The Application Of Discrete Regularization Method To Reconstruction And Extrapolation Of Two Dimensional Band-limited Signal

The reconstruction and extrapolation of two dimensional band-limited signal have a variety of interesting applications in Fourier analysis, spectral estimation and image restoration. Some scholars have done much study on this problem, but they did it mostly on one dimensional problem and under the condition of noise-free. In this thesis, based on Tikhonov抯 regularization theory, we discuss, both in time domain and frequency domain, the discrete regularization method for reconstruction and extrapolation of two dimensional band-limited signal with noise. Some related techniques to realize the discrete regularization method, such as the influence of discrete method and the type of noise on the regularized solution, the choice of regularization parameter without knowing the error Level ?,and the optimization of regularization parameter, are also analyzed arid tested. In order to show the validity of the algorithm, an applied software which is fit to solve the reconstruction and extrapolation of two dimensional band-limited signal with noise is exploited under the environment of MATLAB. And a numerical test is given after analyzing each item. Theoretical analysis and numerical tests indicate that using Tikhonov抯 discrete regularization method to reconstruct and extrapolate the two dimensional band-limited signal has the advantages of high-efficiency, good numerical stability and restraining function against kinds of noise.