Sparse on-line Gaussian processes

We develop an approach for sparse representations of Gaussian Process (GP) models (which are Bayesian types of kernel machines) in order to overcome their limitations for large data sets. The method is based on a combination of a Bayesian online algorithm together with a sequential construction of a relevant subsample of the data which fully specifies the prediction of the GP model. By using an appealing parametrisation and projection techniques that use the RKHS norm, recursions for the effective parameters and a sparse Gaussian approximation of the posterior process are obtained. This allows both for a propagation of predictions as well as of Bayesian error measures. The significance and robustness of our approach is demonstrated on a variety of experiments.

Sparse on-line Gaussian processes

We develop an approach for sparse representations of Gaussian Process (GP) models (which are Bayesian types of kernel machines) in order to overcome their limitations for large data sets. The method is based on a combination of a Bayesian online algorithm together with a sequential construction of a relevant subsample of the data which fully specifies the prediction of the GP model. By using an appealing parametrisation and projection techniques that use the RKHS norm, recursions for the effective parameters and a sparse Gaussian approximation of the posterior process are obtained. This allows both for a propagation of predictions as well as of Bayesian error measures. The significance and robustness of our approach is demonstrated on a variety of experiments.

Projection and interpolation based techniques for structured and impulsive noise filtering

In this chapter we present the relevant mathematical background to address two well defined signal and image processing problems. Namely, the problem of structured noise filtering and the problem of interpolation of missing data. The former is addressed by recourse to oblique projection based techniques whilst the latter, which can be considered equivalent to impulsive noise filtering, is tackled by appropriate interpolation methods.

Visual data mining using principled projection algorithms and information visualization techniques

We introduce a flexible visual data mining framework which combines advanced projection algorithms from the machine learning domain and visual techniques developed in the information visualization domain. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection algorithms, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates and billboarding, to provide a visual data mining framework. Results on a real-life chemoinformatics dataset using GTM are promising and have been analytically compared with the results from the traditional projection methods. It is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework. Copyright 2006 ACM.

Clinical studies of spatial and temporal aspects of vision: an investigation using psychophysical and electrophysiological techniques

Separate physiological mechanisms which respond to spatial and temporal stimulation have been identified in the visual system. Some pathological conditions may selectively affect these mechanisms, offering a unique opportunity to investigate how psychophysical and electrophysiological tests reflect these visual processes, and thus enhance the use of the tests in clinical diagnosis. Amblyopia and optical blur were studied, representing spatial visual defects of neural and optical origin, respectively. Selective defects of the visual pathways were also studied - optic neuritis which affects the optic nerve, and dementia of the Alzheimer type in which the higher association areas are believed to be affected, but the primary projections spared. Seventy control subjects from 10 to 79 years of age were investigated. This provided material for an additional study of the effect of age on the psychophysical and electrophysiological responses. Spatial processing was measured by visual acuity, the contrast sensitivity function, or spatial modulation transfer function (MTF), and the pattern reversal and pattern onset-offset visual evoked potential (VEP). Temporal, or luminance, processing was measured by the de Lange curve, or temporal MTF, and the flash VEP. The pattern VEP was shown to reflect the integrity of the optic nerve, geniculo striate pathway and primary projections, and was related to high temporal frequency processing. The individual components of the flash VEP differed in their characteristics. The results suggested that the P2 component reflects the function of the higher association areas and is related to low temporal frequency processing, while the Pl component reflects the primary projection areas. The combination of a delayed flash P2 component and a normal latency pattern VEP appears to be specific to dementia of the Alzheimer type and represents an important diagnostic test for this condition.

Evaluating techniques to improve visual performance with and assessment of premium intraocular lenses

Premium Intraocular Lenses (IOLs) such as toric IOLs, multifocal IOLs (MIOLs) and accommodating IOLs (AIOLs) can provide better refractive and visual outcomes compared to standard monofocal designs, leading to greater levels of post-operative spectacle independence. The principal theme of this thesis relates to the development of new assessment techniques that can help to improve future premium IOL design. IOLs designed to correct astigmatism form the focus of the first part of the thesis. A novel toric IOL design was devised to decrease the effect of toric rotation on patient visual acuity, but found to have neither a beneficial or detrimental impact on visual acuity retention. IOL tilt, like rotation, may curtail visual performance; however current IOL tilt measurement techniques require the use of specialist equipment not readily available in most ophthalmological clinics. Thus a new idea that applied Pythagoras’s theory to digital images of IOL optic symmetricality in order to calculate tilt was proposed, and shown to be both accurate and highly repeatable. A literature review revealed little information on the relationship between IOL tilt, decentration and rotation and so this was examined. A poor correlation between these factors was found, indicating they occur independently of each other. Next, presbyopia correcting IOLs were investigated. The light distribution of different MIOLs and an AIOL was assessed using perimetry, to establish whether this could be used to inform optimal IOL design. Anticipated differences in threshold sensitivity between IOLs were not however found, thus perimetry was concluded to be ineffective in mapping retinal projection of blur. The observed difference between subjective and objective measures of accommodation, arising from the influence of pseudoaccommodative factors, was explored next to establish how much additional objective power would be required to restore the eye’s focus with AIOLs. Blur tolerance was found to be the key contributor to the ocular depth of focus, with an approximate dioptric influence of 0.60D. Our understanding of MIOLs may be limited by the need for subjective defocus curves, which are lengthy and do not permit important additional measures to be undertaken. The use of aberrometry to provide faster objective defocus curves was examined. Although subjective and objective measures related well, the peaks of the MIOL defocus curve profile were not evident with objective prediction of acuity, indicating a need for further refinement of visual quality metrics based on ocular aberrations. The experiments detailed in the thesis evaluate methods to improve visual performance with toric IOLs. They also investigate new techniques to allow more rapid post-operative assessment of premium IOLs, which could allow greater insights to be obtained into several aspects of visual quality, in order to optimise future IOL design and ultimately enhance patient satisfaction.