多模态生物医学成像联合重建的数学问题  

Mathematical problems of joint reconstruction for biomedical multi-modality imaging techniques

作　　者：姜明[1,2] 何迪[1] 

机构地区：[1]北京大学数学科学学院,北京100871 [2]北京大学未来媒体网络协同创新中心,北京100871

出　　处：《中国科学：数学》2016年第5期571-577,共7页Scientia Sinica：Mathematica

基　　金：国家重点基础研究发展计划(批准号:2015CB351803);国家自然科学基金(批准号:61421062和61520106004);中德科学中心(批准号:GZ 1025)资助项目

摘　　要：生物医学成像技术可得到可视化的结构或功能信息,以供生物研究或临床诊断使用,数学理论在生物医学成像技术中一直起着重要的作用.生物医学成像技术中的一类数学问题是从测量数据重建感兴趣的结构或功能信息,这是一类典型的反问题.最近,生物医学成像技术的一个新进展是多模态成像技术,通过融合多种成像技术实现,目标是提供更加丰富的可视化信息.相对于已有的单模态成像技术,多模态成像技术的图像重建的策略具有多种选择.一个新兴的方向是利用各种模态图像的相似性,或者更严格地讲,是利用不同模态图像在某一特征表示上的部分相似性,进行各种模态图像重建的联合重建.联合重建的优势是可以利用不同模态的数据,通过相似的特征互补性在重建中互相约束,有希望得到更好质量的图像.本文对多模态成像技术中的联合重建问题进行综述,论述有关的关键数学问题,介绍相关的研究进展,其中涉及的一个理论基础Mumford-Shah泛函,张恭庆曾有专著论述.Biomedical imaging aims at visualizing structural or functional information necessary for biological research or clinical diagnosis. Mathematics has played a significant role in biomedical imaging technology. A class of mathematical problems in biomedical imaging techniques is to reconstruct the information of interest from measured data, which typically poses an ill-posed inverse problem. One recent development is the multimodality imaging technique for enriching image information by fusing multiple imaging modalities. In contrast to the existing single-mode imaging technology, there is a variety of strategies for image reconstruction of multimodality imaging techniques. A new direction is the use of the similarity of multi-modality images, or more exactly, the use of the partial similarity of image features from different modality images for achieving the joint reconstruction of multi-modality images. The advantages of joint reconstruction are to utilize the data from different modalities to steer the reconstruction of one modality through the complementary feature information from another modality and to get better quality images. This note is a review of mathematical problems of the joint reconstruction for multi-modality imaging techniques. We introduce the key mathematical problems and report relevant progresses in this field. The fundamental Mumford-Shah functional in this approach has been discoursed in a book by Zhang Gongqing.

关 键 词：生物医学成像 反问题 多模态成像 联合重建 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]