Inverse Problems in Imaging

Course Overview

This course teaches students the mathematical principles and computations that underpin modern imaging systems from an inverse-problems perspective. The course begins with linear and nonlinear regression to establish the broad base of linear algebra and optimization tools needed to solve inverse problems. Once this base has been established, the course will investigate a wide variety of inverse problems in medical (and non-medical) imaging: deconvolution (and blind deconvolution); compressed sensing and non-uniform FFTs (as used in MRI); phase retrieval and ptychography (from Fourier optics); X-ray computed tomography; refracted/bent-ray ultrasound tomography; electrical impedance tomography; diffraction tomography/full-waveform inversion; and aberration correction in ultrasound beamforming.

By covering several different imaging modalities, we show how the mathematical theory is put into practice. This course emphasizes the direct translation of mathematical ideas into practical algorithms that reconstruct images from the raw data. Towards the end of the course, we expose students to automatic differentiation software (e.g., JAX, PyTorch, TensorFlow) that leverages the core mathematical concepts discussed in the course and extend the discussion to the underlying hardware-level considerations (memory bandwidth, latency, checkpointing, and storage-rematerialization tradeoffs).

Syllabus

Download the detailed course syllabus

Course Materials (Coming Soon)

Complete course materials are currently under development. I plan to make the full set of lecture slides (including YouTube lecture playlist), example code, homework assignments, and the final project available here. As part of this effort, I am also revising the course to transition from MATLAB-based scripts to a fully Python-based workflow using Jupyter notebooks. This transition will provide students with an interactive computational environment while making the course materials more accessible. Progress is underway—check back soon for the complete course materials.