基于物理模型的成像算法评价与 SASART 成像算法

MODEL BASED EVALUATION METHOD FOR THE IMAGING INVERSION ALGORITHMS AND SASART ALGORITHM

基于物理模型的图像重建算法评价方法，作者研究设计的ＳＡＳＡＲＴ算法，给出了常用算法ＳＶＤ，ＣＧ，ＬＳＱＲ，阻尼ＬＳＱＲ，ＳＩＲＴ，ＳＡＲＴ及ＳＡＳＡＲＴ的测试结果。测试数据表明：（１）线性成像方程系统的特性（条件数）及解结构都对解精度有影响，解模型越粗糙，解的精度越低；（２）自激励联合迭代重建算法（ＳＡＳＡＲＴ）迭代稳定、抗噪音能力强，用于高噪数据反演能获得合理的图像；（３）各种求解算法都具有平滑效应，同时也都会产生误差很大（＞１５０％）的奇异解；（４）小的数据拟合差并不一定指示解的精度高；（５）对含误差数据，应用阻尼ＬＳＱＲ或ＳＡＳＡＲＴ算法进行成像反演。

Imaging inversion plays an important role in tomography techniques. A model based evaluation method for the imaging inversion algorithms and a new imaging inversion algorithm SASART are introduced in this article. Some algorithms in common use are verified using the model based evaluation method and the test data show that: (1) both the singularity of the linear equation system and the style of the solution model (physical model) have effects on the precision of the solution , the more rough the solution model, the less the precision of the solution will be; (2) algorithm SASART has the power to obtain logical image for high noise data inversion; (3) each algorithm has an effect of smoothing and may, at same time, export some singularity solution elements with large error(>150%); (4) good data fit does not always indicate good solution; (5)for an imaging inversion with high noise in the data, Damping LSQR or SASART should be used.