迭代重建技术(ART)简要介绍

0 说明

本文是基于matlab实现的最简单的迭代重建算法，当然，基于这个算法可以做很多优化。

1. fomula

迭代方法，其实说来都比较简单，最关键就是怎么从当前的x得到下一步的x。
Algebraic reconstruction technique is all about a system of equations which is

Ax = p

In this formula, x = [x1, x2, …, xn]T , p = [p1, p2, …, pm]T , where x is one-dimensional vector of n elements, each representing the pixels of a certain 2-D object, p is one-dimensional vector of m elements, each representing a measurements taken at a certain detector in a certain projection direction, A is called the projection matrix and each value in this matrix called a projection rate defines the contribution of a specific pixel to a specific projection value.

in general medical imaging applications, A is so large that the entire matrix cannot be stored in the computer at the same time. In the process of solving the equations, the value of that row of matrix A is g