Computational Methods for Inverting the Soft X-Ray Transform

这个项目的目的是对软X射线变换的倒置程序进行数学开发、计算实现、测试和评估，软X射线变换是最近从实验细胞生物学中出现的，但以前从未从计算数学的角度进行过严格的处理。软X射线变换是软X射线显微镜(SXM)中获得二维投影的物理过程的合适的数学模型，它具有在自然环境中对整个细胞进行高分辨率成像的独特能力。为了提高从SXM投影重建三维(3D)结构的分辨率，提出了一种新的计算方法来反演SXM的这种精确成像模型。据推测，与目前使用的启发式程序相比，这种处理方法将导致更高的准确性和有效性。在生物学的许多领域，对3D结构的理解提供了一种理解其功能的方法。许多结构，如单分子、病毒、细胞等，都太小了，肉眼无法观察到。显微镜一直在为图像提供有关这些结构的详细信息。然而，未经处理的显微图像呈现出彼此重叠的结构，使得它们很难解释。通过3D重建技术将来自同一结构的不同方向的多个图像组合在一起，可以对这种结构进行准确的可视化。对三维结构形状的理解在许多生物医学领域都很重要，例如在药物设计中。在解开三维生物结构的众多方法中，软X射线显微镜(SXM)具有独特的能力，可以提供自然环境中亚细胞三维结构的高分辨率细节，即整个细胞。这些目前无法获得的结构信息对于理解许多生物过程将是重要的。一个例子是线粒体功能障碍，因为它发生在人类疾病中，了解这一点对于评估线粒体疾病的心血管和神经系统功能很重要。

The aim of this project is the mathematical development, computational implementation, testing and evaluation of procedures for inverting the soft x-ray transform, which has arisen recently from experimental cellular biology, but has not previously been subjected to a rigorous treatment from the computational mathematics point of view. The soft x-ray transform is the appropriate mathematical model for the physical process by which two-dimensional projections are acquired in soft x-ray microscopy (SXM), which has the unique capability of imaging whole cells in their native environment with high resolution. The proposednovel computational methods for inverting this accurate image formation model for SXM are designed to improve the resolution in the reconstructions of the three-dimensional (3D) structures from their SXM projections. It is conjectured that such a treatment will result in improved accuracy and usefulness as compared to the currently used heuristic procedures. In many areas of biology, the understanding of a 3D structure provides a way of understanding its function. Many structures, such as single molecules, viruses, cells, etc., are too small to be viewed with the naked eye. Microscopy has been providing images with information aboutdetails of these structures. However, unprocessed microscopic images present structures that are superimposed over each other, makingthem hard to interpret. Combining multiple images from different directions of the same structure by techniques of 3D reconstruction allows accurate visualization of such structures. The understanding of 3D shapes of structures is important in many biomedical areas, for example, in drug design. Of the many approaches to unraveling 3D biological structures, soft X-ray microscopy (SXM) has the unique capability of providing high-resolution details of subcellular 3D structures in their native environment, i.e., the whole cell. Such currently-unavailable structural information will be important for understanding many biological processes. An example is mitochondrial dysfunction as it occurs in human diseases, understanding of which is important for assessing cardiovascular and nervous system function in mitochondrial disorders.