Mathematical modelling and computational methods for imaging and advanced sensor technology

成像和先进传感器技术的数学建模和计算方法

• 批准号: RGPIN-2020-04561
• 负责人: Lamoureux, Michael
• 金额: $ 1.31万
• 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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740041
• 关键词: Mathematical; modelling; computational; methods; imaging

Our research creates mathematical models, methods and algorithms to support advances in sensing technologies for imaging -- seismic, medical and industrial. Of particular interest are challenges arising with new sensors technology and computational power that permit better, deeper techniques in mathematical analysis and numerical methods.  Most people are familiar with imaging technologies such as medical ultrasounds and CAT scans to see inside the human body, as well as X--ray machines at airport security that can "see" inside our luggage. Related technologies are used in industry, such seismic imaging of the earth's subsurface for locating oil reservoirs, or non-destructive materials testing like microwave-based "stud finders" used to see through walls to find beams, pipes, and wires.    People are less familiar with the fact that these imaging technologies require high powered mathematical and computational methods to transform data collected from sensors (ultrasonic, X--ray, seismic) and turn them into useful images of the physical object under investigation (human body, airport luggage, earth's subsurface).    Our research is on developing the mathematics necessary to support these imaging methods. This includes creating accurate mathematical models of the physical systems under study, models of the sensors recording physical signals, functional analysis to describe signal propagation as mathematical linear operators, harmonic analysis to characterize and decompose these signals, and numerical methods to support fast, accurate computation. Compressive sensing used for randomized placement of sensors; computational neural nets to automatically detect and localize events such as microseismic fracturing, intruders, and traffic patterns. Optimal transport theory is used to support mathematical inverse problems in imaging.    One focus are novel distributed acoustic sensors (DAS), where a fibre optic cable is buried in the ground to monitor a security fence, rail line or oilwell site. While the fibre is an optical device, physical vibrations stretch the fibre, then detected with precise measurements of a laser interferometer. This turns the optical fibre into an acoustic sensor. DAS is remarkable as a cheap fibre cable can be installed along tens of kilometres of infrastructure and can be used to image events all along these many kilometres. DAS effectively creates a continuous stream of "virtual geophones" that can used in imaging algorithms and event monitoring.    Applications include improving the quality of imaging, to enhance geophysical or medical interpretation of the images, and allow introduction of new sensor technologies in novel situations such as DAS monitoring of oil production sites, pipelines, and CO2 storage facilities. Training of highly qualified personnel plays a central role in the program.      This research supports ever advancing technologies in sensor and imaging, using the best results from analysis and numerics.

我们的研究创建了数学模型、方法和算法，以支持成像传感技术的进步——地震、医学和工业。特别令人感兴趣的是新传感器技术和计算能力带来的挑战，这些技术和计算能力允许更好、更深入的数学分析和数值方法技术。大多数人都熟悉成像技术，例如用于观察人体内部的医学超声波和 CAT 扫描，以及机场安检中可以“看到”我们行李内部的 X 光机。相关技术已在工业中使用，例如地震成像。地球地下的用于定位油藏，或无损材料测试，例如用于穿透墙壁寻找梁、管道和电线的微波“螺柱探测器”​人们不太熟悉这些成像技术需要高功率的数学和电线。将传感器（超声波、X 射线、地震）收集的数据转换为所研究的物理对象（人体、机场行李、地球地下）的有用图像的计算方法​我们的研究是。开发支持这些成像方法所需的数学模型，包括创建所研究的物理系统的精确数学模型、记录物理信号的传感器模型、将信号传播描述为数学线性算子的函数分析、表征和分解这些信号的谐波分析。用于支持快速、准确计算的压缩传感；用于自动检测和定位微震破裂、入侵者和交通模式等事件的计算神经网络。成像中的逆问题是新型分布式声学传感器（DAS），其中光纤电缆埋在地下以监控安全围栏、铁路线或油井现场，虽然光纤是一种光学设备，但物理振动会拉伸。光纤，然后通过激光干涉仪的精确测量进行检测，这将光纤转变为声学传感器，这是非常了不起的，因为廉价的光纤电缆可以沿着数十公里的基础设施安装，并且可以用于全程成像事件。这些公里数有效地创建了连续的“虚拟地震检波器”流，可用于成像算法和事件监测，应用包括提高成像质量、增强图像的地球物理或医学解释，并允许引入新的传感器。石油生产现场、管道和二氧化碳储存设施的 DAS 监测等新情况中的技术在该项目中发挥着核心作用。分析和数值的最佳结果。