IMANTS SVALBE

Senior Lecturer BSc (Hons) Physics, 1974 PhD Physics, Univ. of Melb., 1979 Phone +61 (3) 9905 3679 FAX +61 (3) 9905 3637 Email:Imants.Svalbe@sci.monash.edu.au

RECENT RESULTS FRT-based image reconstruction (of a wooden block in the centre of a pipe) obtained from experimental x-ray profiles obtained at digital angles determined by rational fractions from the Farey series (89x 89 image). Data acquired and processed by B.Rad. Honours student Kevin Wan and Dr Russell Horney, DMIRS, Monash. Ghost image formed by a set of projections that have positive and negative contributions that sum to zero over a wide range of discrete projection angles. Ghosts like the one shown here cause artefacts in image reconstructions if the projections are not Katz-sufficient.

RESEARCH INTERESTS

Imants current research is on discrete projections. These are used, for example, in medical imaging as x-ray computed tomography (CT). Over the last ten years, Imants has adapted the Finite Radon Transform (FRT), developed by Matúš and Flusser, as a flexible platform to exploit the information held in discrete projections. The FRT is based on square, prime length arrays that permit an exact interconversion of digital images and their discrete projections.

The FRT projections also are related to the mojette projections developed by Prof. Jean-Pierre Guédon of the Image and Vision Computing group (IVC) at the Polytech’ Nantes in France. Mojette projections provide a very general and flexible representation of digital objects. They have a wide range of uses, ranging from secure data encryption to limited-angle tomographic imaging. The collaboration with Nantes researchers has been active since early 2005, resulting in several exchange visits and a Post Doctoral position at Nantes that was held by Imants’ recent PhD student, Andrew Kingston (now at ANU). Monash and the Université de Nantes have signed an MOU through the Faculty of Science to facilitate student and research exchange.

There is a simple, but powerful criterion (by Katz) that determines whether a set of projections (taken at angles that can be represented as rational fractions) can reconstruct an object exactly. Insufficient or missing information gives rise to artefacts or ghost images in the reconstruction. It turns out that these ghosts provide valuable information that can be used to recover and restore missing projection data.

The above approach is currently being used by PhD student Shekhar Chandra to develop an algorithm to reconstruct images for any Katz-sufficient set of projections by mapping them into the easily-invertible FRT form. Other applications of the FRT are to perform interpolation-free image rotation and as the basis of a method to produce images where the spatial resolution varies systematically with location within the reconstructed image.

Other areas of Imants’ research include micro-beam radiation therapy for cancer treatment (with PhD student, Jeff Crosbie), the high fidelity display of high dynamic range data on conventional imaging devices (with Steve Morton) and an ongoing interest in parallel algorithms for nonlinear operators in mathematical morphology.

SELECTED PUBLICATIONS

1. Generalised finite Radon transform for NxN images, A. Kingston and I. Svalbe, Image and Vision Computing, 25 (2007) 1620-1630.
2. Projective Transforms on Periodic Discrete Image Arrays, Andrew Kingston and Imants Svalbe, Advances in Imaging and Electron Physics, 139 (2006) 75-177.
3. Quantised Angular Momentum Vectors and Projection Angle Distributions for Discrete Radon Transforms, Imants Svalbe, Shekhar Chandra, Andrew Kingston and Jean-Pierre Guédon, LNCS 4245, Discrete Geometry and Computer Imagery, Szeged, Hungary, October, 2006.
4. Sampling Properties of the Discrete Radon Transform, Imants Svalbe, Discrete Applied Mathematics, 139 (2004) 265-281.
5. Reconstruction of Tomographic Images using Analog Projections and the Digital Radon Transform, I. Svalbe and D. van der Spek, Linear Algebra and its Applications, 339 (2001) 125-145.