Lu L, Brown B H, Barber D C, Leathard A D
Department of Medical Physics, Royal Hallamshire Hospital, Sheffield, UK.
Physiol Meas. 1995 Aug;16(3 Suppl A):A39-47. doi: 10.1088/0967-3334/16/3a/004.
This paper presents a model that comprises only two parameters (R/S, fr) and the application of three function minimization algorithms (simplex, Powell and modified Powell) to this model to obtain parametric images. Comparisons among the three algorithms in terms of efficiency and reliability were carried out. It was found that, with proper initialization by taking the shape of the modelled data into consideration, the minimization function can be approximated by a quadratic function near the minimum point, therefore the iteration times can be minimized in the modified Powell method. The results show that with the modified Powell method a substantial reduction of computation time can be achieved in the parametric imaging. This makes it possible to obtain a 16 x 16 parametric image in 1 s.
本文提出了一个仅包含两个参数（R/S，fr）的模型，并将三种函数最小化算法（单纯形法、鲍威尔法和改进的鲍威尔法）应用于该模型以获得参数图像。对这三种算法在效率和可靠性方面进行了比较。结果发现，通过考虑建模数据的形状进行适当初始化，在最小点附近最小化函数可以近似为二次函数，因此在改进的鲍威尔法中迭代次数可以最小化。结果表明，使用改进的鲍威尔法在参数成像中可以大幅减少计算时间。这使得在1秒内获得16×16的参数图像成为可能。
