从不一致数据重建图像的收敛块迭代算法。

Massachusetts Univ., Lowell, MA.

IEEE Trans Image Process. 1997;6(9):1296-304. doi: 10.1109/83.623192.

It has been shown that convergence to a solution can be significantly accelerated for a number of iterative image reconstruction algorithms, including simultaneous Cimmino-type algorithms, the "expectation maximization" method for maximizing likelihood (EMML) and the simultaneous multiplicative algebraic reconstruction technique (SMART), through the use of rescaled block-iterative (BI) methods. These BI methods involve partitioning the data into disjoint subsets and using only one subset at each step of the iteration. One drawback of these methods is their failure to converge to an approximate solution in the inconsistent case, in which no image consistent with the data exists; they are always observed to produce limit cycles (LCs) of distinct images, through which the algorithm cycles. No one of these images provides a suitable solution, in general. The question that arises then is whether or not these LC vectors retain sufficient information to construct from them a suitable approximate solution; we show that they do. To demonstrate that, we employ a "feedback" technique in which the LC vectors are used to produce a new "data" vector, and the algorithm restarted. Convergence of this nested iterative scheme to an approximate solution is then proven. Preliminary work also suggests that this feedback method may be incorporated in a practical reconstruction method.

已经表明，通过使用重新缩放的块迭代（BI）方法，可以显著加速包括同时 Cimmino 型算法、最大似然法（EMML）和同时乘法代数重建技术（SMART）在内的许多迭代图像重建算法的解的收敛速度。这些 BI 方法涉及将数据分成不相交的子集，并且在迭代的每一步只使用一个子集。这些方法的一个缺点是，在不一致的情况下它们无法收敛到近似解，在这种情况下，不存在与数据一致的图像；它们总是被观察到产生不同图像的极限环（LC），算法通过这些环循环。通常情况下，这些图像中没有一个提供合适的解决方案。然后出现的问题是这些 LC 向量是否保留了足够的信息来从中构建合适的近似解；我们证明它们确实如此。为了证明这一点，我们采用了一种“反馈”技术，其中使用 LC 向量来生成新的“数据”向量，并重新启动算法。然后证明这个嵌套迭代方案收敛到近似解。初步工作还表明，这种反馈方法可以结合到实际的重建方法中。