Machine Learning for Inverse Problems
Modern imaging systems employ advanced computational imaging techniques to enable various types of imaging beyond what is achievable by conventional imaging methods. Applications for such systems are ubiquitous, ranging from medical diagnosis to astronomy to agriculture. Designing efficient solutions for such imaging systems typically involves developing a mathematical model of the system, analyzing it using tools and techniques from information theory, signal processing, and machine learning, and finally using a great amount of artful engineering to develop a solution that works in practice.
In this course we will look into various computational imaging solutions. In addition to methods that been around for decades now, we will also look into emerging solutions such as snapshot compressive imaging. For each system, we will start by a brief overview of the physics of the problem, and then will focus on the mathematical modeling of the corresponding inverse problem, and different methods to solve such inverse problems.
Announcements:
Homework 1 posted on Canvas. Due date: Feb 6
Homework 2 posted on Canvas. Due date: Feb 23
Tentative syllabus:
Introduction to computational imaging and inverse problems
Compressed sensing:
Under-determined linear systems
Example application: MRI
Algorithm design approaches
Classic signal structure: Sparsity
Classic methods: BP, OMP, ISTA and FISTA
Beyond sparsity:
Complex source structures
Compression-based models
Generative models
Deep image prior & Deep decoder
Deep learning for solving inverse problems:
End-to-end methods
Unrolled solutions
Iterative solutions
Non-linear inverse problems:
Phase retrieval
Application: Crystallography
Geometric optics vs. wave optics
Coherent imaging methods
Examples: Digital holography, SAR, OCT
Key issue: Speckle noise
Other topics:
ADMM method and its applications in computational imaging
Snapshot compressive imaging