一种改进的梯度加速Landweber算法及其在ECT图像重建中的应用  

Application of an improved gradient accelerated landweber algorithm in ECT image reconstruction

作　　者：严春满[1] 穆哲 Yan Chunman;Mu Zhe(College of Physics and Electronic Engineering,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学物理与电子工程学院,兰州730070

出　　处：《电子测量与仪器学报》2021年第6期169-175,共7页Journal of Electronic Measurement and Instrumentation

基　　金：国家自然科学基金(61861041)项目资助。

摘　　要：图像重建算法是电容层析成像技术(electrical capacitance tomography, ECT)在工业应用中的关键。Landweber迭代算法在图像重建的精度和速度上取得了较好的折衷性,但其收敛速度较慢,且迭代后期具有不稳定性,无明确的迭代停止准则。提出一种改进的梯度加速Landweber迭代算法,依据级数理论对梯度加速Landweber迭代算法进行深入分析,通过构造残差矩阵并添加约束因子获得新的迭代公式,并将其应用于ECT图像重建。数值仿真结果表明,改进算法对各流型的相对误差及相关系数均可在较少次迭代后稳定收敛于某一确定值,具有明确的迭代停止准则,且对于大多数流型的重建图像在主观质量上更接近于原始流型,从而验证了改进算法的稳定性及有效性。Image reconstruction algorithm is the key to the industrial application of electrical capacitance tomography. The Landweber iterative algorithm has achieved a good compromise in the accuracy and speed of image reconstruction, but its convergence speed is slow, and the late iteration is unstable, there is no clear iteration stop criterion. In this paper, an improved gradient accelerated Landweber iterative algorithm is proposed, based on the series theory, the gradient accelerated Landweber iterative algorithm is deeply analyzed, a new iterative formula is obtained by constructing the residual matrix and adding constraint factors, and it is applied to ECT Image reconstruction. Numerical simulation results show that the relative error and correlation coefficient of the improved algorithm can converge to a certain value after less iteration steps, and has a clear iteration stop criterion. Moreover, for most flow patterns, the reconstructed images are closer to the original flow patterns in subjective quality, which verifies the stability and effectiveness of the improved algorithm.

关 键 词：电容层析成像 图像重建 梯度加速Landweber算法 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]