Bernard's Research

My interests in computer science as a tool for investigating problems in medicine led me to postgraduate studies at the University of Western Australia. This page serves as a resource page for this and subsequent research.

Ph.D. dissertation

Dissertation title: Reconstruction for Visualisation of Discrete Data Fields using Wavelet Signal Processing

Abstract: available here

Full text: gzipped Postscript (3.0MB), gzipped PDF (4.8MB)

My dissertation is primarily concerned with the study of wavelet signal processing for the reconstruction of the true natural phenomena, which are continuous, from measurement discrete data. In the ideal sampling and measurement case this is a problem encompassed by the Sampling Theorem of signal processing. Practical measurement data require practical reconstruction techniques.Wavelets provide a toolkit of methods to attack this problem under a unified framework. This framework defines a multiresolution analysis, filtering, interpolation and other operations necessary for manipulation of discrete data and the reconstructed continuous representations. These problems are fundamental to many disciplines, including medical imaging which led me down this research path.

While completing my dissertation write-up, I came across this quotation by Jim Blinn in his article A Bright and Shiny Future in the first issue of the year 2000 IEEE Computer Graphics and Applications journal. Blinn talks about finding better "atoms" than pixels to store digital pictures in this future perspective article. I think it summarises my dissertation research perfectly:

... I want pixels to go away as an image archiving and processing method. An image is actually a continuous function. Converting it to pixels requires choosing a resolution and throwing away information beyond that resolution. Choosing a lower resolution generates fewer pixels to store, but throws away more information. When you really think about it, representing an image as pixels is just a bad image compression technique. Better techniques built on discrete cosine transforms or wavelets are attempts to find better sets of image ``atoms''. Building pictures out of these atoms is more representative of actual images. However, we need still better picture ``atoms''. Converting images to pixels should be a last minute operation for display purposes only ...

A PowerPoint presentation entitiled Wavelets: from Duplo to Lego which summarises some of my work in a (hopefully) accessable and intuitive manner is available for download.

Documents and Software for download

Research in isolation is a fruitless endeavor - it may shine briefly, but quickly fades as it is forgotten. In the spirit of waving the flag of reproducible research and to share the result of my work with the research community I provide some of the more polished bits of software and documents.

Mathematica packages	The reason for implementing algorithms in Mathematica is to make use of the powerful symbolic representation and computation that this software suite provides.
NewPolyLift.m	This package implements the Fast Lifted Wavelet Transform and lifting wavelet filter constructing scheme (see Wim Sweldens' research) for point and average interpolating filters. It also includes various supporting algorithms such as a translation invariant version of the transform, approximation, interpolation, derivative computation and plotting functions. The transforms are implemented in 1D (there's no point trying to run this over 2D data - Matlab numerical algorithms are much more suited for this)
WaveletTools.m	A utility package containing wavelet plotting routines (requires the standard Mathematica Wavelet package), and a number of numerical algorithms to compute approximation order and smoothness of a scaling function, approximation power of scaling functions, scaling function moments, explicit computation of filter coefficients for biorthogonal coiflets and others.

MATLAB packages

Matlab is an excellent tool for prototyping of numerical algorithms. Its many available functions and visualisation tools make the task of algorithm development a lot easier.

please email me if you wish to obtain this package

This is an archive of 1D and 2D Fast Lifted Wavelet Transform algorithms for point and average interpolating filters. This is essentially a numeric implementation of the symbolic Mathematica algorithms. Supporting algorithms include plotting routines, translation invariant transform, approximation, interpolation and derivative interpolation.

The archive includes a number of scripts which run a suite of processing operations on test signals which form the experimental part of my thesis (script_XX.m) - the functions to implement the point and average interpolation filters as well as B-spline filters (first 6 orders) into the Matlab wavelet toolbox are also included and necessary to run the scripts. Routines implementing the visualisation reconstruction filters developed by Torsten Moeller are also included. It still needs a bit of a clean up, hence I'm not making it directly available.

A number of Mathematica notebooks which explore a wide variety of topics on wavelets that I have put together will be available here shortly. Some of these notebooks explore wavelet fundamentals, others explore a particular specialisation experimentally. A few of the most general notebooks are included here. If you do not have access to the Mathematica package, you can download the free MathReader from Wolfram Research, Inc. I will also provide PDF versions of the notebooks for convenience.

D4Analysis.nb	This notebook covers the basics of wavelets based on experiments with the 4-tap Daubechies filters. The experiments are based on material in the excellent book by Gilbert Strang and Truong Nguyen, Wavelets and Filter Banks. The algebraic, vector and frequency domain forms of the dilation equation are explored.
DaubHalfband.nb	Another notebook based on the Strang/Nguyen book - Daubechies filters are explored from the angle of halfband filter factorisation.
BiorHalfband.nb	The halfband filter which gives rise to the orthogonal Daubechies filter is explored for other factorisations which lead to biorthogonal filters.

Old publications (new ones will be included soon)

Refereed Publications:

Bernard Cena, Nick Spadaccini, "Wavelet Shrinkage of Ultrasound Data". In proceedings of Summer School on Wavelets, pp.11-18, Zakopane, Poland, Aug 31-Sept 4, 1996.
ISBN 83-904743-3-6
Fiona M. Wood, Kris Currie, R Bruce Backman, Bernard Cena, "The Current Difficulties and the Possible Future Directions in Scar Assessment". In proceedings of International Symposium for Hypertrophic Scarring, Hong Kong, May, 1995; also published in Burns, Journal of the International Society for Burn Injuries, Butterworth-Heinemann, UK., Vol. 22, No. 6, pp. 455-458, 1996.
ISSN 0305-4179

Unrefereed Publications:

Bernard Cena and Nick Spadaccini, "A Wavelet Based Data Visualisation System". In proceedings of 1997 Department of Computer Science Conference, pp. 37-41, Apr 3-4, Yanchep, WA, 1997.
Bernard Cena, R. Bruce Backman, Fiona Wood, "Image Processing Techniques for Building an Objective Scar Quality Assessment Tool". In Handbook of The Australian and New Zealand Burn Association's 21th Annual International and Regional Congress, Aug 28-30, Adelaide, South Australia, Australia, 1996.
Bernard Cena and Nick Spadaccini, "De-noising Ultrasound Images with Wavelets". In proceedings of 1996 Department of Computer Science Conference, Apr 11-12, Yanchep, WA, 1996.
Bernard Cena, R Bruce Backman, Kris Booth, Fiona Wood, "Computerized Integration of Multimodality Imaging in Scar Assessment". In Handbook of The Australian and New Zealand Burn Association's 20th Annual International and Regional Congress, Aug 22-25, Gold Coast, Queensland, Australia, 1995.
R Bruce Backman, Bernard Cena, Fiona M. Wood, " Scientific Visualization as an Aide to Quantifying the Extent of the Burn Injury". In Handbook of The Australian and New Zealand Burn Association's 20th Annual International and Regional Congress, Aug 22-25, Gold Coast, Queensland, Australia, 1995.

page updated 06 August, 2000.