Mathematical analysis and inverse theory for seismic and medical imaging

地震和医学成像的数学分析和反演理论

• 批准号: RGPIN-2015-06038
• 负责人: Lamoureux, Michael
• 金额: $ 1.24万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=656513
• 关键词: Mathematical; analysis; inverse; theory; seismic

The objective of this program is to develop accurate mathematical theories and efficient algorithms for improving the resolution of seismic and medical images.***While the applications in seismic (earth) and medical (human) imaging are very different, the physical and mathematical principles behind the technologies are very similar. Energy is transmitted into the body under study (earth, or human) in the form of sound waves, or electromagnetic waves, and reflected off objects in the interior to recording devices on the surface. Complex mathematical algorithms are applied to the data and an image is created that can be viewed on the screen. Such images are used to identify oil and gas deposits in the earth, or the presence of organs, injuries, or even tumours within the human body.***Seismic imaging needs to be improved so that not just geological structures can be identified, but also their exact location and the nature of the rocks and fluids contained therein. This will improve the economics of oil and gas discovery and recovery, as well as advance the technology of carbon capture and storage in the earth's subsurface. ***Similarly, medical imaging needs to be improved so that higher resolution, dynamic images can be generated, to better identify and diagnose pathologies inside the body. By using non-invasive data collection such as ultrasound, or tissue sensing adaptive radar, medical teams can diagnose and prescribe treatment without harmful, invasive procedures on the human body.***The focus of this research is the development of  mathematical theories and computational methods that makes improvements in this imaging possible. ***We develop novel tools from functional and harmonic analysis, pseudodifferential operators, integral operators, and other spectral methods, to better model the physical processes of wave propagation, viscoelastic effects of the earth and of living tissue, as well as signal generation and capture, to improve the analysis and processing of the physical data gathered in industrial seismic surveys and practical medical instruments. Mathematical inverse theory provides a promising approach to tackle these problems in a uniform, advanced manner. ********

该计划的目标是开发准确的数学理论和有效的算法，以提高地震和医学图像的分辨率。***虽然地震（地球）和医学（人类）成像的应用有很大不同，但物理和数学原理背后的技术非常相似。能量以声波或电磁波的形式传输到所研究的身体（地球或人类），并从内部物体反射到表面的记录设备。应用于数据并创建图像可以在屏幕上查看此类图像，用于识别地球上的石油和天然气沉积物，或人体内是否存在器官、损伤，甚至肿瘤。***地震成像需要改进，以便不仅仅是识别。不仅可以识别地质结构，还可以识别它们的确切位置以及其中所含岩石和流体的性质，这将提高石油和天然气发现和回收的经济性，并推进地球地下碳捕获和储存技术。 。 ***同样，医学成像也需要改进，以便可以生成更高分辨率的动态图像，以便通过使用超声波或组织传感自适应雷达、医疗等非侵入性数据收集来更好地识别和诊断体内的病变。团队可以在不对人体进行有害、侵入性操作的情况下进行诊断和治疗。***这项研究的重点是数学理论和计算方法的发展，使这种成像的改进成为可能***我们从功能性角度开发新颖的工具。和调和分析、伪微分算子、积分算子等频谱方法，更好地模拟波传播的物理过程、地球和活体组织的粘弹性效应以及信号生成和捕获，改进对工业地震勘测和实用医疗仪器中收集的物理数据的分析和处理数学逆理论提供了一种有希望的方法来以统一、先进的方式解决这些问题。