Towards the development of a new wavelet for ECG classification

In this paper an attempt has been made to determine the number of Premature Ventricular Contraction (PVC) cycles accurately from a given Electrocardiogram (ECG) using a wavelet constructed from multiple Gaussian functions. It is difficult to assess the ECGs of patients who are continuously monitored over a long period of time. Hence the proposed method of classification will be helpful to doctors to determine the severity of PVC in a patient. Principal Component Analysis (PCA) and a simple classifier have been used in addition to the specially developed wavelet transform. The proposed wavelet has been designed using multiple Gaussian functions which when summed up looks similar to that of a normal ECG. The number of Gaussians used depends on the number of peaks present in a normal ECG. The developed wavelet satisfied all the properties of a traditional continuous wavelet. The new wavelet was optimized using genetic algorithm (GA). ECG records from Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) database have been used for validation. Out of the 8694 ECG cycles used for evaluation, the classification algorithm responded with an accuracy of 97.77%. In order to compare the performance of the new wavelet, classification was also performed using the standard wavelets like morlet, meyer, bior3.9, db5, db3, sym3 and haar. The new wavelet outperforms the rest

Evolution of Better Wavelet Coefficients for Fingerprint Image Compression using cropped images

This paper explains the Genetic Algorithm (GA) evolution of optimized wavelet that surpass the cdf9/7 wavelet for fingerprint compression and reconstruction. Optimized wavelets have already been evolved in previous works in the literature, but they are highly computationally complex and time consuming. Therefore, in this work, a simple approach is made to reduce the computational complexity of the evolution algorithm. A training image set comprised of three 32x32 size cropped images performed much better than the reported coefficients in literature. An average improvement of 1.0059 dB in PSNR above the classical cdf9/7 wavelet over the 80 fingerprint images was achieved. In addition, the computational speed was increased by 90.18 %. The evolved coefficients for compression ratio (CR) 16:1 yielded better average PSNR for other CRs also. Improvement in average PSNR was experienced for degraded and noisy images as well

Development of Directionally Adaptive Techniques for Single Image Super-Resolution

Super Resolution problem is an inverse problem and refers to the process of producing a High resolution (HR) image, making use of one or more Low Resolution (LR) observations. It includes up sampling the image, thereby, increasing the maximum spatial frequency and removing degradations that arise during the image capture namely aliasing and blurring. The work presented in this thesis is based on learning based single image super-resolution. In learning based super-resolution algorithms, a training set or database of available HR images are used to construct the HR image of an image captured using a LR camera. In the training set, images are stored as patches or coefficients of feature representations like wavelet transform, DCT, etc. Single frame image super-resolution can be used in applications where database of HR images are available. The advantage of this method is that by skilfully creating a database of suitable training images, one can improve the quality of the super-resolved image. A new super resolution method based on wavelet transform is developed and it is better than conventional wavelet transform based methods and standard interpolation methods. Super-resolution techniques based on skewed anisotropic transform called directionlet transform are developed to convert a low resolution image which is of small size into a high resolution image of large size. Super-resolution algorithm not only increases the size, but also reduces the degradations occurred during the process of capturing image. This method outperforms the standard interpolation methods and the wavelet methods, both visually and in terms of SNR values. Artifacts like aliasing and ringing effects are also eliminated in this method. The super-resolution methods are implemented using, both critically sampled and over sampled directionlets. The conventional directionlet transform is computationally complex. Hence lifting scheme is used for implementation of directionlets. The new single image super-resolution method based on lifting scheme reduces computational complexity and thereby reduces computation time. The quality of the super resolved image depends on the type of wavelet basis used. A study is conducted to find the effect of different wavelets on the single image super-resolution method. Finally this new method implemented on grey images is extended to colour images and noisy images

Interannual and interdecadal oscillations in hydrological variables: Sources and modeling of the persistence in the Elbe River Basin

