Mathematical modelling and computational methods for imaging and advanced sensor technology

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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.