Course Outline


The course starts with a review of sampling and reconstruction in one and multiple dimensions. Then it goes on to look at several fundamental problems that occur in medical imaging systems: reconstruction from frequency domain data, reconstruction from projection data, hybrid systems that combine both image and frequency domain information, systems where the data is fundamentally undersampled, and systems where a time series of images is reconstructed. This will provide a wide range of tools for the final projects to use. During the last few weeks we will look at specific systems, including 3D CT systems, and PET systems. The last week will be devoted to well studied and well known imaging problems in MRI.


Week 0: Course Introduction

Week 1: Sampling and Reconstruction

  • Sampling and reconstruction in 1D

  • Sampling, reconstruction, and resampling in 2D

Week 2: Frequency Domain Data

  • Image reconstruction from sampled frequency domain data

  • Non-Cartesian reconstruction: gridding and the NuFFT

  • Examples from MRI

Week 3: Automatic Focusing

  • Off-resonance Correction in MRI

  • Automatic focusing

Weeks 4: Image and Frequency Domain Encoded Data

  • Reconstruction from image and frequency domain encoded data

  • Parallel imaging in MRI

  • The SENSE and GRAPPA algorithms

Week 5: Compressed Sensing

  • Reconstruction from undersampled data

  • Compressed sensing

  • Examples from MRI

Week 6: Compressed Sensing and Machine Learning

  • Training networks to perform image reconstruction

Week 7: Projection Data

  • Image Reconstruction from projection data

  • Fan beam reconstruction: filtered backprojection and rebinning

  • Examples from CT

Week 8: PET Reconstruction

  • PET system models

  • Iterative reconstruction algorithms

Week 9: Special Topics

  • 3D and Spiral CT

  • Hybrid imaging systems (PETCT and PETMR)

  • Projection operator perspective of imaging systems