In spring 2019 I will teach a new course on inverse problems and learning (ECE598ID).

Inverse problems are central in engineering and science. Most interesting inverse problems are ill-posed and need to be regularized. This course will cover fundamentals of inverse problems theory including elements from functional analysis, regularization theory, and optimization. The idea is to do a mathematical introduction to the theory of inverse problems and regularization and then address the major machine learning and -driven techniques. A special emphasis will be placed on the theory and applications of machine learning in inverse problems, in particular dictionary and transform learning and applications of deep neural networks and generative adversarial networks.

Link to the current offering is here.

Course description

  1. Introduction to inverse problems, regularization, and learning
  2. Concepts from functional analysis
  3. Classical regularization theory
  4. Statistical perspective on inverse problems
  5. Sparsity-based regularization, duality and recovery theory, compressed sensing + representation and convergence theory in Banach spaces
  6. Learning sparse models (dictionaries, sparsifying transforms)
  7. Plug-and-play regularization, regularization by denoising
  8. Quadratic and bilinear inverse problems (phase retrieval, low-rank matrix recovery)
  9. Deep neural networks for inverse problems
    • Neural networks and approximation results
    • Learned iterative methods, LISTA
    • Regularization by generative adversarial networks
  10. Applications of machine learning in inverse problems
    • Amortised MAP for deblurring and super-resolutions
    • U-Nets for normal equations in computed tomography
    • Recursive structures for multiple scattering problems

Prerequisites

  • ECE 313, ECE490, ECE513, or their equivalents
  • Programming in Python (Matlab)