Details of Grant 

EPSRC Reference:	GR/S64059/01
Title:	Multiple 2-Dimensional Morse Wavelet Analysis with Applications in Geophysics
Principal Investigator:	Olhede, Professor SC
Other Investigators:
Researcher Co-Investigators:	Dr FJM Simons
Project Partners:
Department:	Mathematics
Organisation:	Imperial College London
Scheme:	First Grant Scheme Pre-FEC
Starts:	01 May 2004	Ends:	30 April 2006	Value (£):	115,380
EPSRC Research Topic Classifications:	Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:	Environment
Related Grants:
Panel History:
Summary on Grant Application Form
Multi-dimensional processes are ubiquitous in the Physical Sciences, and therefore their analysis is of great importance. Unfortunately the processes would in many cases fail to satisfy common simplifying assumptions, and the estimation of characteristics of the process is often unstable. Greater understanding of these processes could be achieved if better estimation procedures were available. Possible areas of application range from analysing data-sets acquired in the study of gravity, planetary problems and seafloor topography, and would so contribute to the understanding of the physical systems we live in. The key to better estimation methods lie in appropriate modeling and suitable implementation procedures, with statistical methods providing measures of the uncertainty associated with the estimation. We propose to center our modelling around the multi-dimensional Hilbert transform, and the variance-stabilizing multiple use of orthogonal filters, which should allow us to better recognize patterned features of the process, in a stable fashion. The Hilbert transform allows us in a sensible fashion to distinguish between amplitude and phase of signals, and will allow us to account for this in the modelling. In essence we hope to better characterise the underlying processes, and then using a suitable averaging mechanism achieve better stability. This should provide more information of the important physical properties of the processes analysed.
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Organisation Website:	http://www.imperial.ac.uk