Computation of the one-dimensional unwrapped phase

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 101-102). "Cepstrum bibliography" (p. 67-100).In this thesis, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 27r discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This thesis presents existing algorithms for computing the unwrapped phase, discussing their weaknesses and strengths. Then two composite algorithms are proposed that use the existing ones, combining their strengths while avoiding their weaknesses. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.by Zahi Nadim Karam.S.M

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Similarity measures for clustering sequences and sets of data

The main object of this PhD. Thesis is the definition of new similarity measures for data sequences, with the final purpose of clustering those sequences. Clustering consists in the partitioning of a dataset into isolated subsets or clusters. Data within a given cluster should be similar, and at the same different from data in other clusters. The relevance of data sequences clustering is ever-increasing, due to the abundance of this kind of data (multimedia sequences, movement analysis, stock market evolution, etc.) and the usefulness of clustering as an unsupervised exploratory analysis method. It is this lack of supervision that makes similarity measures extremely important for clustering, since it is the only guide of the learning process. The first part of the Thesis focuses on the development of similarity measures leveraging dynamical models, which can capture relationships between the elements of a given sequence. Following this idea, two lines are explored: • Likelihood-based measures: Based on the popular framework of likelihood-matrix-based similarity measures, we present a novel method based on a re-interpretation of such a matrix. That interpretations stems from the assumption of a latent model space, so models used to build the likelihood matrix are seen as samples from that space. The method is extremely flexible since it allows for the use of any probabilistic model for representing the individual sequences. • State-space trajectories based measures: We introduce a new way of defining affinities between sequences, addressing the main drawbacks of the likelihood-based methods. Working with state-space models makes it possible to identify sequences with the trajectories that they induce in the state-space. This way, comparisons between sequences amounts to comparisons between the corresponding trajectories. Using a common hidden Markov model for all the sequences in the dataset makes those comparisons extremely simple, since trajectories can be identified with transition matrices. This new paradigm improves the scalability of the affinity measures with respect to the dataset size, as well as the performance of those measures when the sequences are short. The second part of the Thesis deals with the case where the dynamics of the sequences are discarded, so the sequences become sets of vectors or points. This step to be taken, without harming the learning process, when the statical features (probability densities) of the different sets are informative enough for the task at hand, which is true for many real scenarios. Work along this line can be further subdivided in two areas: • Sets-of-vectors clustering based on the support of the distributions in a feature space: We propose clustering the sets using a notion of similarity related to the intersection of the supports of their underlying distributions in a Hilbert space. Such a clustering can be efficiently carried out in a hierarchical fashion, in spite of the potentially infinite dimensionality of the feature space. To this end, we propose an algorithm based on simple geometrical arguments. Support estimation is inherently a simpler problem than density estimation, which is the usual starting step for obtaining similarities between probability distributions. • Classifer-based affinity and divergence measures: It is quite natural to link the notion of similarity between sets with the separability between those sets. That separability can be quantified using binary classifiers. This intuitive idea is then extended via generalizations of the family of f-divergences, which originally contains many of the best-known divergences in statistics and machine learning. The proposed generalizations present interesting theoretical properties, and at the same time they have promising practical applications, such as the development of new estimators for standard divergences. -----------------------------------------------------------------------------------------------------------------------------------------------------------------------El objetivo de esta Tesis Doctoral es la definición de nuevas medidas de similitud para secuencias y conjuntos de datos, con la finalidad de servir de entrada a un algoritmo de agrupamiento o clustering [Xu and Wunsch-II, 2005]. El agrupamiento es una de las tareas más habituales dentro del ámbito del aprendizaje máquina (machine learning) [Mitchell, 1997]. Dicha tarea consiste en la partición de un conjunto de datos en subconjuntos aislados (clusters), de tal forma que los datos asignados a un mismo subconjunto sean parecidos entre sí, y distintos a los datos pertenecientes a otros subconjuntos. Una de sus principales particularidades es que se trata de una tarea no supervisada, lo cual implica que no requiere de un conjunto de ejemplos etiquetados. De esta forma se reduce la interacción humana necesaria para el aprendizaje, haciendo del agrupamiento una herramienta ideal para el análisis exploratorio de datos complejos. Por otro lado, es precisamente esta falta de supervisión la que hace fundamental el disponer de una medida adecuada de similitud entre elementos, ya que es la única guía durante el proceso de aprendizaje. El agrupamiento de secuencias es una tarea cada día más importante debido al reciente auge de este tipo de datos. Cabe destacar el ámbito multimedia, en el que muchos contenidos presentan características secuenciales: señales de voz, audio, vídeo, etc. No es un ejemplo aislado, ya que en muchos otros ámbitos se producen casuísticas similares: desde los datos de bolsa y mercados financieros diversos al problema del análisis de movimiento. En la mayoría de estos casos la complejidad de los datos de entrada se une a la dificultad y elevado coste del etiquetado manual de dichos datos. Es precisamente en este tipo de escenarios en los que el agrupamiento es especialmente útil, debido a que no requiere de un etiquetado previo. En muchos casos es posible prescindir de la dinámica de las secuencias sin perjudicar el proceso de aprendizaje. Son aquellos casos en los que las características estáticas de los datos de entrada son suficientemente discriminativas. Al obviar la dinámica, las secuencias se transforman en conjuntos de datos, que se interpretan como muestras (no necesariamente independientes) de unas determinadas distribuciones de probabilidad subyacentes. Ejemplos prácticos de ámbitos en los que se trabaja con conjuntos de datos incluyen el agrupamiento de locutores [Campbell, 1997], los modelos de bolsa de palabras (bag of words) para texto/imagen [Dance et al., 2004], etc. En la presente Tesis propondremos métodos y, sobre todo, puntos de vista innovadores para la definición de similitudes entre secuencias o conjuntos de datos. Todos los métodos propuestos han sido analizados desde un punto de vista tanto teórico como empírico. Desde la perspectiva experimental se ha tratado de trabajar con la mayor cantidad de datos reales posibles, haciendo especial hincapié en las tareas de agrupamiento de locutores y reconocimiento de género musical

