Collaborative Research: Mathematical Techniques for Emerging Methods in Biomedical Imaging

近几十年来，许多廉价、安全和高对比度的医学成像技术如电阻抗断层成像(EIT)和光学断层成像(OT)被引入。然而，EIT和OT受到不稳定和低分辨率的困扰。为了克服这些困难，目前正在开发结合不同类型的辐射(例如，超声波和电磁波)的新型混合方法。我们的想法是结合这些浪潮的优势，同时缓解它们各自的不足。在这些方法中，该项目将主要集中在热声层析成像、超声调制光学层析成像和声电层析成像，以及可能出现的一些较新的成像方式。它致力于开发这些技术所需的数学分析和数值工具，目前这些技术还处于早期(有时是婴儿)发展阶段。计算机层析成像是生物医学成像以及工业无损检测、地质学和其他领域的主要方法。已经开发了各种方式，包括例如通常的X射线临床‘’CAT扫描‘’、MRI、光学、超声和电阻抗断层扫描。它们在分辨率、成本和安全性方面都有各自的优势和不足。因此，对新的更安全、更便宜和可靠的方法的探索仍在继续。近年来，新的混合方法不断涌现，有望成为廉价、安全和有效的医疗诊断工具。该项目解决了它们开发过程中的核心数学问题，因为图像必须通过复杂的数学程序获得，而不是直接获取。除了对几种新的廉价和安全的生物医学成像方法的开发和实施产生重大影响外，人们还可以预见将其应用于非破坏性工业测试和其他需要对非透明对象进行成像的领域的可能性。

A number of inexpensive, safe, and high contrast medical imaging procedures like Electrical Impedance Tomography (EIT) and Optical Tomography (OT) have been introduced in the recent decades. However, EIT and OT are plagued by instability and low resolution. To overcome these difficulties, novel hybrid methods are being currently developed that combine different types of radiation (e.g., ultrasound and electromagnetic waves). The idea is to combine the advantages of these waves, while alleviating their individual deficiencies. Among these methods, the project will concentrate mostly on the Thermoacoustic Tomography, Ultrasound-Modulated Optical Tomography, and Acousto-Electric Tomography, as well as possibly some newer emerging imaging modalities. It is devoted to developing mathematical analytic and numerical tools needed in these techniques, which are currently in their early (sometimes infant) stages of development.Computerized tomography is a major method of biomedical imaging, as well as of industrial non-destructive testing, geology, and other areas. Various modalities have been developed, including for instance the usual X-ray clinical ``CAT scan'', MRI, Optical, Ultrasound, and Electrical Impedance Tomography. All of them have their advantages and deficiencies in terms of resolution, cost, and safety. Thus a quest continues for new safer, cheaper, and reliable methods. In recent years, novel hybrid methods have been emerging, which promise to become cheap, safe and effective medical diagnostics tools. The project addresses the mathematical issues that are central in their development, since images have to be obtained by complex mathematical procedures rather than direct acquisition. Besides the significant impact on the development and implementation of several new inexpensive and safe methods of biomedical imaging, one can also envision a possibility of applications to non-destructive industrial testing and other areas where imaging of non-transparent objects is required.