Computational Methods for Inverting the Soft X-Ray Transform

软 X 射线变换逆变换的计算方法

• 批准号: 1114901
• 负责人: Gabor Herman
• 金额: $ 24万
• 依托单位: CUNY Graduate School University Center
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2014-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1114901&HistoricalAwards=false
• 关键词: Computational; Methods; Inverting; Soft; Ray

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.

该项目的目的是数学的发展，计算实现，测试和评估的程序，用于反转软X射线变换，这是最近出现的实验细胞生物学，但以前没有受到严格的处理从计算数学的角度来看。软X射线变换是在软X射线显微镜（SXM）中获得二维投影的物理过程的适当数学模型，其具有在其天然环境中以高分辨率成像整个细胞的独特能力。提出了一种新的计算方法，用于反演这种精确的SXM图像形成模型，以提高从SXM投影重建三维（3D）结构的分辨率。 据证实，这样的治疗将导致改善的准确性和实用性相比，目前使用的启发式程序。在生物学的许多领域，对3D结构的理解提供了理解其功能的方法。许多结构，如单分子、病毒、细胞等，太小了，肉眼无法看到。显微镜已经提供了这些结构的细节信息的图像。然而，未经处理的显微图像呈现的结构相互叠加，使它们难以解释。通过3D重建技术组合来自相同结构的不同方向的多个图像允许对这样的结构进行准确的可视化。理解结构的3D形状在许多生物医学领域中是重要的，例如在药物设计中。在解开3D生物结构的许多方法中，软X射线显微镜（SXM）具有在其天然环境中提供亚细胞3D结构的高分辨率细节的独特能力，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非常重要。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中的心血管和神经系统功能非常重要。