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This class covers the mathematics of inverse problems involving waves, with examples taken from reflection seismology, synthetic aperture radar, and computerized tomography. There will be occasional problem sets and an oral presentation of a good (landmark, foundational) paper from the literature. Presentations will take place during the class sessions. Topics will be covered such as Scattering Series, inversion, Computerized Tomography and Radon Transform.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer need to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: MIT
Course Curriculum
| Full set of lecture notes in one file | 02:15:00 | ||
| Front Matter, including Table of Contents | 00:10:00 | ||
| Chapter 1 Wave Equations | 00:35:00 | ||
| Chapter 2 Geometrical Optics | 00:15:00 | ||
| Chapter 3 Scattering Series | 00:20:00 | ||
| Chapter 4 Adjoint-state Methods | 00:15:00 | ||
| Chapter 5 Synthetic-aperture Radar | 00:30:00 | ||
| Chapter 6 Computerized Tomography | 00:05:00 | ||
| Chapter 7 Seismic Imaging | 00:05:00 | ||
| Chapter 8 Microlocal Analysis of Imaging | 00:20:00 | ||
| Chapter 9 Optimization | 00:05:00 | ||
| Appendix A Calculus of Variations, Functional Derivatives | 00:05:00 | ||
| Appendix B Finite Difference Methods for Wave Equations | 00:05:00 | ||
| Appendix C Stationary Phase | 00:05:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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