二维带限信号正则重构和外推的快速算法

A Fast Algorithm for the Regularization Reconstruction and Extrapolation of 2-D Band-Limited Signals

本文给出用离散正则化方法进行二维带限信号重构和外推的快速算法。其基本思想是将正则化方法与快速Ｆｏｕｒｉｅｒ变换（ＦＦＴ）结合起来，而正则参数的选取则基于偏差原理和作者提出的三阶收敛算法来实现，并进行数值了模拟。计算结果表明本文给出的新算法具有快速、稳定和抑制高频噪音干扰等优点。

A Fast algorithm for the extrapolation of 2-D band-limited Signals by using discrete regularization is presented in this paper. The new algorithm integrates reguarization method with 2-D FFT, while the regularized parameter is selected by discrepancy principle and determined numerically by a cubic convergence method. Theoretical analysis and numerical simulation indicates that the new algorithm possesses the advantages of high-speed, good stability and the inhibitation function against the noise of high frequencies.