Inverse problems and imaging

This course is taught to Master 2 ESTEL students.

Description

The objective of this course is to present a unified approach to solve inverse problems in imagery.

Content

1. Introduction of image processing
   • Elementary image transforms, edge detection
   • Convolutions in space domain and Fourier domain, border conditions
   • Matrix representation of convolution and properties
   • Inverse problem formalism, regularization
2. Introduction to convex optimization
   • Convexity of sets and functions
   • Convex optimization problem
   • Duality and KKT conditions
   • Descent algorithms, projected gradient
   • Interior point algorithms
3. Application to deconvolution
   • Tikhonov regularization and Wiener filtering
   • ISRA algorithm
4. Image reconstruction in radioastronomy
   • Basics of radio-interferometry
   • Effects of long baselines and wide field of view
   • Measurement model and algorithms

Practical work

A large part of the course is devoted to practical projects, where the students will code various algorithms and compare theoretical results with simulation results. The computations will be preferentially carried out in julia or python.