A Fast Extrapolation Algorithm For One-Dimensional Band-Limited Signal Without Knowing Error Level

The extrapolation of one-dimensional band-limited signal, as a typical ill-posed problem, has a variety of interesting applications in Fourier analysis, spectral estimation and image restoration. Some scholars have done much study on this problem, but little attention has been paid to stable restoration technique under the case without knowing error level of input data, and this is not agreed with the new development of regularization theory.In this thesis, we discuss related theoretic and technical problems of applying Tikhonov Regularization to the signal restoration without knowing the error level. The emphasis is focused on the application of some selection strategies of regularization parameter, including Engl criterion and L-curve criterion so on, to reconstruct the one-dimensional band-limited signal under the condition without knowing the error level in a stable way. Related algorithms with its fast numerical implementation are designed.The theoretic analysis and numerical tests have shown that the method proposed in this paper is stable and highly effective.