# The Role of Analytic Methods in Image Reconstruction from Projections

Research Director, CNRS, Hubert Curien Laboratory, Saint Etienne, France and Adjunct Professor, Department of Physics, Carleton University

September 29, 2015 13:00 - 14:30

Mackenzie Building Room 3356, Carleton University

Registration not required.

# abstract

Image reconstruction from projections is the field that deals with theory and algorithms for tomographic imaging. The main application area of this field is in the reconstruction of medical images from positron emission tomography (PET) scanners, from single photon emission computed tomography (SPECT) scanners, and from x-ray computed tomography (CT) scanners, all of which share the same first-order imaging model.

Algorithms for image reconstruction fall into two broad categories: analytic methods and iterative methods. Analytic methods follow an "inverse problems" approach where the forward problem is treated mathematically and an explicit inversion formula is sought, which is then discretized for implementation. For iterative methods, the forward problem is immediately discretized to form a huge system of linear equations which is solved using a "guess and update" approach. In general, analytic methods are regarded as computationally much faster, but less accurate because only highly simplified versions of the forward problem are tractable. However, the analytic methods provide insights into the nature of the tomographic reconstruction problem whereas the iterative methods are usually generic and could be applied to any large system of equations.

These points will be reviewed during the presentation. Although analytic algorithms are still used in some situations where the matrix system is still too large for reasonable image reconstruction times using iterative methods, the benefits of a more accurate forward model are driving the current trend to replacing analytic methods with iterative approaches. The ultimate role of analytic methods will be discussed.

# biography

Dr. Clackdoyle attended Fisher Park High School here in Ottawa, followed by a BSc in Mathematics and a MSc in Computer Science at Queen's University in the area of image reconstruction for a 3D PET camera. He held research positions at CERN (Geneva, Switzerland) and the Royal Marsden Hospital (London, UK), prior to completing his PhD in Mathematics at Dalhousie University on Minkowski geometry and the isoperimetric problem. Dr. Clackdoyle completed postdoctoral studies at the Medical Imaging Research Laboratory (MIRL) at the University of Utah and at the Mathematics Institute in the University of Freiburg, Germany. He then became a Professor of Radiology, MIRL, University of Utah. His current position is a Research Director with the CNRS, Hubert Curien Laboratory, in Saint Etienne, France for the past 9 years. His principle research interests are the theory and algorithms for image reconstruction with applications to PET, SPECT, and CT modalities.

Last updated September 24, 2015