Sofia Olhede
– Research Interests
My fundamental research interest is modelling complex
and heterogeneous phenomena observed in time or space. The tools to easily form
models for such phenomena come from harmonic analysis and correspond to Fourier
transforms, or local alternatives to such decompositions. Because very few
signals appear identical when observed at multiple instances, I model structure
as stochastic, and design methods to estimate such signal population structure.
Analysis of
MRI data
Magnetic Resonance Imaging (MRI) allows us to measure
the Fourier transform of a time/space domain signal. For diffusion weighted
magnetic resonance imaging this corresponds to the Fourier transform of a
probability density function (PDF) of spatial diffusion. I have been developing
nonparametric methods to quantify the spatial structure of such a PDF. I also
design inference methods for other signal modalities such as EEG data.
Publication:
Olhede, S. and Whitcher B., A statistical
framework to characterise microstructure in high angular
resolution diffusion imaging, Biomedical
Imaging: From Nano to Macro, 2008. ISBI 2008. 5th
IEEE International Symposium on 14-17 May 2008 Page(s):899 – 902.
Inference
for Noisy Diffusions
Stochastic Differential Equations are used to model
processes in Finance, Oceanography and a variety of other areas. Modern data
acquisition protocols enable the high frequency sampling of such processes.
Unfortunately most sampling procedures are not noise-free and so any analysis
method must cope with additional noise structure. This can be a very hard
problem to tackle in the time domain, as information across several different
scales must be combined to get a good appreciation of the noise level. In the
Fourier domain, the problem simplifies considerably and leads to simple and
effective inference procedures.
Publication:
Olhede S. C., Sykulski A.
and Pavliotis G. Multiscale
Inference for High-Frequency Data, Department of Statistical Science Reseach Report 290. Version available at http://arxiv.org/abs/0803.0392
To appear in SIAM MMS.
Analysis of Nonstationary Multiple Time series
Temporal phenomena are rarely observed in isolation,
and often we wish to infer the joint properties of multiple phenomena. This is
a very difficult problem, and standard notions of defining nonstationary
multiple processes are less than perfectly elegant, requiring very strong
assumptions on joint structure or smoothness. I have been developing flexible
analysis methods for pairs of nonstationary signals
observed in physical oceanography.
Publications:
Lilly J. and Olhede S. C. Higher Order Properties of Analytic Wavelet IEEE Transactions on Signal Processing , 57, Page(s):146 – 160.
Lilly J.
and Olhede S. C. Bivariate Instantaneous Frequency
and Bandwidth, To appear in IEEE Transactions on
Signal Processing, http://arxiv.org/abs/0902.4111
.
Analysis of phenomena
in 2-D and 3-D
Spatial phenomena are distinct from temporal
processes. For temporal processes, time has not just structure but also
directionality: most phenomena should not operate identically under
time-reversal. Spatial processes usually do not exhibit any natural ‘ordering’,
and so are fundamentally different from temporal phenomena. Spatial phenomena
are often local, and highly heterogeneous. I have been developing methods of
characterising local heterogeneous spatial structure using triplets of wavelet
functions.
Publications:
Metikas, G. and Olhede, S. C. Multiple
Multidimensional Morse Wavelets. IEEE
Transactions on Signal Processing, 55, 921—936.
Olhede, S. C. Hyperanalytic Denoising. IEEE Transactions on Image Processing, 16, 1522—1537.
Olhede, S. C. Localisation of Geometric Anisotropy. IEEE Transactions on Signal Processing, 56, 2133—2138.
Olhede S
and Metikas G. The
Monogenic Wavelet Transform, Appeared in IEEE Transactions on Signal
Processing, 57, Pages: 3426-3441 .