Recovering missing slices of the discrete fourier transform using ghosts

The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n\log-{2}n) (for an n=N\times N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT

Functional magnetic resonance imaging : methods and applications

The technique of functional magnetic resonance imaging is rapidly moving from one of technical interest to wide clinical application. However, there are a number of questions regarding the method that need resolution. Some of these are investigated in this thesis. High resolutionf MRI is demonstrated at 3.0 T, using an interleaved echo planar imaging technique to keep image distortion low. The optimum echo time to use in fMRI experiments is investigated using a multiple gradient echo sequence to obtain six images, each with a different echo time, from a single free induction decay. The same data are used to construct T2* maps during functional stimulation. Various techniques for correcting the N/2 ghost are tested for use in fMRI experiments, and a method for removing the image artefact caused by external r. f. interference in a non-linearly sampled matrix is presented. The steps in the analysis of fMRI data are detailed, and two new non-directed analysis techniques, particularly for data from single events, as opposed to epoch based paradigms, are proposed. The theory behind software that has been written for fMRI data analysis is also given. Finally, some of the results from an fMRI study into the initiation of movement are presented, illustrating the power of single event experiments in the separation of cognitive processes

Coded aperture breast tumour imaging using a full-size clinical gamma camera

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Projections et distances discrètes

Le travail se situe dans le domaine de la géométrie discrète. La tomographie discrète sera abordée sous l'angle de ses liens avec la théorie de l'information, illustrés par l'application de la transformation Mojette et de la "Finite Radon Transform" au codage redondant d'information pour la transmission et le stockage distribué. Les distances discrètes seront exposées selon les points de vue théorique (avec une nouvelle classe de distances construites par des chemins à poids variables) et algorithmique (transformation en distance, axe médian, granulométrie) en particulier par des méthodes en un balayage d'image (en "streaming"). Le lien avec les séquences d'entiers non-décroissantes et l'inverse de Lambek-Moser sera mis en avant

Functional magnetic resonance imaging : methods and applications

The technique of functional magnetic resonance imaging is rapidly moving from one of technical interest to wide clinical application. However, there are a number of questions regarding the method that need resolution. Some of these are investigated in this thesis. High resolutionf MRI is demonstrated at 3.0 T, using an interleaved echo planar imaging technique to keep image distortion low. The optimum echo time to use in fMRI experiments is investigated using a multiple gradient echo sequence to obtain six images, each with a different echo time, from a single free induction decay. The same data are used to construct T2* maps during functional stimulation. Various techniques for correcting the N/2 ghost are tested for use in fMRI experiments, and a method for removing the image artefact caused by external r. f. interference in a non-linearly sampled matrix is presented. The steps in the analysis of fMRI data are detailed, and two new non-directed analysis techniques, particularly for data from single events, as opposed to epoch based paradigms, are proposed. The theory behind software that has been written for fMRI data analysis is also given. Finally, some of the results from an fMRI study into the initiation of movement are presented, illustrating the power of single event experiments in the separation of cognitive processes

Characterisation of concentrating solar optics by Light Field Method

Abstract: This dissertation develops ideas and techniques for the measurement of the light field produced by the concentrating optics that are used in solar thermal power systems. The research focussed on developing a framework and the principles for the implementation of a scalable technology that is suitable, in principle, for cost effective industrial implementation in the field. Investigation from first principles and technological surveys resulted in formulation of a number of model techniques, from which one was developed. A key component of the proposed model was evaluated using a novel reformulation and application of electrical impedance tomography (EIT). This was to implement an information transform effecting a highly non-linear compressive sensing mechanism, offsetting manufacturing and material complexity in the measurement of high solar flux levels. The technique allows sensing of a wide range of phenomena over arbitrary manifolds in three-dimensional space by utilizing passive transducers. An inverse reconstruction method particular to the structure of the device was proposed, implemented, and tested in a full simulation of intended operation. The parameter space of internal configurations of the method were the subject of a uniform, statistical search, with results also indicating geometrical properties of the transform used. A variety of design guides were developed to better optimize the implementation of the techniques in a range of applications.M.Ing. (Mechanical Engineering Science

Methodology for taking a computer-aided breast cancer screening system from the laboratory to the marketplace

