Topics in Mathematical Data Science

Course Description

Computational imaging studies how computation and mathematical modeling can be used to form images from indirect, incomplete, or noisy measurements. This course introduces the mathematical and computational foundations of modern computational imaging, with an emphasis on inverse problems and reconstruction algorithms.

Lecture Topics

Intro to Computational Imaging
Images as Functions and Vectors
Image Restoration (Denoising and Inpainting)
Image Restoration (Deblurring and Super-resolution)
Image Reconstruction (CT)
Image Reconstruction (MRI)
Ill-Posedness and Regularization
Bayesian Inverse Problems
Smooth Optimization
Nonsmooth Optimization
Proximal Gradient Method
Alternating Direction Method of Multipliers
Sparse Models and Compressed Sensing
Total Variation Regularization