The research presented in this dissertation pertains to the development of a real time SLAM solution that can be performed by a low cost autonomous underwater vehicle equipped with low cost and memory constrained computing resources. The design of a custom rangefinder for underwater applications is presented. The rangefinder makes use of two laser line generators and a camera to measure the unknown distance to objects in an underwater environment. A visual odometry algorithm is introduced that makes use of a downward facing camera to provide our underwater vehicle with localization information. The sensor suite composed of the laser rangefinder, downward facing camera, and a digital compass are verified, using the Extended Kalman Filter based solution to the SLAM problem along with the particle filter based solution known as FastSLAM, to ensure that they provide in- formation that is accurate enough to solve the SLAM problem for out low cost underwater vehicle. Next, an extension of the FastSLAM algorithm is presented that stores the map of the environment using an occupancy grid is introduced. The use of occupancy grids greatly increases the amount of memory required to perform the algorithm so a version of the Fast- SLAM algorithm that stores the occupancy grids using the Haar wavelet representation is presented. Finally, a form of the FastSLAM algorithm is presented that stores the occupancy grid in compressed form to reduce the amount memory required to perform the algorithm. It is shown in experimental results that the same result can be achieved, as that produced by the algorithm that stores the complete occupancy grid, using only 40% of the memory required to store the complete occupancy grid. / Ph. D.

Human postural control is a complex process, but that is critical to understand in order to reduce the prevalence of occupational falls. Localized muscle fatigue (LMF), altered sensory input, and inter-individual differences (e.g. age and gender) have been shown to influence postural control, and numerous methods have been developed in order to quantify such effects. Recently, methods based on statistical mechanics have become popular, and when applied to center of pressure (COP) data, appear to provide new information regarding the postural control system. This study addresses in particular the stabilogram diffusion and Hurst exponent methods. An existing dataset was employed, in which sway during quiet stance was measured under different visual and surface compliance conditions, among both genders and different age groups, as well as before and after induction of localized muscle fatigue at the ankle, knee, torso, and shoulder. The stabilogram diffusion method determines both short-term and long-term diffusion coefficients, which correspond to open- and closed-loop control of posture, respectively. To do so, a "critical point" (or critical time interval) needs to be determined to distinguish between the two diffusion regions. Several limitations are inherent in existing methods to determine this critical point. To address this, a new algorithm was developed, based on a wavelet transform of COP data. The new algorithm is able to detect local maxima over specified frequency bands within COP data; therefore it can identify postural control mechanisms correspondent to those frequency bands. Results showed that older adults had smaller critical time intervals, and indicating that sway control of older adults was essentially different from young adults. Diffusion coefficients show that among young adults, torso LMF significantly compromised sway stability. In contrast, older adults appeared more resistance to LMF. Similar to earlier work, vision was found to play a crucial role in maintaining sway stability, and that stability was worse under eyes-closed (EC) than eyes-opened (EO) conditions. It was also found that the short-term Hurst exponent was not successful at detecting the effects of LMF on sway stability, likely because of a small sample size. The new critical point identification algorithm was verified to have better sensitivity and reliability than the traditional approach. The new algorithm can be used in future work to aid in the assessment of postural control and the mechanisms underlying this control. / Master of Science

DNA copy number change is an important form of structural variation in human genome. Somatic copy number alterations (CNAs) can cause over expression of oncogenes and loss of tumor suppressor genes in tumorigenesis. Recent development of SNP array technology has facilitated studies on copy number changes at a genome-wide scale, with high resolution. Quantitative analysis of somatic CNAs on genes has found broad applications in cancer research. Most tumors exhibit genomic instability at chromosome scale as a result of dynamically accumulated genomic mutations during the course of tumor progression. Such higher level cancer genomic characteristics cannot be effectively captured by the analysis of individual genes. We introduced two definitions of chromosome instability (CIN) index to mathematically and quantitatively characterize genome-wide genomic instability. The proposed CIN indices are derived from detected CNAs using circular binary segmentation and wavelet transform, which calculates a score based on both the amplitude and frequency of the copy number changes. We generated CIN indices on ovarian cancer subtypes' copy number data and used them as features to train a SVM classifier. The experimental results show promising and high classification accuracy estimated through cross-validations. Additional survival analysis is constructed on the extracted CIN scores from TCGA ovarian cancer dataset and showed considerable correlation between CIN scores and various events and severity in ovarian cancer development. Currently our methods have been integrated into G-DOC. We expect these newly defined CINs to be predictors in tumors subtype diagnosis and to be a useful tool in cancer research. / Master of Science

