Parkinson’s Disease is a neurological degenerative disease affecting more than six million people worldwide. It is a progressive disease, impacting a person’s movements and thought processes. In recent years, computer vision and machine learning researchers have been developing techniques to aid in the diagnosis. This thesis is motivated by the exploration of hand tremor symptoms in Parkinson’s patients from the Archimedean Spiral test, a paper-and-pencil test used to evaluate hand tremors. This work presents a novel Fourier Domain analysis technique that transforms the pencil content of hand-drawn spiral images into frequency features. Our technique is applied to an image dataset consisting of spirals drawn by healthy individuals and people with Parkinson’s Disease. The Fourier Domain analysis technique achieves 81.5% accuracy predicting images drawn by someone with Parkinson’s, a result 6% higher than previous methods. We compared this method against the results using extracted features from the ResNet-50 and VGG16 pre-trained deep network models. The VGG16 extracted features achieve 95.4% accuracy classifying images drawn by people with Parkinson’s Disease. The extracted features of both methods were also used to develop a tremor severity rating system which scores the spiral images on a scale from 0 (no tremor) to 1 (severe tremor). The results show correlation to the Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) developed by the International Parkinson and Movement Disorder Society. These results can be useful for aiding in early detection of tremors, the medical treatment process, and symptom tracking to monitor the progression of Parkinson’s Disease. / M.S. / Parkinson’s Disease is a neurological degenerative disease affecting more than six million people worldwide. It is a progressive disease, impacting a person’s movements and thought processes. In recent years, computer vision and machine learning researchers have been developing techniques to aid in the diagnosis. This thesis is motivated by the exploration of hand tremor symptoms in Parkinson’s patients from the Archimedean Spiral test, a paper-and-pencil test used to evaluate hand tremors. This work presents a novel spiral analysis technique that converts the pencil content of hand-drawn spirals into numeric values, called features. The features measure spiral smoothness. Our technique is applied to an image dataset consisting of spirals drawn by healthy and Parkinson’s individuals. The spiral analysis technique achieves 81.5% accuracy predicting images drawn by someone with Parkinson’s. We compared this method against the results using extracted features from pre-trained deep network models. The VGG16 pre-trained model extracted features achieve 95.4% accuracy classifying images drawn by people with Parkinson’s Disease. The extracted features of both methods were also used to develop a tremor severity rating system which scores the spiral images on a scale from 0 (no tremor) to 1 (severe tremor). The results show a similar trend to the tremor evaluations rated by the Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) developed by the International Parkinson and Movement Disorder Society. These results can be useful for aiding in early detection of tremors, the medical treatment process, and symptom tracking to monitor the progression of Parkinson’s Disease.

When patients move during an MRI examination, severe artifacts arise in the reconstructed image and motion correction is therefore often desired. An in-plane motion correction algorithm suitable for PRESTO-CAN, a new 3D functional MRI method where sampling of k-space is radial in kx-direction and kz-direction and Cartesian in ky-direction, was implemented in this thesis work. Rotation and translation movements can be estimated and corrected for sepa- rately since the magnitude of the data is only affected by the rotation. The data were sampled in a radial pattern and the rotation was estimated by finding the translation in angular direction using circular correlation. Correlation was also used when finding the translation in x-direction and z-direction. The motion correction algorithm was evaluated on computer simulated data, the motion was detected and corrected for, and this resulted in images with greatly reduced artifacts due to patient movements. / När patienter rör sig under en MRI-undersökning uppstår artefakter i den rekonstruerande bilden och därför är det önskvärt med rörelsekorrigering. En 2D- rörelsekorrigeringsalgoritm som är anpassad för PRESTO-CAN har tagits fram. PRESTO-CAN är en ny fMRI-metod för 3D där samplingen av k-rummet är radiell i (kx,kz)-planet och kartesisk i ky-riktningen. Rotations- och translationsrörelser kan estimeras separat då magnituden av signalen bara påverkas av rotationsrörelser. Eftersom data är samplat radiellt kan rotationen estimeras genom att hitta translationen i vinkelled med hjälp av cirkulär korrelation. Korrelation används även för att hitta translationen i i x- och z-riktningen. Test på simulerat data visar att rörelsekorrigeringsalgoritmen både detekterar och korrigerar för rörelser vilket leder till bilder med mycket mindre rörelseartefakter.

