多模态医学影像处理中的反问题与高效算法研究

医学影像处理已经成为应用数学领域的一个研究热点，部分原来无法解决的图像问题用数学反问题的方法能得以解决。多模态医学影像处理在精准的疾病诊断和临床治疗方案设计上具有广泛的应用。本项目旨在促进反问题的正则化方法在图像处理中的应用，深入研究迎合临床医学诊断的多模态医学影像的变分模型，进一步设计高效地数值计算方法和正则参数选择方法。与已有的图像反问题的建模和求解方法的研究工作相比，我们将注重于通过对图像特征和事先给定的先验信息开展比较具体的分析和研究，设计一些衡量局部统计高维特征的匹配性的新的能量泛函，在此基础上建立医学影像重构、解剖学结构提取和多模态影像配准与融合的正则化能量泛函，我们还将根据图像的高维特征设计自适应网格，提出新的精度高，实现简单且快速有效的模型的求解方法。本课题的研究是一项具有重要理论意义和实际应用价值的工作，有利于医学图像处理的发展。

Medical image processing has currently become one of most popular topics in the field of applied mathematics. Many challenging image problems can be solved by using mathematical theories of inverse problems. This project is to promote the application of regularization methods for inverse problems in image processing, the work will focus on studying multimodality medical image variational modeling in clinical diagnosis, and proposing fast and effective numerical schemes and methods capturing an optimal regularization parameter. Comparing with the exist modeling methods of image inverse problems, we should mainly study the geometric characteristics of the medical images and a given priori information, establish the new energy functional matching local statistical feature based on a high dimensional vector, and give the regularized functional about medical image reconstruction, extraction of single anatomical structures, multimodality medical image registration and fusion, we should also design many adaptive-grid-based algorithms solving the models. The work is of great both theoretical and practical significance, is conducive to the development of multimodality medical image processing.