Wenn man die Existenz von physikalischen Mechanismen ignoriert, die für die Struktur hydrologischer Zeitreihen verantwortlich sind, kann das zu falschen Schlussfolgerungen bzgl. des Vorhandenseins möglicher Gedächtnis (memory) -Effekte, d.h. von Persistenz, führen. Die hier vorgelegte Doktorarbeit spürt der niedrigfrequenten klimatischen Variabilität innerhalb den hydrologischen Zyklus nach und bietet auf dieser "Reise" neue Einsichten in die Transformation der charakteristischen Eigenschaften von Zeitreihen mit einem Langzeitgedächtnis. Diese Studie vereint statistische Methoden der Zeitreihenanalyse mit empirisch-basierten Modelltechniken, um operative Modelle zu entwickeln, die in der Lage sind (1) die Dynamik des Abflusses zu modellieren, (2) sein zukünftiges Verhalten zu prognostizieren und (3) die Abflusszeitreihen an unbeobachteten Stellen abzuschätzen. Als solches präsentiert die hier vorgelegte Dissertation eine ausführliche Untersuchung zu den Ursachen der niedrigfrequenten Variabilität von hydrologischen Zeitreihen im deutschen Teil des Elbe-Einzugsgebietes, den Folgen dieser Variabilität und den physikalisch basierten Reaktionen von Oberflächen- und Grundwassermodellen auf die niedrigfrequenten Niederschlags-Eingangsganglinien. Die Doktorarbeit gliedert sich wie folgt: In Kapitel 1 wird als Hintergrundinformation das Hurst Phänomen beschrieben und ein kurzer Rückblick auf diesbezügliche Studien gegeben. Das Kapitel 2 diskutiert den Einfluss der Präsenz von niedrigfrequenten periodischen Zeitreihen auf die Zuverlässigkeit verschiedener Hurst-Parameter-Schätztechniken. Kapitel 3 korreliert die niedrigfrequente Niederschlagsvariabilität mit dem Index der Nord-Atlantischen Ozillations (NAO). Kapitel 4-6 sind auf den deutschen Teil des Elbe-Einzugsgebietes fokussiert. So werden in Kapitel 4 die niedrigfrequenten Variabilitäten der unterschiedlichen hydro-meteorologischen Parameter untersucht und es werden Modelle beschrieben, die die Dynamik dieser Niedrigfrequenzen und deren zukünftiges Verhalten simulieren. Kapitel 5 diskutiert die mögliche Anwendung der Ergebnisse für die charakteristische Skalen und die Verfahren der Analyse der zeitlichen Variabilität auf praktische Fragestellungen im Wasserbau sowie auf die zeitliche Bestimmung des Gebiets-Abflusses an unbeobachteten Stellen. Kapitel 6 verfolgt die Spur der Niedrigfrequenzzyklen im Niederschlag durch die einzelnen Komponenten des hydrologischen Zyklus, nämlich dem Direktabfluss, dem Basisabfluss, der Grundwasserströmung und dem Gebiets-Abfluss durch empirische Modellierung. Die Schlussfolgerungen werden im Kapitel 7 präsentiert. In einem Anhang werden technische Einzelheiten zu den verwendeten statistischen Methoden und die entwickelten Software-Tools beschrieben.

