Joint Sino-German Research projekt: Feature based bi-modal image reconstruction

生物医学成像的目的是可视化生物和药物研究或临床诊断所需的结构或功能信息。相关的数学挑战是从测量数据中重建感兴趣的信息，这通常构成不适定的逆问题。最近的一些发展集中在多模态技术上，以通过融合多种成像模态来丰富图像信息。该策略是使用多种模式进行成像，例如，同时或顺序进行扩散光学断层扫描（DOT）和X射线计算机断层扫描（XCT）。经典的方法分别和顺序地解决相关的逆问题，例如首先计算XCT重建，然后添加DOT重建。激发当前项目的自然观察是，同一对象的图像，尽管从不同的模态获得，但具有相似的互补特征信息。这种特征信息特别是图像边缘和用于有效表示的学习字典。因此，来自一个模态的互补特征信息可以以迭代方式改善和引导另一模态的重建，反之亦然。我们的假设是，多模态系统的图像重建可以联合执行，通过其特征信息的通信，以提高图像质量与较少的测量数据。本项目的创新之处在于联合解决多个逆成像问题，而不是像以前的方法顺序。该项目的具体目标和里程碑是：M1）发展多成像领域特征表示的数学理论，包括特征的相似性定义，并将其应用于多模态数据联合重建的正则化方案; M2）建立多模态特征正则化逆问题的有效算法及其实现; M3）MALDI + XCT和DOT + XCT的方法验证。本课题的完成，将为多模态图像融合提供一种新的理论基础，并将为多模态图像融合提供有效的算法和实现手段。

Biomedical imaging aims at visualizing structural or functional information necessary for biological and pharmaceutical research or clinical diagnosis. The associated mathematical challenge is to reconstruct the information of interest from measured data, which typically poses an ill-posed inverse problem. Some recent developments focus on multi-modality technologies to enrich image information by fusing multiple imaging modalities. The strategy is to conduct imaging with multiple modalities, for example, performing diffuse optical tomography (DOT) and X-ray computerized tomography (XCT), simultaneously or sequentially. Classical approaches solve the related inverse problems separately and sequentially, such as computing an XCT reconstruction first followed by adding a DOT reconstruction.The natural observation that motivates the current project is that images of the same object, though obtained from different modalities, possess similar complementary feature information. Such feature information is in particular image edges and learned dictionaries for efficient representations. Hence, the complementary feature information from one modality can improve and steer the reconstruction of another modality, and vice versa, in an iterative manner. Our hypothesis is that image reconstructions for multi-modality systems can be jointly performed with enhanced image quality with less measured data via the communication through their feature information.The innovation of this project is to jointly solve the multiple inverse imaging problems rather than sequentially as previous approaches. Specific aims and milestones of this project are: M1) to develop a mathematical theory for feature representations from multiple imaging domains including similarity definitions of features and to apply them in regularization schemes for joint reconstruction from multi-modality data; M2) to establish efficient algorithms and their implementations for multi-modality feature regularized inverse problem; M3) validation of the methods for MALDI plus XCT and for DOT plus XCT. Upon the completion of this project, a new theory for imaging modality fusion will be established together with efficient algorithms and implementations.