带限信号重构问题的迭代正则化方法

Iterative regularization method for reconstruction of band-limited signal

针对带限信号重构问题的迭代正则化方法,提出用Landweber迭代法和最速下降法求解低频带限信号重构问题,导出正则化问题的预条件梯度迭代格式,并对三种方法进行比较,进行数值模拟的结果表明:最速下降法与Landweber迭代法具有非常相似的迭代公式,最速下降法既是正则化方法,又可以最优选取迭代步长,比Land-weber迭代法具有更快的收敛性,将预条件方法用到正则化问题上可以起到稳定和快速求解的作用.通过数值算例表明,在计算效率上预条件梯度迭代正则化方法优于Landweber迭代算法和传统的最速下降法.

Aimed at the iterative regularization methods for band-limited signal reconstruction, Land- weber iterative method and steepest descent method were presented for solving the low-frequency band- limited signal reconstruction problem. The preconditioning gradient iterative format was derived for regularization problem. Numerical simulations were also performed and compared for above-mentioned meth- ods. It was concluded that although the steepest descent method and Landweber iterative method had very similar iterative formula, the former was not only a regularization method but also could optimally choose the iterative step length, having faster convergency than the Landweber iterative method. By using the preconditioning technique for the regularization problem, the stability and fast solution could be obtained. It was shown by a numeric example that in connection of computational efficiency the preconditioning gra- dient descent method was better than the Landweber iterative method and the traditional steepest descent method.