In this work, we first analyze the behavior of the acoustic wave from the theoretical point of view using a simplified 1-dimensional model. The model was developed based on the conservation of mass, the conservation of momentum, and the state equation; in addition, the fluid medium obeys Stokes assumption and it is homogeneous, adiabatic and isentropic. Experiment and simulation results show consistency to theoretical calculation. The second part of this thesis focuses on the PD signal analysis from an on-site PD measurement of the in-house design fiber optic sensors (by Virginia Tech, Center for Photonics Technology). Several commercial piezoelectric transducers (PZTs) were also used to compare the measurement results. The signal analysis employs the application of wavelet-based denoising technique to remove the noises, which mainly came from vibration, EMI, and light sources, embedded in the PD signal. The denoising technique includes the discrete wavelet transform (DWT) decomposition, thresh-holding of wavelet coefficients, and signal recovery by inverse discrete wavelet transform. Several approaches were compared to determine the optimal mother wavelet. The threshold limits are selected to remove the maximum Gaussian noises for each level of wavelet coefficients. The results indicate that this method could extract the PD spike from the noisy measurement effectively. The frequency of the PD pulse is also analyzed; it is shown that the frequencies lie in the range of 70 kHz to 250 kHz. In addition, with the assumed acoustic wave propagation delay between PD source and sensors, it was found that all PD activities occur in the first and third quadrant in reference to the applied sinusoidal transformer voltage. / Master of Science

One component of wireless communications of increasing necessity in both civilian and military applications is the process of automatic modulation classification. Modulation of a detected signal of unknown origin requiring interpretation must first be determined before the signal can be demodulated. This thesis presents a novel architecture for a modulation classifier that determines the most likely modulation using Grey Relational Analysis with the extraction and combination of multiple signal features. An evaluation of data preprocessing methods is conducted and performance of the classifier is investigated with the addition of each new signal feature used for classification. / Master of Science

Diese Dissertation beschäftigt sich mit zwei der wesentlichen Herausforderungen, welche bei der Bearbeitung großer Datensätze auftreten, der Dimensionsreduktion und der Datenentstörung. Der erste Teil dieser Dissertation liefert eine Zusammenfassung über Dimensionsreduktion. Ziel der Dimensionsreduktion ist eine sinnvolle niedrigdimensionale Darstellung eines vorliegenden hochdimensionalen Datensatzes. Insbesondere diskutieren und vergleichen wir bewährte Methoden des Manifold-Learning. Die zentrale Annahme des Manifold-Learning ist, dass der hochdimensionale Datensatz (approximativ) auf einer niedrigdimensionalen Mannigfaltigkeit liegt. Störungen im Datensatz sind bei allen Dimensionsreduktionsmethoden hinderlich. Der zweite Teil dieser Dissertation stellt eine neue Entstörungsmethode für hochdimensionale Daten vor, eine Wavelet-Shrinkage-Methode für die Glättung verrauschter Abtastwerte einer zugrundeliegenden multivariaten stückweise stetigen Funktion, wobei die Abtastpunkte gestreut sein können. Die Methode stellt eine Verallgemeinerung und Weiterentwicklung der für die Bildkompression eingeführten "Easy Path Wavelet Transform" (EPWT) dar. Grundlage ist eine eindimensionale Wavelet-Transformation entlang (adaptiv) zu konstruierender Pfade durch die Abtastpunkte. Wesentlich für den Erfolg der Methode sind passende adaptive Pfadkonstruktionen. Diese Dissertation beinhaltet weiterhin eine kurze Diskussion der theoretischen Eigenschaften von Wavelets entlang von Pfaden sowie numerische Resultate und schließt mit möglichen Modifikationen der Entstörungsmethode.

