Krawtchouk矩的误差传递分析及算法改进

提出了Krawtchouk矩的误差传递模型,分析了其误差传递的机理,提出一种基于GMP大数库的分段迭代算法来精确计算Krawtchouk多项式,且此方法对参数p取任意值均有效。该方法的原理为：根据经典Krawtchouk矩的传递误差累积趋势,将其迭代过程分为若干段,每段迭代的初值均由GMP库计算得到,通过保证初值的精确性和控制迭代的次数来降低多项式计算的误差,提高高阶矩计算的精度。实验证明该方法确实能有效抑制且在一定程度上控制高阶Krawtchouk矩的累积误差,消除重构图像的劣化。

Error Propagation Analyses and Algorithm Improvement of Krawtchouk Moments

A error propagation model of Krawtchouk moments is proposed and the mechanism of the error propagation has been analyzed.In order to accurately compute Krawtchouk polynomials,a piecewise recursive algorithm based GMP bignum library,which is useful for the arbitrary parameter p,has been present.According to tendency of error accumulation of the classic Krawtchouk moments,the process of iteration has been divided into several sections,and the initial values of the each section is caculated from GMP bignum library.By the means of insuring the accuracy of the initial values and regulate the iteration times,the error of the polynomials is reduced largely and then the precision of high-order moments can be guaranteed.The experiment prove that the propose method can effectively restrain and control the accumulation error of the high-order Krawtchouk moments to a certain extent,and finally eliminate the degradation of reconstruction images.