带限函数外推算法收敛性研究

Convergence on Extrapolation for Band-limited Function

Gerchberg Papoulis(G-P)算法是解决带限信号外推问题的一个广泛使用的迭代算法。在数据存在噪声时,本文论证了G-P迭代算法的收敛性不再成立,其原因是相应的线性算子在L2范数下是非压缩算子,并以数值模拟说明了这一问题。针对这一问题,我们提出改进的Gerchberg Papoulis(IG-P)算法,并研究了该算法在L2范数下的收敛性质。数值模拟结果表明,IG-P迭代算法具有较好的信号分辨能力和收敛性质。

The Gerchberg-Papoulis (G-P) algorithm is a widely applied iterative method for the extrapolation of band-limited signals. When the observed data are corrupted with noise, the G-P algorithm is not convergent any more because the corresponding linear operator is not contractive under the L^2 norm. This phenomenon is also illustrated with numerical simulation. We propose an improved Gerchberg-Papoulis(IG-P) algorithm and study its convergence properties. It is proved that the IG-P algorithm is convergent under the L^2 norm. Numerical stimulation is provided to demonstrate that the convergence and signal resolving power of I-GP are better than those of the original G-P algorithm when the data are corrupted with noise.