method outgoes the Tikhonov regularized method.The Heat Flow Cryptosystem based on Pseudo-parabolic Partial Differential Equation is an unconventional new cryptosystem. This cryptosystem has lots of useful conclusions, but there well be many problems needed to be solved if it is being put into practice. In chapter 3, the paper discusses the fast realization of encryption and decryption which based on the two-dimensional Pseudo-parabolic Partial Differential Equation. First, the paper proves the well-posedness of the encryption and decryption problems, which provides theoretical bases for experiments of encryption and decryption; Then presents a fast iterative algorithm, which is proposed based on the special sparse structure of the coefficient matrix of the two-dimensional C-N difference scheme, and successfully experiments on images encryption and decryption; At the end, the security of the methods of images encryption and decryption based on the two-dimensional Pseudo -parabolic Partial Differential Equation is experimented and discussed particularly.