Mathematical linguistics

but in fact this is still an early draft, version 0.56, August 1 2001. Please d

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

Suprasegmental representations for the modeling of fundamental frequency in statistical parametric speech synthesis

Statistical parametric speech synthesis (SPSS) has seen improvements over recent years, especially in terms of intelligibility. Synthetic speech is often clear and understandable, but it can also be bland and monotonous. Proper generation of natural speech prosody is still a largely unsolved problem. This is relevant especially in the context of expressive audiobook speech synthesis, where speech is expected to be fluid and captivating. In general, prosody can be seen as a layer that is superimposed on the segmental (phone) sequence. Listeners can perceive the same melody or rhythm in different utterances, and the same segmental sequence can be uttered with a different prosodic layer to convey a different message. For this reason, prosody is commonly accepted to be inherently suprasegmental. It is governed by longer units within the utterance (e.g. syllables, words, phrases) and beyond the utterance (e.g. discourse). However, common techniques for the modeling of speech prosody - and speech in general - operate mainly on very short intervals, either at the state or frame level, in both hidden Markov model (HMM) and deep neural network (DNN) based speech synthesis. This thesis presents contributions supporting the claim that stronger representations of suprasegmental variation are essential for the natural generation of fundamental frequency for statistical parametric speech synthesis. We conceptualize the problem by dividing it into three sub-problems: (1) representations of acoustic signals, (2) representations of linguistic contexts, and (3) the mapping of one representation to another. The contributions of this thesis provide novel methods and insights relating to these three sub-problems. In terms of sub-problem 1, we propose a multi-level representation of f0 using the continuous wavelet transform and the discrete cosine transform, as well as a wavelet-based decomposition strategy that is linguistically and perceptually motivated. In terms of sub-problem 2, we investigate additional linguistic features such as text-derived word embeddings and syllable bag-of-phones and we propose a novel method for learning word vector representations based on acoustic counts. Finally, considering sub-problem 3, insights are given regarding hierarchical models such as parallel and cascaded deep neural networks