Breast cancer is one of the most common causes of death in women, and yet is one of the more 'curable' cancers if caught early. Since its inception in 1987, the Breast Screening Programme has been the principal tool in the National Health Service's fight to reduce the number of cancer related deaths in the UK. Breast screening using mammography is widely viewed as the most effective way of detecting early breast cancer, with the UK population of women over the age of 50 being invited to a screening session every three years. However, national shortages of clinical staff willing to enter and remain in this field mean that the NHS Breast Screening Programme is severely understaffed. This thesis discusses one way in which technology can assist in the screening programme; specifically, the use of a computer-aided cancer detection system. Here, we will present the design and analysis of a sequence of experiments used to develop and evaluate such a system. PROMAM (PROmpting for MAMmography) involved the scanning and digitising of mammograms, and the subsequent analysis of the digital image by a series of algorithms. Initial evaluation was done to ensure that the algorithms were performing satisfactorily at a technical level before being introduced into a clinical setting. Two large experiments with the algorithms were designed and evaluated: 1. offering radiologists three levels of algorithm prompting and, as a control, an unprompted level, on samples of mammographic films, with outcomes being their recall rate and subjective views at each prompting level, 2. a pre-clinical experiment, conducted under semi-clinical conditions, where two readers would see a batch of films seeded with higher than normal numbers of cancers, with readers allocated randomly to prompted and unprompted views of films. The first experiment was designed using a Graeco-Latin Square, with three 'nuisance' variables and the treatment factor of prompting levels (no prompts, low level of prompt¬ ing, medium and high). Four radiologists read at each level of prompting once, on dif¬ ferent sets of films. One of the more interesting results was that the recall rate did not increase as the prompting rate rose - contrary to prior expectations. Most of the differ¬ ences seen between the prompting rates could be explained as radiologist differences. Once these were taken into account, the level of prompting had little effect. Addition¬ ally, although the time taken to read a set of films increased as the prompting rate increased (as would be expected), it was only an increase of 26% from the unprompted set to the set with the highest number of prompts. Observational data suggested that the lowest level of prompting was not maintaining the interest of the radiologist, thus leading them to neglect the prompts. The following experiment moved the system a step closer to a true clinical demonstra¬ tion of the efficacy of PROMAM, being conducted under semi-clinical conditions. Using a method of minimisation, the number of cancers each radiologist viewed as first reader, second reader, prompted or unprompted were balanced. Preliminary exploratory anal¬ ysis indicated that the recall rate declined with the introduction of the prompting system, but more detailed, analysis indicated that much of this difference was due to a radiologist effect. Although cancer detection was slightly lower with the prompting system, examination of the 11 cancers missed by the prompted radiologist showed that six of these had been correctly prompted by the algorithms. This demonstrated scope to improve the cancer detection rate by nearly 5%. These experiments determined the 'production' version of the prompting system. A design to evaluate the system in a sample of 100,000 women in six centres was produced, but due to circumstances beyond the project team's control, it was not possible to take this work to the stage of a full 'trial' of the system. The design concept can, however, apply to the evaluation of any similar prompting system. The recommended design is therefore presented, together with an analysis of data from a simulated application of this design. This simulation has allowed recommendations to be made on the most appropriate ways to analyse the extensive and complicated dataset that will be obtained. In particular, it identified technical problems that can arise from the application on one candidate analytical method, and an explanation for the failure obtained It is quite clear from the evidence presented in this thesis that there is much scope for improvement in the cancer detection rate by the use of a prompting system, with¬ out a corresponding loss in the specificity. With the shortage of radiologists and ra¬ diographers, and the increasing demand placed on the Breast Screening Programme, technology could play a beneficial role in screening for breast cancer in the coming year

Quantum state visualization, verification and validation via phase space methods

Since its introduction in the 1930s by Wigner, and its generalisations by Moyal and Weyl, the ability to associate an operator on Hilbert space by a quasi-probability distribution function on phase space has found extensive use in the physics of con- tinuous variable systems. Lacking, however, is finite system applications; to date, such functions have taken a back seat to state vector, path integration, and Heisen- berg representations.In recent work, this lack of application has been addressed by giving a general framework to generate phase-space distribution functions for any system. Where the Wigner function for any system can be expressed in displaced parity form. This construction of a general framework for treating quantum mechanics in phase space will be presented in full in this thesis. Demonstrating a general approach to quantum mechanics as a statistical theory.Using this work, it will be shown how varied quantum systems can be easily represented in phase space as well as visualise certain quantum properties, such as entanglement, within these systems. In particular, formalism is applied to directly measure phase space coordinates of multiple qubit states, including a five-qubit GHZ state, on IBM’s Quantum Experience. Further, how these methods can be extended for use in general composite quantum systems, such as hybrid atom-cavity systems, will be presented, demonstrating how these phase-space methods are an optimal method for quantum state analysis, entanglement testing, and state characterisations.</div

Robust density modelling using the student's t-distribution for human action recognition

The extraction of human features from videos is often inaccurate and prone to outliers. Such outliers can severely affect density modelling when the Gaussian distribution is used as the model since it is highly sensitive to outliers. The Gaussian distribution is also often used as base component of graphical models for recognising human actions in the videos (hidden Markov model and others) and the presence of outliers can significantly affect the recognition accuracy. In contrast, the Student's t-distribution is more robust to outliers and can be exploited to improve the recognition rate in the presence of abnormal data. In this paper, we present an HMM which uses mixtures of t-distributions as observation probabilities and show how experiments over two well-known datasets (Weizmann, MuHAVi) reported a remarkable improvement in classification accuracy. © 2011 IEEE

New Directions in Impedance Spectroscopy for High Accuracy, Augmented Information Extraction and Low Power Implementation

This thesis provides new directions in the impedance spectroscopy, making it an interesting investigation technique for emerging smart sensors. Modern technologies increasingly require sensors capable of giving accurate measurements extracted among a lot of undesired surrounding information while maintaining low power consumptions. In this scenario, the main focuses of this thesis are: 1) developing an accurate complex impedance system, 2) extracting the augmented information using multivariate statistical analysis and 3) implementing IS-based systems with low power consumptions. The first project shows the design of a miniaturized, low power and accurate vector analyser for multi-parameter measurements in real-time. It is a versatile platform well-suited to be interfaced with various impedance-based sensors. The vector analyser, based on an accurate application specific integrated circuit and a digital interface, has been statistically characterized in order to evaluate accuracy and resolution. The validation of the entire system was performing on two real-time biomedical applications. The second project concerns the combination of powerful statistical methods inside moisture content sensors. The multivariate statistical approaches boost the prediction capability of the sensors exploiting the impedance mismatch between a transmitting and reflecting excitation on a soil. Two probe systems have been manufactured and associated with linear and non-linear models for being tested on three soil types. The third project shows a low-power implementation of an impedance sensor based on a digital random excitation. The entire system is almost digital, made up by an ultra-low power platform with the aim to become a wearable device. In future developments, these new investigated directions can be simultaneously applied in the design of IS based sensors which extract the desired information with high accuracy and reduced power budget. The potential of such improved system can be employed in a lot of smart sensors, involving electrochemical, environmental, food, biological applications and wearable devices