提出了一个由不完备投影数据重建图象的有理逼近方法.该方法首先引入图象象素间连续的假设,然后导出满足最优解的线性方程组,再通过在此方程组中引入一个人工参数将其变形,并用摄动展开方法解新形成的线性方程组,再利用向量值函数的有理逼近来构造原线性方程组的解.该方法还避免了原方程组直接求解计算量非常大的问题,因为使用该有理逼近方法,只需展开几项,便可获得较满意的重建图象.

This paper is focused on image reconstructions from incomplete projecting data. Based on the assumption of continuity among image pixels, the linear system which the optimal solution satisfies is derived for incomplete projecting data. An artifitial parameter is then introduced and a new linear system is formed from the original one. First, the new system is solved by perturbation method and the expansion cofficients are computed by an iteration; second, the solution to the original system is achieved by applying rational approximation of vector-valued funcation to the perturbation solution. The difficulty of the high computation amount of the direct solution of the original linear system is overcome by the proposed method. Numerical examples indicate that when only three items in the perturbation expansion are used, satisfactory approximations to the original images can be achieved by the rational approximation method.