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Data Consistency Conditions in Image Reconstruction from Projections

Dr. Rolf Clackdoyle

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

November 3, 2014 11:30 - 12:30

Canal Building Room 2400, Carleton University

Organizer: Dr. James Green

Registration not required.

abstract

In tomographic imaging such as PET, SPECT, X-ray CT, the data consists of a collection of measured projections. An image reconstruction algorithm is used to process these projections and form an image of the underlying physical parameter of the scanned "object". The physical parameter would be the internal radioisotope distribution for PET and SPECT, and the electron density for X-ray CT.

Even though the projections view the object from different directions, the information about the object is not completely independent from projection to projection. Consistency conditions are mathematical expressions that precisely describe the overlap of information between projections. In a mathematical context, consistency conditions are sometimes called range conditions, where the imaging model is expressed as a mathematical operator acting on a domain of object functions and mapping to a co-domain of projection functions (sometimes called the sinogram domain).

The talk will discuss consistency conditions in tomography, and show how they can be applied to directly estimate the parameters of undesired physical effects (such as beam hardening, scatter, motion artifacts). These effects can then be subtracted from the measurement data, thereby restoring the basic tomographic model. The idea is that the consistency conditions can mathematically separate the physical effects from the tomographic component of the model. Consequently, the reconstruction task is greatly simplified: the smaller (and typically non-linear) estimation problem can be resolved independently of the huge linear system of tomographic equations.

New consistency conditions for truncated projections will be presented, with an example application in patient motion correction.

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.