"Imaging" means a lot of different things in different contexts and applications but one thing is clear: it is an interdisciplinary science that is (a) profoundly mathematical, (b) challenging in its demands on scientific computing, and (c) challenging in its demands on data analysis. In this course I will concentrate on "Coherent Imaging", which means imaging when arrival time (or phase) information is available at the sensors or the sensor array, and not only intensity. I will consider both passive and active sensor arrays. In the latter, the sensors emit probe signals and then record the echoes (scattered signals) from the object to be imaged. Roughly one third of this course will be devoted to the careful analysis of the main algorithm that is commonly used: Time reversal (or travel time migration, or Kirchhoff migration) in its various settings (narrowband-broadband, large-small arrays, etc) and the resolution that it yields. I will also consider several other issues such as optimization methods and algorithms in sensor imaging, optimal illumination and waveform design, robustness to clutter in the environment and loss of resolution from it, matched field imaging and signal to noise ratio issues, intererometric imaging, etc. Applications come from seismic imaging, ultrasonic non-destructive testing and medical diagnostics, radar, sonar, etc., and some will be considered in some detail.
| Name | Office | Phone | Office Hours | |
|---|---|---|---|---|
| George Papanicolaou | 383V | 723-2081 | Tuesday 2:00-4:00pm and by appointment | papanicolaou@stanford.edu |
The course grade will be based on a project with an in-class presentation. There is no final or other exam. Papers will be posted on the web site so that they can be considered for possible selection for the presentation. The presentation topic must be selected by the first week of May. The presentations will be in the second half of May.