T-3: Iterative methods for image reconstruction

Date: Wednesday, May 14

Presented by

Jeff Fessler, University of Michigan, USA

Abstract

This tutorial will give a general introduction to the field of iterative image reconstruction. This field has become increasingly important recently. In particular, an important milestone in this field took place in the late 1990's: the commercial release of 2D and 3D statistical image reconstruction methods for PET and SPECT systems. These methods have now been adopted for routine use in clinical PET and SPECT imaging. As computer speeds continue to improve, there is also increasing interest in iterative reconstruction methods for CT and MRI. This tutorial will provide an orderly overview of the potpourri of iterative methods for image reconstruction, emphasizing the fundamental issues that one must consider when choosing between different reconstruction approaches. The focus will be on models, cost functions, regularization, and algorithms. Examples will be drawn from PET, SPECT, CT, and MRI.

Short breaks will be taken between the different sections of this course. However, those breaks may not correspond to the timing of the "Part 1" and "Part 2" of the other courses. Attendees are welcome to leave after 2 hours to attend a different "Part 2" or to come to this course half way through the time, but the presentation will be organized as one complete course rather than as two halves.

Outline (tentative):

1. Introduction
• Overview
• Mathematical statement of the reconstruction problem
2. The Statistical Framework
• Image parameterization
• Bases
• System physical modeling
• detector response
• projector/backprojectors
• Statistical modeling of measurements
• Objective functions
• Contrast with "algebraic" methods
• Bayesian estimation: Maximum a posteriori (MAP) methods
• Data-fit terms
• likelihood, quadratic, robust
• Regularization
• none
• separable
• quadratic
• convex
• nonconvex, entropy, ...
• Object constraints
3. Iterative algorithms for statistical image reconstruction
• EM based (EM, GEM, SAGE, OSEM)
• Direct optimization (Coordinate Descent, Conjugate Gradient, Surrogate Functions)
• Considerations (nonnegativity, parallelizability, convergence rate)
• Optimization transfer / surrogate functions
• Ordered subsets / block iterative algorithms
• acceleration properties
• convergence issues
4. Iterative reconstruction algorithm characterization
• Spatial resolution properties
• Noise properties
5. Example applications
• X-ray CT
• MRI
• Compressed sensing approaches for under-sampled data

(A fairly extensive bibliography will be provided.)

Speaker Biography

Jeff Fessler received the BSEE degree from Purdue University in 1985, the MSEE degree from Stanford University in 1986, and the M.S. degree in Statistics from Stanford University in 1989. From 1985 to 1988 he was a National Science Foundation Graduate Fellow at Stanford, where he earned a Ph.D. in electrical engineering in 1990. He has worked at the University of Michigan since then. From 1991 to 1992 he was a Department of Energy Alexander Hollaender Post-Doctoral Fellow in the Division of Nuclear Medicine. From 1993 to 1995 he was an Assistant Professor in Nuclear Medicine and the Bioengineering Program. He is now a Professor in the Departments of Electrical Engineering and Computer Science, Radiology, and Biomedical Engineering.

Dr. Fessler is a Fellow of the IEEE. He received the Francois Erbsmann award for his IPMI93 presentation. He serves as an associate editor for IEEE Transactions on Medical Imaging and is a past associate editor for the IEEE Transactions on Image Processing and the IEEE Signal Processing Letters. He was co-chair of the 1997 SPIE conference on Image Reconstruction and Restoration, technical program co-chair of the 2002 IEEE International Symposium on Biomedical Imaging (ISBI), and was general chair of ISBI 2007. His research interests are in statistical aspects of imaging problems, and he has supervised doctoral research in PET, SPECT, X-ray CT, MRI, and optical imaging problems. His web site contains an extensive image reconstruction toolbox.