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Description
(Text)
In this paper a regularized spectral estimation formula and a regularized iterative algorithm for band-limited extrapolation are presented. The ill-posedness of the problem is taken into account. First a Fredholm equation is regularized. Then it is transformed to a differential equation in the case where the time interval is {bf R}. A fast algorithm to solve the differential equation by the finite differences is given and a regularized spectral estimation formula is obtained. Then a regularized iterative extrapolation algorithm is introduced and compared with the Papoulis and Gerchberg algorithm. A time-frequency regularized extrapolation algorithm is presented in the two-dimensional case. The Gibbs phenomenon is analyzed. Then the time-frequency regularized extrapolation algorithm is applied to image restoration and compared with other algorithms.
(Author portrait)
Weidong Chen received the Master's degree in software engineering from the Department of Computer and Information Science and the Ph.D. degree in mathematics from Kansas State University. Now he is teaching mathematics in the Department of Computer Science, Mathematics and Physics at Missouri Western State University, Saint Joseph, Missouri.
