A broad overview of mathematical and computational methods for inverse problems, with applications in data and physical sciences. The course assumes some affinity with undergraduate mathematics, but is otherwise suited to graduate students from all departments. The evaluation will consist of homework problems, and a project of the student's choice. The project can either consist in reproducing results from the literature, or can be research-oriented.

**Topics:**

- Regression, regularization, and iterative schemes for smooth optimization
- Maximum likelihood estimation and the Bayesian framework
- Duality and recovery theory for sparse regression and matrix completion
- Dimension reduction by random projection
- Proximal and primal-dual iterative schemes for nonsmooth optimization
- Algebraic methods of superresolution

Notes: 02/08, 02/13, 02/15, 02/22, 02/27, 03/01, 03/06, 03/08, 03/13, 03/20, 03/22, 04/03, 04/10, 04/12, 04/19, 04/24, 04/26, 05/01, 05/03, 05/08.

There is no required textbook. The material will be inspired from various sources beyond the notes, list TBA.

Some code used in class: descents.zip.

**Prerequisites:** Some undergraduate familiarity with: Linear algebra and matrix computations, including least-squares,
eigenvalues, and singular values. Basic probability. Numerical analysis. Fourier transform/series.

We will meet T-Th from 2:30 pm to 4:00 pm in room 2-146. Instructor: Laurent Demanet. Contact info. Office hours: W 2-4, or else email.

The evaluation will consist in problem sets and a project. The project can be computational or theoretical; related to your research or not; or can consist in the oral presentation of a good (landmark, foundational) paper from the literature. Talk to your advisor or to me if you'd like a recommendation of a good paper. Propose a topic for your project to me by early March. Breakdown: 50% hw, 50% project. The presentations will be in class on May 15 and May 17. The project report should be at most 5 pages, typeset, and is due on May 17 for everyone.

**Homework problems:**