Wavelets and multiscale techniques

Research into wavelets and multiscale techniques carried out at the University of Bristol’s School of Mathematics has found application in areas as diverse as hair analysis, banking, image compression, digital signal processing, marketing and finance.

The techniques have improved on existing methods and have been incorporated into software packages that are used by millions of users across the globe.

“Wavelets and multiscale techniques are important because they permit more realistic modelling of many real-world phenomena compared to previous techniques and they are fast and efficient.” - Professor Guy Nason

Fabric wear

People believe that tasks such as determining whether a piece of fabric is worn or in good condition are relatively simple. However, objectively analysing fabric wear, for a large number of fabric samples, is actually a time-consuming and difficult task.

Computers can solve this task by the use of complex innovative statistical methods. Such methods can also be vital for other problems such as analysing and forecasting large amounts of financial data, efficiently compressing images and cleaning up noisy medical scans.

Thanks to work by researchers from Bristol’s School of Mathematics, international company Unilever now uses specific types of mathematical functions, called wavelets, to assess the effectiveness of washing detergents on textiles and also the effect of shampoo on hair.

Working with researchers at Unilever, Bristol researchers developed texture analysis modelling and simulation methods for hair product development and new ways of analysing fabric pilling, the surface defects of textiles caused by wear. More classical methods could not easily cope with changing patterns on textiles or sudden changes in texture.

Applications for wavelet statistical methods

The wavelet methods that the Bristol groups of Professor Guy Nason and Professor Bernard Silverman developed have not only helped Unilever, but they’ve also advanced applications in several other industries such as banking, digital signal processing, marketing and finance.

“Wavelets and multiscale techniques are important because they permit more realistic modelling of many real-world phenomena compared to previous techniques,” said Professor Nason from the University of Bristol’s School of Mathematics.

“Wavelets are also fast and efficient. For example, they can be used to clean up X-ray and magnetic-resonance images whilst retaining intricate edge structures. They can also be used to compress images using methods as described by the JPEG2000 standard.”

Estimating inflation

The work done by the Bristol group was also used by Reserve Bank of New Zealand (RBNZ) for estimating inflation. New Zealand was the first world economy to introduce inflation targeting, dramatically improving its inflation performance from the worst to among the middle of the pack.

One of the main problems with measuring inflation concerns the presence of short-lived shocks that should not influence policy makers’ actions.

Wavelets were specifically designed for isolating short-lived phenomena from long term trends in a signal. Bristol’s research and software helped influence RBNZ to explore multiscale methods and wavelet shrinkage methods to assist inflation control in New Zealand.

Embodied in software

The Bristol work is now embodied in software used by researchers and companies across the globe for a wide variety of applications.

This software includes freeware, distributed via international online repositories, and major commercial software, such as Matlab, an important numerical computing environment and programming language with over one million users worldwide.

Matlab’s customers use their wavelet software for a wide variety of applications including oceanography, sensor validation, medical imaging, homeland security imaging and fault detection in manufacturing.