Technisch quantitative Investmentstrategien

Spätestens seit der Formulierung der modernen Portfoliotheorie durch Harry Markowitz (1952) wird den aktiven Portfoliomanagementstrategien besondere Aufmerksamkeit in Wissenschaft und Anlagepraxis gewidmet. Diese Arbeit ist im Schnittstellenbereich zwischen neoklassischer Kapitalmarkttheorie und technischer Analyse angesiedelt. Es wird untersucht, inwieweit eine passive Buy&Hold-Strategie, die als einzige im Einklang mit der Effizienzmarkthypothese nach Fama (1970) steht, durch Verwendung von aktiven Strategien geschlagen werden kann. Der Autor präsentiert einen Wavelet-basierten Ansatz für die Analyse der Finanzzeitreihen. Die Wavelet-Transformation wird als ein mathematisches Datenaufbereitungstool herangezogen und ermöglicht eine Multiskalendarstellung einer Datenreihe, durch das Aufspalten dieser in eine Approximationszeitreihe und eine Detailszeitreihe, ohne dass dadurch Informationen verloren gehen. Diese Arbeit beschränkt sich auf die Verwendung der Daubechies Wavelets. Die Multiskalendarstellung dient als Grundlage für die Entwicklung von zwei technischen Indikatoren. Der Wavelet Stochastik Indikator greift auf die Idee des bekannten Stochastik-Indikators zurück und verwendet nicht mehr die Kurszeitreihe, sondern die Approximationszeitreihe als Input. Eine auf diesem Indikator basierende Investmentstrategie wird umfangreicher Sensitivitätsanalyse unterworfen, die aufzeigt, dass eine Buy&Hold-Strategie durchaus outperformt werden kann. Die Idee des Momentum-Indikators wird durch den Wavelet Momentum Indikator aufgegriffen, welcher die Detailszeitreihen als Input heranzieht. Im Rahmen der Sensitivitätsanalyse einer Wavelet Momentum Strategie wird jedoch die Buy&Hold -Strategie nicht immer geschlagen. Ein Wavelet-basiertes Prognosemodell verwendet ähnlich wie die technischen Indikatoren die Multiskalendarstellung. Die Approximationszeitreihen werden dabei durch das Polynom 2. Grades und die Detailszeitreihen durch die Verwendung der Sinusregression extrapoliert. Die anschließende Aggregation der extrapolierten Zeitreihen führt zu prognostizierten Wertpapierkursen. Kombinierte Handelsstrategien zeigen auf, wie Wavelet Stochastik Indikator, Wavelet Momentum Indikator und das Wavelet-basierte Prognosemodell miteinander verknüpft werden können. Durch die Verknüpfung einzelner Strategien gelingt es, die Buy&Hold-Strategie zu schlagen. Der letzte Abschnitt der Arbeit beschäftigt sich mit der Modellierung von Handelssystem-portfolios. Angestrebt wird eine gleichzeitige Diversifikation zwischen Anlagen und Strategien, die einer ständigen Optimierung unterworfen wird. Dieses Verfahren wird als ein systematischer, an bestimmte Optimierungskriterien gebundener Investmentprozess verstanden, mit welchem es gelingt, eine passive Buy&Hold-Strategie zu outperformen. Die Arbeit stellt eine systematische Verknüpfung zwischen der diskreten Wavelet Transformation und technisch quantitativen Investmentstrategien her. Es werden auch die Problemfelder der durchaus viel versprechenden Verwendung der Wavelet Transformation im Rahmen der technischen Analyse beleuchtet.

Learning-Based Approach to Real Time Tracking and Analysis of Faces

This paper describes a trainable system capable of tracking faces and facialsfeatures like eyes and nostrils and estimating basic mouth features such as sdegrees of openness and smile in real time. In developing this system, we have addressed the twin issues of image representation and algorithms for learning. We have used the invariance properties of image representations based on Haar wavelets to robustly capture various facial features. Similarly, unlike previous approaches this system is entirely trained using examples and does not rely on a priori (hand-crafted) models of facial features based on optical flow or facial musculature. The system works in several stages that begin with face detection, followed by localization of facial features and estimation of mouth parameters. Each of these stages is formulated as a problem in supervised learning from examples. We apply the new and robust technique of support vector machines (SVM) for classification in the stage of skin segmentation, face detection and eye detection. Estimation of mouth parameters is modeled as a regression from a sparse subset of coefficients (basis functions) of an overcomplete dictionary of Haar wavelets.

A Trainable Object Detection System: Car Detection in Static Images

This paper describes a general, trainable architecture for object detection that has previously been applied to face and peoplesdetection with a new application to car detection in static images. Our technique is a learning based approach that uses a set of labeled training data from which an implicit model of an object class -- here, cars -- is learned. Instead of pixel representations that may be noisy and therefore not provide a compact representation for learning, our training images are transformed from pixel space to that of Haar wavelets that respond to local, oriented, multiscale intensity differences. These feature vectors are then used to train a support vector machine classifier. The detection of cars in images is an important step in applications such as traffic monitoring, driver assistance systems, and surveillance, among others. We show several examples of car detection on out-of-sample images and show an ROC curve that highlights the performance of our system.

Representaciones conjuntas espacio-frecuencia en psicofísica visual : fundamentos 1D.