In many scenarios, events such as singularities and transients that carry important information about a signal undergo spreading during acquisition or transmission and it is important to localize the events. For example, edges in an image, point sources in a microscopy or astronomical image are blurred by the point-spread function (PSF) of the acquisition system, while in a speech signal, the epochs corresponding to glottal closure instants are shaped by the vocal tract response. Such events can be extracted with the help of techniques that promote sparsity, which enables separation of the smooth components from the transient ones. In this thesis, we consider development of such sparsity promoting techniques. The contributions of the thesis are three-fold: (i) an auditory-motivated continuous wavelet design and representation, which helps identify singularities; (ii) a sparsity-driven deconvolution technique; and (iii) a sparsity-driven deconvolution technique for reconstruction of nite-rate-of-innovation (FRI) signals. We use the speech signal for illustrating the performance of the techniques in the first two parts and super-resolution microscopy (2-D) for the third part. In the rst part, we develop a continuous wavelet transform (CWT) starting from an auditory motivation. Wavelet analysis provides good time and frequency localization, which has made it a popular tool for time-frequency analysis of signals. The CWT is a multiresolution analysis tool that involves decomposition of a signal using a constant-Q wavelet filterbank, akin to the time-frequency analysis performed by basilar membrane in the peripheral human auditory system. This connection motivated us to develop wavelets that possess auditory localization capabilities. Gammatone functions are extensively used in the modeling of the basilar membrane, but the non-zero average of the functions poses a hurdle. We construct bona de wavelets from the Gammatone function called Gammatone wavelets and analyze their properties such as admissibility, time-bandwidth product, vanishing moments, etc.. Of particular interest is the vanishing moments property, which enables the wavelet to suppress smooth regions in a signal leading to sparsi cation. We show how this property of the Gammatone wavelets coupled with multiresolution analysis could be employed for singularity and transient detection. Using these wavelets, we also construct equivalent lterbank models and obtain cepstral feature vectors out of such a representation. We show that the Gammatone wavelet cepstral coefficients (GWCC) are effective for robust speech recognition compared with mel-frequency cepstral coefficients (MFCC). In the second part, we consider the problem of sparse blind deconvolution (SBD) starting from a signal obtained as the convolution of an unknown PSF and a sparse excitation. The BD problem is ill-posed and the goal is to employ sparsity to come up with an accurate solution. We formulate the SBD problem within a Bayesian framework. The estimation of lter and excitation involves optimization of a cost function that consists of an `2 data- fidelity term and an `p-norm (p 2 [0; 1]) regularizer, as the sparsity promoting prior. Since the `p-norm is not differentiable at the origin, we consider a smoothed version of the `p-norm as a proxy in the optimization. Apart from the regularizer being non-convex, the data term is also non-convex in the filter and excitation as they are both unknown. We optimize the non-convex cost using an alternating minimization strategy, and develop an alternating `p `2 projections algorithm (ALPA). We demonstrate convergence of the iterative algorithm and analyze in detail the role of the pseudo-inverse solution as an initialization for the ALPA and provide probabilistic bounds on its accuracy considering the presence of noise and the condition number of the linear system of equations. We also consider the case of bounded noise and derive tight tail bounds using the Hoe ding inequality. As an application, we consider the problem of blind deconvolution of speech signals. In the linear model for speech production, voiced speech is assumed to be the result of a quasi-periodic impulse train exciting a vocal-tract lter. The locations of the impulses or epochs indicate the glottal closure instants and the spacing between them the pitch. Hence, the excitation in the case of voiced speech is sparse and its deconvolution from the vocal-tract filter is posed as a SBD problem. We employ ALPA for SBD and show that excitation obtained is sparser than the excitations obtained using sparse linear prediction, smoothed `1=`2 sparse blind deconvolution algorithm, and majorization-minimization-based sparse deconvolution techniques. We also consider the problem of epoch estimation and show that epochs estimated by ALPA in both clean and noisy conditions are closer to the instants indicated by the electroglottograph when with to the estimates provided by the zero-frequency ltering technique, which is the state-of-the-art epoch estimation technique. In the third part, we consider the problem of deconvolution of a specific class of continuous-time signals called nite-rate-of-innovation (FRI) signals, which are not bandlimited, but specified by a nite number of parameters over an observation interval. The signal is assumed to be a linear combination of delayed versions of a prototypical pulse. The reconstruction problem is posed as a 2-D SBD problem. The kernel is assumed to have a known form but with unknown parameters. Given the sampled version of the FRI signal, the delays quantized to the nearest point on the sampling grid are rst estimated using proximal-operator-based alternating `p `2 algorithm (ALPAprox), and then super-resolved to obtain o -grid (O. G.) estimates using gradient-descent optimization. The overall technique is termed OG-ALPAprox. We show application of OG-ALPAprox to a particular modality of super-resolution microscopy (SRM), called stochastic optical reconstruction microscopy (STORM). The resolution of the traditional optical microscope is limited by di raction and is termed as Abbe's limit. The goal of SRM is to engineer the optical imaging system to resolve structures in specimens, such as proteins, whose dimensions are smaller than the di raction limit. The specimen to be imaged is tagged or labeled with light-emitting or uorescent chemical compounds called uorophores. These compounds speci cally bind to proteins and exhibit uorescence upon excitation. The uorophores are assumed to be point sources and the light emitted by them undergo spreading due to di raction. STORM employs a sequential approach, wherein each step only a few uorophores are randomly excited and the image is captured by a sensor array. The obtained image is di raction-limited, however, the separation between the uorophores allows for localizing the point sources with high precision. The localization is performed using Gaussian peak- tting. This process of random excitation coupled with localization is performed sequentially and subsequently consolidated to obtain a high-resolution image. We pose the localization as a SBD problem and employ OG-ALPAprox to estimate the locations. We also report comparisons with the de facto standard Gaussian peak- tting algorithm and show that the statistical performance is superior. Experimental results on real data show that the reconstruction quality is on par with the Gaussian peak- tting.

