An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

Abstract

In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection (VP) method. Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection (IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method, without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio (SNR) for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.

A decomposition method for the simultaneous reconstruction of temperature and soot volume fraction distributions in axisymmetric flames

“…Projection intensities were simulated according to equation (11), and then the temperature and soot volume fraction distributions were calculated using the proposed method. In the simulations, the Tikhonov regularization method [33,34] was used to solve equations ( 11) and ( 13), and all the regularization coefficients were set to 10 -6 , which is two orders of magnitude smaller than the spatial scales of the simulated meshes. Moreover, to examine the anti-noise performance of the proposed method, normal random errors were generated and superimposed on the simulated projection intensities according to the following equation:…”

Discussion on the development of a 3D, dynamic and real-time digital boiler

“…本文作者团队提出了一种非 相关虚拟投影信息构造方法, 从而有效增加了检测信 息的数量, 提高了从低维信息中重建高维分布信息的 能力, 图 9 给出了该方法的重建效果并对比了源项分 布. 这项成果对一般反问题求解都有借鉴作用 [73,74] . [73,74] 发功率, 是典型的"快-慢-快"的过程 [75] .…”

“…这项成果对一般反问题求解都有借鉴作用 [73,74] . [73,74] 发功率, 是典型的"快-慢-快"的过程 [75] . 现有的火电 机组缺乏充分考虑炉内燃烧及水冷壁和过热器/再热 器传热过程特性的机组负荷控制新技术.…”