One of the main features of digital technology is that the digital media can be duplicated and reproduced easily. However, this allows unauthorized and illegal use of information, i.e. data piracy. To protect digital media against illegal attempts a signal, called watermark, is embedded into the multimedia data in a robust and invisible manner. A watermark is a short sequence of information, which contains owner&rsquo / s identity. It is used for evidence of ownership and copyright purposes. In this thesis, we use fractional Fourier transformation (FrFT) domain, which combines space and spatial frequency domains, for watermark embedding and implement well-known secure spread spectrum watermarking approach. However, the spread spectrum watermarking scheme is fragile against geometrical attacks such as rotation and scaling. To gain robustness against geometrical attacks, an invisible template is inserted into the watermarked image in Fourier transformation domain. The template contains no information in itself but it is used to detect the transformations undergone by the image. Once the template is detected, these transformations are inverted and the watermark signal is decoded. Watermark embedding is performed by considering the masking characteristics of the Human Visual System, to ensure the watermark invisibility. In addition, we implement watermarking algorithms, which use different transformation domains such as discrete cosine transformation domain, discrete Fourier transformation domain and discrete wavelet transformation domain for watermark embedding. The performance of these algorithms and the FrFT domain watermarking scheme is experimented against various attacks and distortions, and their robustness are compared.

A multilayered system is a good model for many optical systems. An optical coherence tomography (OCT) system can provide fundamental information about the refractive index distribution of the sample and enables images to be corrected for geometric accuracy, but this requires the separation of refractive index and physical thickness for each layer from the measured optical paths. In this thesis a novel approach for simultaneous extraction of index and thickness of multi layer systems and the last medium index of refraction in a single experiment using only the object’s spectral response available by any Fourier Domain OCT system without using any additional outside measurements is introduced. The method is based on a novel matrix equation that uses the reflected spectrum from the object and the measured optical thickness. In the presence of slight error of measuring optical thickness, the parameters extraction has wavenumber dependency. A novel method is used to select the suitable set of spectral components that reduces the extracted parameters error. The parameters extraction method is followed by a fitting process for optimized results. The method works the best for low contrast index distribution even in the presence of relatively large optical thickness measurement error.

Constrained by practical and economical considerations, one often uses seismic data with missing traces. The use of such data results in image artifacts and poor spatial resolution. Sometimes due to practical limitations, measurements may be available on a perturbed grid, instead of on the designated grid. Due to algorithmic requirements, when such measurements are viewed as those on the designated grid, the recovery procedures may result in additional artifacts. This paper interpolates incomplete data onto regular grid via the Fourier domain, using a recently developed greedy algorithm. The basic objective is to study experimentally as to what could be the size of the perturbation in measurement coordinates that allows for the measurements on the perturbed grid to be considered as on the designated grid for faithful recovery. Our experimental work shows that for compressible signals, a uniformly distributed perturbation can be offset with slightly more number of measurements.