Nowadays, a significant proportion of the population in the world is affected by cerebral diseases like epilepsy. In this study, frequency domain features of electroencephalography (EEG) signals were studied and analyzed, with a view being able to detect epileptic seizures more easily. The power spectrum and spectrogram were determined by using fast fourier transform (FFT) and the scalogram was found by performing continuous wavelet transform (CWT) on the testing EEG signal. In addition, two schemes, i.e. method 1 and method 2, were implemented for detecting epileptic seizures and the applicability of the two methods to electrocardiogram (ECG) signals were tested. A third method for anomaly detection in ECG signals was tested. / En signifikant del av population påverkas idag av neurala sjukdomar som epilepsi. I denna studie studerades och analyserades egenskaper inom frekvensdomänen av elektroencefalografi (EEG), med sikte på att lättare kunna upptäcka epileptiska anfall. Effektspektrumet och spektrogramet bestämdes med hjälp av en snabb fouriertransform och skalogrammet hittades genom att genomföra en kontinuerlig wavelet transform (CWT) på testsignalen från EEGsignalen. I addition till detta skapades två system, metod 1 och metod 2, som implementerades för att upptäcka epileptiska anfall. Användbarheten av dessa två metoder inom elektrokardiogramsignaler (ECG) testades. En tredje metod för anomalidetektering i ECGsignaler testades.

