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.  

Tentative syllabus:

1. Introduction to computational imaging and inverse problems

2. Compressed sensing:

   • Under-determined linear systems

   • Example application: MRI

   • Algorithm design approaches

   • Classic signal structure:  Sparsity

   • Classic methods: BP, OMP, ISTA and FISTA

3. Beyond sparsity:

   • Complex source structures

   • Compression-based models

   • Generative models

   • Deep image prior & Deep decoder

4. Deep learning for solving inverse problems:

   • End-to-end methods

   • Unrolled solutions

   • Iterative solutions

5. Non-linear inverse problems:

   • Phase retrieval

   • Application: Crystallography 

6. Geometric optics vs. wave optics 

7. Coherent imaging methods

   • • Examples: Digital holography, SAR, OCT

     • Key issue: Speckle noise

8. Other topics:

   • • ADMM method and its applications in computational imaging

     • Snapshot compressive imaging