Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Prerequisites
There are no official prerequisites for this course, but permission of the instructor is required. Student should have some undergraduate familiarity with partial differential equations, Fourier transforms, distributions (the Dirac delta), linear algebra and least squares, as well as some basic physics. A knowledge of basic computer programming is also needed.
Description
This class covers the mathematics of inverse problems involving waves, with examples taken from reflection seismology, synthetic aperture radar, and computerized tomography. The course is suitable for graduate students from all departments who have affinities with applied mathematics.
Textbook
There is not one textbook. The material will be inspired from various sources. See the readings section for a list of references that sometimes go way beyond what we’ll do in class.
Requirements
There will be occasional problem sets and an oral presentation of a good (landmark, foundational) paper from the literature. The presentations will take place during the last two class sessions.
Grading
The lowest homework score will be dropped.
| ACTIVITIES | PERCENTAGES |
|---|---|
| Problem Sets | 70% |
| Oral Presentation | 30% |
Topics
| WEEK # | TOPICS |
|---|---|
| 1–2 | Acoustic, Elastic, Electromagnetic Wave Equations |
| 3 | Scattering Series and Inversion |
| 4–5 | Migration and Backprojection: Adjoint-state Methods |
| 6–7 | Radar Imaging, Filtered Backprojection, Ambiguity and Resolution |
| 8 | Computerized Tomography, Radon Transform |
| 9–11 | Seismic Imaging, Geometrical Optics, Generalized Radon Transform |
| 12–13 | Optimization, Regularization, Velocity Estimation, Autofocus |
| 14 | Student Presentations |
