Inverse problems are central in engineering and science. Most interesting inverse problems are ill-posed and need to be regularized. This course will cover the fundamentals of inverse problems theory including elements from functional analysis, regularization theory, and optimization. After covering the fundamentals of inverse problems, the theory and applications of machine learning to solve inverse problems will be addressed.

A good part of the course will be on the major machine learning and data driven techniques. In particular dictionary learning, transform learning and applications of deep neural networks and generative adversarial networks will be covered.

Tuesday and Thursday, 12:30–1:50pm, 2013 ECEB

Instructor: Ivan Dokmanić, dokmanic at illinois dot edu (Office hours: Tuesdays 4:30pm–5:30pm, CSL 313)

Teaching assistant: Sidharth Gupta, gupta67 at illinois dot edu (Office hours: TBD)

January 15 2019: Course begins!

TBD

Week 1 (1/14–1/18)

Lecture 1: Introduction to inverse problems

Notes: Introduction

Lecture 2: Background in functional analysis

Additional material: Survey paper: Definitions and examples of inverse and ill-posed problems

Additional material: Introduction to Inverse Problems

Week 2 (1/21–1/25)

Lecture 1: Examples forward and inverse problems

Lecture 2: Classical regularization

Week 3 (1/28–2/1)

Lecture 1: Statistical perspective on inverse problems and regularization

40% homeworks

30% one midterm

30% class project

Scherzer, Otmar, Markus Grasmair, Harald Grossauer, Markus Haltmeier, and Frank Lenzen.

*Variational methods in imaging*. Springer Science+ Business Media LLC, 2009.