Nonstationary Image Reconstruction in Ultrasonic Transmission Tomography Using Kalman Filter and Dimension Reduction

Abstract

As a noninvasive and nonradiation imaging modality, ultrasonic transmission tomography (UTT) has gained much attention in process parameter detections, such as multiphase flow measurement and combustion diagnosis. However, traditional static UTT image reconstruction methods suffer from the problems of image smearing and blurring when reconstructing time-varying process parameters. To overcome this problem, a nonstationary UTT image reconstruction method is proposed based on the Bayesian inversion framework, where the nonstationary UTT inverse problem is formulated as a state estimation problem using a pair of state evolution and observation update equations. The nonstationary UTT inverse problem is solved by the Kalman filter, and a prior-based dimension reduction method is proposed to reduce the computational complexity. In addition, a dimension reduction Kalman smoother is proposed and applied for postprocessing the Kalman filter results, which can improve the imaging quality, especially for the initial states. A series of numerical and experimental tests are carried out to evaluate the performance of the proposed methods. The results show that the proposed nonstationary UTT image reconstruction methods have higher temporal resolution and better imaging quality in nonstationary process parameter estimation compared with the traditional static UTT image reconstruction methods.