| 严春满,穆 哲.一种改进的梯度加速 Landweber 算法及其在
ECT 图像重建中的应用[J].电子测量与仪器学报,2021,35(6):169-175 |
| 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 landweberalgorithm in ECT image reconstruction |
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| DOI： |
| 中文关键词: 电容层析成像 图像重建 梯度加速 Landweber 算法 |
| 英文关键词:electrical capacitance tomography image reconstruction gradient acceleration Landweber algorithm |
| 基金项目:国家自然科学基金（61861041）项目资助 |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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