This thesis is concerned with (a) the development of full-field, multi-axis and phase contrast wavelength scanning interferometer, using an electronically tuned CW Ti:Sa laser for the study of depth resolved measurements in composite materials such as GFRPs and (b) the development of temporal phase unwrapping algorithms for depth re-solved measurements. Item (a) was part of the ultimate goal of successfully extracting the 3-D, depth-resolved, constituent parameters (Young s modulus E, Poisson s ratio v etc.) that define the mechanical behaviour of composite materials like GFRPs. Considering the success of OCT as an imaging modality, a wavelength scanning interferometer (WSI) capable of imaging the intensity AND the phase of the interference signal was proposed as the preferred technique to provide the volumetric displacement/strain fields (Note that displacement/strain fields are analogous to phase fields and thus a phase-contrast interferometer is of particular interest in this case). These would then be passed to the VFM and yield the sought parameters provided the loading scheme is known. As a result, a number of key opto-mechanical hardware was developed. First, a multiple channel (x6) tomographic interferometer realised in a Mach-Zehnder arrangement was built. Each of the three channels would provide the necessary information to extract the three orthogonal displacement/strain components while the other three are complementary and were included in the design in order to maximize the penetration depth (sample illuminated from both sides). Second, a miniature uniaxial (tensile and/or compression) loading machine was designed and built for the introduction of controlled and low magnitude displacements. Last, a rotation stage for the experimental determination of the sensitivity vectors and the re-registration of the volumetric data from the six channels was also designed and built. Unfortunately, due to the critical failure of the Ti:Sa laser data collection using the last two items was not possible. However, preliminary results at a single wavelength suggested that the above items work as expected. Item (b) involved the development of an optical sensor for the dynamic monitoring of wavenumber changes during a full 100 nm scan. The sensor is comprised of a set of four wedges in a Fizeau interferometer setup that became part of the multi-axis interferometer (7th channel). Its development became relevant due to the large amount of mode-hops present during a full scan of the Ti:Sa source. These are associated to the physics of the laser and have the undesirable effect of randomising the signal and thus preventing successful depth reconstructions. The multi-wedge sensor was designed so that it provides simultaneously high wavenumber change resolution and immunity to the large wavenumber jumps from the Ti:Sa. The analysis algorithms for the extraction of the sought wavenumber changes were based on 2-D Fourier transform method followed by temporal phase unwrapping. At first, the performance of the sensor was tested against that of a high-end commercial wavemeter for a limited scan of 1nm. A root mean square (rms) difference in measured wavenumber shift between the two of ~4 m-1 has been achieved, equivalent to an rms wavelength shift error of ~0.4 pm. Second, by resampling the interference signal and the wavenumber-change axis onto a uniformly sampled k-space, depth resolutions that are close to the theoretical limits were achieved for scans of up to 37 nm. Access of the full 100 nm range that is characterised by wavelength steps down to picometers level was achieved by introducing a number of improvements to the original temporal phase unwrapping algorithm reported in ref [1] tailored to depth resolved measurements. These involved the estimation and suppression of intensity background artefacts, improvements on the 2-D Fourier transform phase detection based on a previously developed algorithm in ref [2] and finally the introduction of two modifications to the original TPU. Both approaches are adaptive and involve signal re-referencing at regular intervals throughout the scan. Their purpose is to compensate for systematic and non-systematic errors owing to a small error in the value of R (a scaling factor applied to the lower sensitivity wedge phase-change signal used to unwrap the higher sensitivity one), or small changes in R with wavelength due to the possibility of a mismatch in the refractive dispersion curves of the wedges and/or a mismatch in the wedge angles. A hybrid approach combining both methods was proposed and used to analyse the data from each of the four wedges. It was found to give the most robust results of all the techniques considered, with a clear Fourier peak at the expected frequency, with significantly reduced spectral artefacts and identical depth resolutions for all four wedges of 2.2 μm measured at FWHM. The ability of the phase unwrapping strategy in resolving the aforementioned issues was demonstrated by successfully measuring the absolute thickness of four fused silica glasses using real experimental data. The results were compared with independent micrometer measurements and showed excellent agreement. Finally, due to the lack of additional experimental data and in an attempt to justify the validity of the proposed temporal phase unwrapping strategy termed as the hybrid approach, a set of simulations that closely matched the parameters characterising the real experimental data set analysed were produced and were subsequently analysed. The results of this final test justify that the various fixes included in the hybrid approach have not evolved to solve the problems of a particular data set but are rather of general nature thereby, highlighting its importance for PC-WSI applications concerning the processing and analysis of large scans.

