Wavelets, ICA and statistical parametric mapping : with application to agitation-sedation modelling, detecting change points & to neuroinformatics
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The wavelet methods developed, advocated and used in this thesis are primarily based on the discrete wavelet transform (DWT), wavelet thresholding and density estimation via wavelet smoothing. First a suite of wavelet techniques are advocated, based on the DWT, and applied successfully to assess whether an ICU patient's simulated" agitation-sedation (A-S) status reflects their true dynamic A-S profile. The use of quantitative modelling to enhance understanding of the A-S system and the provision of an A-S simulation platform are key tools in this area of patient critical care. Secondly novel wavelet density metrics are developed, a wavelet time coverage index (WTCI) and a wavelet probability band (WPB), based on Bayesian density estimation. This led to the development of two numeric metrics, the average normalized wavelet density and the relative average normalized wavelet density; both shown to be in close agreement to our DWT and earlier metrics."The DWT and WPB approaches also yield excellent visual assessment tools and are generalisable to any study involving bivariate time series of a large number of units (patients, households etc) and of significant length. P Wavelet thresholding and independent component analysis (ICA) are tested as denoising methods, and applied to brain image data, as part of the neuro-informatics study of Turner et al. (2003). ICA methods are then implemented for denoising all the cerebral function data, at a voxel by voxel basis. This is performed as a preprocessing step to the creation of statistical parametric maps (SPMs), used to model brain function with respect to personality as non-linear models. The results derived from our novel SPM-ICA approach support the theory of a biological basis for personality and report more de/activation clusters in the brain, as related to specific personality traits than Turner et al. (2003). Our work gives credence to a growing body of thought for the need of non-linear modelling in psychometric research (Cloninger, 2008). Our work also has the potential to increase momentum for patient specific drugs for depressives. Lastly we develop a DWT based methodology for change point analysis that uses modified, maximal overlap DWT (MODWT) coefficients to link to a novel shifting DWT (SDWT) methodology - a combination of the DWT and MODWT for the change point detection problem, which is shown to provide an accurate and computationally efficient change point location method. SWDT can be generalized to find multiple change points, by way of a binary segmentation procedure and iteration.