不适定逆成像问题的多准则正则化求解方法

不适定性（ｉｌｌ－ｐｏｓｅｄｎｅｓｓ）是图像重建（Ｘ射线ＣＴ的投影重建、心电ＥＣＧ及电ＥＥＧ信号的逆成像重建）逆问题求解中非常普遍的情况，由于对观测数据及正问题数字离散化过程中所产生的误差极为敏感，它在银行大程度上将影响到重建图像的质量、稳定性和求解精度。通过对由投影重建图像逆问题求解过程中的不适宜性分析，给出了求解不适定逆成像问题的多准则正则化方法及其理论基础，实验结果表明该方法比传统的单准则正

Multicriterion Regularization Approach to the Solution of Ⅲ-posed lnverse lmaging Problems

In most cases, ill posedness exists inherently in the solution process of inverse imaging problems (X ray CT image reconstruction from projections, ECG and EEG inverse mapping), and affects seriously the quality, stability and accuracy of the reconstructed images with the susceptibility to the errors in measurement data and the errors in the numerical solution of forward problems. This paper will give a study on the ill posedness of image reconstruction from projections and discuss the characteristics of the ghost function which affects imaging quality and accuracy in the reconstruction process. A new approach to solve the ill posed inverse imaging problems, the multicriterion regularization approach, will be presented with its theory basis and the experiment results. This approach has been successfully applied in the areas of CT and NMR image reconstruction, solution to ECG inverse problems and atmospheric turbulence image reconstruction.