Wavelet transform

Multiresolution Applications for Image and Data Analysis

A privileged insight into data and information. Applications in medicine, astronomy, surveillance and security, Earth observation, telecommunications, financial engineering, multimedia, plasma physics, and other fields.

Starck, J.-L., and Murtagh, F., Astronomical Image and Data Analysis, Springer-Verlag, 2002. (Hardcover, ISBN 3-540-42885-2.) Online version of 1st end. 2nd edn., 2006.
Starck, J.-L., Murtagh, F. and Bijaoui, A., Image Processing and Data Analysis: The Multiscale Approach, Cambridge University Press, 1998. (Hardback and softback, ISBN 0-521-59084-1 and 0-521-59914-8.) Online version.

MR/1 logo

MR Multiresolution Analysis Software Package
100,000 lines of C++, 5000 lines of IDL
Executables for major Unix and Windows platforms

All about the MR Multiresolution Analysis package

Examples of Applications

MR/1 Edge Detection with examples from oceanography, land processes, and echocardiography. (Added: 2001.1.23)
Wavelet-based lossless image compression, a short paper in Postscript, published in the Irish Astronomical Journal in 1999, showing a simple, exact relationship between low resolution versions of an image with the full resolution version.
Seismology - looking for transient events in a signal.
Financial modeling and prediction - and use in environmental modeling or for process control.
Comet nucleus - looking into the nucleus and surroundings of a comet.
Echocardiography - using ulstrasound to non-invasively see the structure of the heart.
Surveillance - where is the minefield?
Galaxy and stars - separating into layers what we observe.
Noise - an ever-present foe.
Mammogram - for image transfer to breast cancer specialists.
Radar view of Earth - as seen from the ERS synthetic aperture radar satellites.
Architectural backbone - the edges of an image.
Earth observation - urban and rural landscapes.
Jetstream - superimposed environmental fluctuations.
Predicting the S&P 500 index - financial engineering, using the elasticity of time.
Web middleware engineering - understanding telecommunications traffic.
Text and hypertext - information discovery and retrieval.
Cluster analysis - tackling the curse of dimensionality in multivariate data analysis.
Further astronomical examples - X-ray image filtering, deconvolution.
Geographic information systems - US agricultural and financial policy-making.
AFM images of semiconductor quantum dots - counting using mr_detect.
Integrated deconvolution and vision modeling
Microstructure of concrete - speckle removal from SEM images.

Some Further Pointers
MR/1 and MR/2 can be used on the command line (Unix, Dos), in IDL, or via a Java user interface.

Program - mr_transform - the multiresolution transform program.
Program - mr_filter - the multiresolution filtering program.
Program - mr_pfilter - filtering X-ray or point pattern data.
A Quick Start to Using the MR/1 Software Package with images for downloading.
Notes on deconvolution - what makes this approach very effective.
Notes on compression - again, what makes this approach both effective and efficient.

Last update: November 1999. Contact: fmurtagh@acm.org This page: http://strule.cs.qub.ac.uk/~fmurtagh/multires