L'échocardiographie est une modalité d'imagerie sûre, non-invasive, qui est utilisée pour évaluer la fonction et l'anatomie cardiaque en routine clinique. Mais la cadence maximale d’imagerie atteinte est limitée en raison de la vitesse limitée du son. Afin d’augmenter la fréquence d'image, l'utilisation d’ondes planes ou d’ondes divergentes en transmissinon a été proposée afin de réduire le nombre de tirs nécessaires à la reconstruction d'une image. L'objectif de cette thèse consiste à développer un procédé d'imagerie par ultrasons ultra-rapide en échocardiographie 2/3D basé sur une insonification par ondes divergentes et réalisant une reconstruction dans le domaine de Fourier. Les contributions principales obtenues au cours de la thèse sont décrites ci-dessous. La première contribution de cette thèse concerne un schéma de transmission dichotomique pour l'acquisition linéaire en analysant mathématiquement la pression générée. Nous avons ensuite montré que ce système de transmission peut améliorer la qualité des images reconstruites pour une cadence constante en utilisant les algorithmes de reconstruction conventionnels. La qualité des images reconstruites a été évaluée en termes de résolution et de contraste au moyen de simulations et acquisitions expérimentales réalisées sur des fantômes. La deuxième contribution concerne le développement d'une nouvelle méthode d'imagerie 2D en ondes plane opérant dans le domaine de Fourier et basée sur le théorème de la coupe centrale. Les résultats que nous avons obtenus montrent que l'approche proposée fournit des résultats très proches de ceux fournit par les méthodes classiques en termes de résolution latérale et contraste de l'image. La troisième contribution concerne le développement d'une transformation spatiale explicite permettant d'étendre les méthodes 2D opérant dans le domaine de Fourier d'une acquisition en géométrie linéaire avec des ondes planes à la géométrie sectorielle avec des ondes divergente en transmission. Les résultats que nous avons obtenus à partir de simulations et d'acquisitions expérimentales in vivo montrent que l'application de cette extension à la méthode de Lu permet d'obtenir la même qualité d’image que la méthode spatiale de Papadacci basée sur des ondes divergentes, mais avec une complexité de calcul plus faible. Finalement, la formulation proposée en 2D pour les méthodes ultra-rapides opérant dans le domaine de Fourier ont été étendues en 3D. L'approche proposée donne des résultats compétitifs associés à une complexité de calcul beaucoup plus faible par rapport à la technique de retard et somme conventionnelle. / Three-dimensional echocardiography is one of the most widely used modality in real time heart imaging thanks to its noninvasive and low cost. However, the real-time property is limited because of the limited speed of sound. To increase the frame rate, plane wave and diverging wave in transmission have been proposed to drastically reduce the number of transmissions to reconstruct one image. In this thesis, starting with the 2D plane wave imaging methods, the reconstruction of 2D/3D echocardiographic sequences in Fourier domain using diverging waves is addressed. The main contributions are as follows: The first contribution concerns the study of the influence of transmission scheme in the context of 2D plane wave imaging. A dichotomous transmission scheme was proposed. Results show that the proposed scheme allows the improvement of the quality of the reconstructed B-mode images at a constant frame rate. Then we proposed an alternative Fourier-based plane wave imaging method (i.e. Ultrasound Fourier Slice Beamforming). The proposed method was assessed using numerical simulations and experiments. Results revealed that the method produces very competitive image quality compared to the state-of-the-art methods. The third contribution concerns the extension of Fourier-based plane wave imaging methods to sectorial imaging in 2D. We derived an explicit spatial transformation which allows the extension of the current Fourier-based plane wave imaging techniques to the reconstruction of sectorial scan using diverging waves. Results obtained from simulations and experiments show that the derived methods produce competitive results with lower computational complexity when compared to the conventional delay and sum (DAS) technique. Finally, the 2D Fourier-based diverging wave imaging methods are extended to 3D. Numerical simulations were performed to evaluate the proposed method. Results show that the proposed approach provides competitive scores in terms of image quality compared to the DAS technique, but with a much lower computational complexity.

Cílem téhle práce je navrhnutí nových technik pro robustní neviditelné značení digitálních signálů. Nejdříve je prezentován současný stav tohoto odvětví a dostupné softwarové řešení. Poté následuje návrh několika algoritmů pro neviditelné značení, přičemž každý z nich je založen na jiném principu. Dále je připravena sada digitálních testovacích signálů společně s testovacím softwarem pro otestování navržených řešení a jejích porovnání s vybraným dostupným softwarem. Poté následuje srovnání naměřených výsledků, výkonu a jejích diskuze.