Arithmetic Design And Realization In Image Process Based On Regularization Model

The most effective methods that can tackle the ill-posed problems are the so-called regularization methods during the inverse process. This thesis introduces and analyses in detail the research and application of regularization in image process, the main contributions and creativities are listed as follows:Firstly, this paper researches the solution of linear ill-posed equations using the idea during the inverse process, then presents a decomposition method that split the solution space into a Krylov subspace by an accelerated GMRES method and an auxiliary subspace that can be chosen to help represent pertinent features of the solution. Numerical results show the reliability and efficiency of the new method: With the same precision, the CPU time is only one fifths of that of the GMRES method; and with the same iterative steps, the precision is higher, for instance, the MSE is three fifths of that of the GMRES method on average. The method is applied to solve the problems of regularized image restoration. Simulation results show that the Signal to Noise Ratio (SNR) is higher than the CG method and the vision effect are also improved.Secondly, this paper introduces the regularization method for SAR image superresolution in frequency domain, complex image domain and power image domain. Based on point scattering model, mathematical theories are applied to design new solving algorithms and many methods including Gauss elimination method, conjugate gradient algorithm, Newton quadratic iterative method are combined to solve the regularization model for SAR image superesolution. The convergence and complexity of algorithms are investigated.