Modern day society is vastly complex, with information and data constantly being posted, shared, and collected everywhere. There is often an abundance of massive amounts of unlabeled data that can not be leveraged in a supervised machine learning context. Thus, there exists an incentive to research and develop machine learning methods which can learn without labels. Selfsupervised learning (SSL) is a newly emerged machine learning paradigm that aims to learn representations that can later be used in domain specific downstream tasks. In this degree project three SSL models based on the Simple Framework for Contrastive Learning of Visual Representations (SimCLR) are evaluated. Each model aims to learn sleep deprivation related representations on magnetoencephalography (MEG) measurements. MEG is a non-invasive neuroimaging technique that is used on humans to investigate neuronal activity. The data was acquired through a collaboration with Karolinska Institutet and Stockholm University, where the SLEMEG project was conducted to study the neurophysiological response to partial sleep deprivation. The features extracted by the SSL-models are analyzed both qualitatively and quantitatively, and also used to perform classification and regression tasks on subject labels. The results show that the evaluated Signal- and Recording SimCLR models can learn sleep deprivation related features, whilst simultaneously learning other co-occuring information also. Furthermore, the results indicate that the learned representations are informative and can be utilized for multiple downstream tasks. However, it is noted that what has been learned is mostly related to subject-specific individual variance, which leads to poor generalization performance on classification and regression downstream tasks. Thus, it is believed that the models would perform better with access to more MEG data, and that source localized MEG data could remove part of the individual variance that is learned. / Den moderna dagens samhälle är enormt komplext, information och data blir konstant postat, delat, och insamlat överallt. På grund av det så finns det ofta ett överflöd av massiva mängder omärkt data some inte kan användas i ett övervakat maskininlärnings-sammanhang. Därmed finns det ett incitament att forska om och utveckla maskininlärningsmetoder som kan lära modeller utan tillgång till märkningar. Självövervakad inlärning (SSL) är en modern metod som nyligen har fått mycket fokus, vars mål är att lära sig representationer av datat som sedan kan användas i domänspecifika nedströmsuppgifter. I det här examensarbetet så är tre SSL metoder evaluerade där de alla strävar efter att lära sig representationer relaterat till sömndeprivering på magnetoencefalografi (MEG) mätningar. MEG är en icke-invasiv metod som används på människor för att undersöka neuronal aktivitet. Datat var förvärvat genom ett sammarbeta med Karolinska Institutet och Stockholms Universitet, där SLEMEG studien hade blivit genomförd för att studera neurofysiologisk respons på sömndeprivering. De av SSL-modellerna extraherade särdragen är analyserade både kvalitativt samt kvantitativt, och sedan använda för att genomföra klassificerings och regressions-uppgifter. Resultaten visar på att de evaluerade Signal- och Recording SimCLR modellerna kan lära sig särdrag relaterade till sömndepriverad, men samtidigt också lära sig annan samförekommande information. Dessutom så indikerar resultaten att de lärda representationerna är informativa och kan då användas i flera olika nedströmsuppgifter. Dock så noteras det att det som blivit inlärt är mestadels relaterat till individ-specifik varians, vilket leder till dålig generaliseringsprestanda. Således är det trott att modellerna hade presterat bättre med tillgång till mer MEG data, samt att källlokalisering av MEG datat hade kunnat ta bort en del av den individuella variansen som blir inlärd.

Ο μετασχηματισμός κυματιδίου (wavelet transform) είναι ένα αποτελεσματικό εργαλείο για την ανάλυση σημάτων. Ο κυριότερος λόγος είναι ότι προσφέρει το πλεονέκτημα της χρήσης μεγάλων χρονικών παραθύρων εκεί όπου απαιτείται ακρίβεια σε πληροφορίες χαμηλής συχνότητας και μικρότερων χρονικών παραθύρων εκεί όπου απαιτείται ακρίβεια σε πληροφορίες υψηλής συχνότητας. Δηλαδή έχει την ικανότητα “τοπικής ανάλυσης”, δηλ. να αναλυθεί μία εντοπισμένη περιοχή ενός μεγαλύτερου σήματος. Στην εργασία αυτή προτείνεται μια νέα υλοποίηση φίλτρου που υλοποιεί το μετασχηματισμό κυματιδίου, με δομικά στοιχεία μη γραμμικούς διαγωγούς στο πεδίο του υπερβολικού ημιτόνου. Το φίλτρο χρησιμοποιείται για την “τοπική ανάλυση“ του καρδιακού σήματος με στόχο την ανίχνευση καρδιακών βλαβών. Κύρια πλεονεκτήματα αποτελούν η δυνατότητα λειτουργίας σε πολύ χαμηλή τάση τροφοδοσίας (0.6V), η χαμηλή κατανάλωση ισχύος, και η ρύθμιση των χαρακτηριστικών του φίλτρου από το ρεύμα πόλωσης. Η εξομοίωση της λειτουργίας του κυκλώματος καθώς και η φυσική σχεδίαση έγιναν με χρήση του λογισμικού Cadence, σε τεχνολογία AMS 0.35μm. / The wavelet transform is an efficient tool for signal analysis. The main reason of its efficiency is that it offers the advantage of using large time windows where precision is required in the low frequency information and shorter windows required accuracy at high frequencies information. It has the ability of “local analysis” i.e. to analyze a localized area to a larger signal. In this paper we propose a new implementation of a filter that materializes the wavelet transform, with nonlinear transconductor components in sinh domain. The filter used for “local analysis” of the cardiac signal in order to detect heart malfunctions. Main advantages are the abilities to operate at very low supply voltage (0.6V), low power consumption and regulation characteristics of the filter from the bias current. The simulation process of the circuit and physical design were done using the Cadence software, in AMS 0.35mm technology.