图象重建的最小距离算法

本文提出了图象重建的一种凸集投影算法.它的重建图象是所有满足投影约束的图象中与先验图象的距离最小者.该算法是就连续分布的图象导出的,重建图象时也不需在空域与频域间进行变换,是一种较OSPR方法更直接、更简单的方法.还对最小距离算法重建结果的存在性、唯一性、幂等性等性质作了证明.

MINIMUM DISTANCE ALGORITHM FOR IMAGE RECONSTRUCTION

A convex projection technique named Minimum Distance Algorithm(MDA) for image reconstruction is presented in this paper. The new algorithm yields a solution that is closest to a priori estimate and is the one with minimum distance among all of the solutions consistent with the available data. The derivation of MDA is based on the assumption that the source is' continuous and belongs to a certain Hilbert space. It is not necessary to calculate the Fourier transform and the inverse Fourier transform. The suggested algorithm is more direct and less complicated than OSPR. Properties such as existence, uniqueness and idempotency of the developed method are demonstrated and a necessary and sufficient condition of the minimum distance solution is also investigated.