An Explicable Neighboring-Pixel Reconstruction Algorithm for Temperature Distribution by Acoustic Tomography

Acoustic process tomography is a powerful tool for monitoring multiphase flow and combustion. However, its capability of revealing details of the interrogation zone is restricted by the ill-posed and rank deficiency problems. In each projection, a probing sound beam only passes the pixels along its propagation path, resulting in a large number of zero-valued elements in the measurement matrix. This is more pronounced as the resolution of the imaging zone becomes gradually finer, which is detrimental to image reconstruction. In this study, a mathematically explicable reconstruction algorithm of regularization is proposed by assigning each zero-valued pixel with a combination of the values of the neighboring pixels, ruled by the appropriate regularization factors. The formula to determine the regularization factors is also derived. Simulations are carried out to verify this new approach, and some representative cases are presented. As a result, the ambiguity of the inverse process is removed, and the accuracy of the image reconstruction is significantly improved. The results show the robustness of the algorithm and certain advantages over the standard Tikhonov regularization formula.