In this course we will define inverse problems and discuss some general methodology for their solution. In particular we will focus on linear inverse problem. Using these tools, we will study some classic and modern inverse problems. About half of the course will be theoretical development and the other half will be application to specific problems.
This course will provides full details on a vriety of inverse problem-solving techniques, includes examples and algorithms.
1. Introduction / Linear Algebra
2. Linear Inverse Problems
4. Singular value decomposition
5. Nonlinear inverse problems
6. Generalized Inverse
7. Least Squares (smoothness, weighting)
8. Maximum Liklihood and EM Algorithm
9. Baysian Estimation
10. Theory of the Computed Tomography
""Inverse engineering hand book"" K.A.Woodbury, CRC Press
""Computed Tomography,"" J.Hsieh, SPIE Press
This class requires knowledge of fundamentals on the numerical analysis the signal processing in undergraduate levels.
Evaluation will be based on the term-end examination.