Resumen basado en el del autor. Resumen en español e inglésîp. 219-220

A hybrid approach of knowledge-based reasoning for structural assessment

La idea básica de detección de defectos basada en vibraciones en Monitorización de la Salud Estructural (SHM), es que el defecto altera las propiedades de rigidez, masa o disipación de energía de un sistema, el cual, altera la respuesta dinámica del mismo. Dentro del contexto de reconocimiento de patrones, esta tesis presenta una metodología híbrida de razonamiento para evaluar los defectos en las estructuras, combinando el uso de un modelo de la estructura y/o experimentos previos con el esquema de razonamiento basado en el conocimiento para evaluar si el defecto está presente, su gravedad y su localización. La metodología involucra algunos elementos relacionados con análisis de vibraciones, matemáticas (wavelets, control de procesos estadístico), análisis y procesamiento de señales y/o patrones (razonamiento basado en casos, redes auto-organizativas), estructuras inteligentes y detección de defectos. Las técnicas son validadas numérica y experimentalmente considerando corrosión, pérdida de masa, acumulación de masa e impactos. Las estructuras usadas durante este trabajo son: una estructura tipo cercha voladiza, una viga de aluminio, dos secciones de tubería y una parte del ala de un avión comercial.

Comparison of extrasystolic ECG signal classifiers using discrete wavelet transforms

This work compares and contrasts results of classifying time-domain ECG signals with pathological conditions taken from the MITBIH arrhythmia database. Linear discriminant analysis and a multi-layer perceptron were used as classifiers. The neural network was trained by two different methods, namely back-propagation and a genetic algorithm. Converting the time-domain signal into the wavelet domain reduced the dimensionality of the problem at least 10-fold. This was achieved using wavelets from the db6 family as well as using adaptive wavelets generated using two different strategies. The wavelet transforms used in this study were limited to two decomposition levels. A neural network with evolved weights proved to be the best classifier with a maximum of 99.6% accuracy when optimised wavelet-transform ECG data wits presented to its input and 95.9% accuracy when the signals presented to its input were decomposed using db6 wavelets. The linear discriminant analysis achieved a maximum classification accuracy of 95.7% when presented with optimised and 95.5% with db6 wavelet coefficients. It is shown that the much simpler signal representation of a few wavelet coefficients obtained through an optimised discrete wavelet transform facilitates the classification of non-stationary time-variant signals task considerably. In addition, the results indicate that wavelet optimisation may improve the classification ability of a neural network. (c) 2005 Elsevier B.V. All rights reserved.

A continuous wavelet transform and classification method for delirium motoric subtyping

The usefulness of motor subtypes of delirium is unclear due to inconsistency in subtyping methods and a lack of validation with objective measures of activity. The activity of 40 patients was measured over 24 h with a discrete accelerometer-based activity monitor. The continuous wavelet transform (CWT) with various mother wavelets were applied to accelerometry data from three randomly selected patients with DSM-IV delirium that were readily divided into hyperactive, hypoactive, and mixed motor subtypes. A classification tree used the periods of overall movement as measured by the discrete accelerometer-based monitor as determining factors for which to classify these delirious patients. This data used to create the classification tree were based upon the minimum, maximum, standard deviation, and number of coefficient values, generated over a range of scales by the CWT. The classification tree was subsequently used to define the remaining motoric subtypes. The use of a classification system shows how delirium subtypes can be categorized in relation to overall motoric behavior. The classification system was also implemented to successfully define other patient motoric subtypes. Motor subtypes of delirium defined by observed ward behavior differ in electronically measured activity levels.

Linear-wavelet models for non-linear identification applied to a pressure plant

A nonlinear regression structure comprising a wavelet network and a linear term is proposed for system identification. The theoretical foundation of the approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such models is described and the approach is tested with experimental data.

Linear-wavelet models applied to the identification of a two-link manipulator

This paper shows that a wavelet network and a linear term can be advantageously combined for the purpose of non linear system identification. The theoretical foundation of this approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such nonlinear regression structures, termed linear-wavelet models, is described. For illustration, sim ulation data are used to identify a model for a two-link robotic manipulator. The results show that the introduction of wavelets does improve the prediction ability of a linear model.

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

Linear-wavelet networks

This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated fermentation process, it is shown that a linear-wavelet network yields a smaller approximation error when compared with a wavelet network with the same number of regressors. The proposed technique is also applied to the identification of a pressure plant from experimental data. In this case, the results show that the introduction of wavelets considerably improves the prediction ability of a linear model. Standard errors on the estimated model coefficients are also calculated to assess the numerical conditioning of the identification process.