Dimension Reduction for Time Series in a Blind Source Separation Context Using R

Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first reducing the dimension of the series and then modelling the resulting uncorrelated signals univariately, avoiding the need for any covariance parameters. A popular and effective framework for this is blind source separation. In this paper we review the dimension reduction tools for time series available in the R package tsBSS. These include methods for estimating the signal dimension of second-order stationary time series, dimension reduction techniques for stochastic volatility models and supervised dimension reduction tools for time series regression. Several examples are provided to illustrate the functionality of the package

Dimension Reduction for Time Series in a Blind Source Separation Context Using R

Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first reducing the dimension of the series and then modelling the resulting uncorrelated signals univariately, avoiding the need for any covariance parameters. A popular and effective framework for this is blind source separation. In this paper we review the dimension reduction tools for time series available in the R package tsBSS. These include methods for estimating the signal dimension of second-order stationary time series, dimension reduction techniques for stochastic volatility models and supervised dimension reduction tools for time series regression. Several examples are provided to illustrate the functionality of the package.</p

A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images

Speckle is a granular disturbance, usually modeled as a multiplicative noise, that affects synthetic aperture radar (SAR) images, as well as all coherent images. Over the last three decades, several methods have been proposed for the reduction of speckle, or despeckling, in SAR images. Goal of this paper is making a comprehensive review of despeckling methods since their birth, over thirty years ago, highlighting trends and changing approaches over years. The concept of fully developed speckle is explained. Drawbacks of homomorphic filtering are pointed out. Assets of multiresolution despeckling, as opposite to spatial-domain despeckling, are highlighted. Also advantages of undecimated, or stationary, wavelet transforms over decimated ones are discussed. Bayesian estimators and probability density function (pdf) models in both spatial and multiresolution domains are reviewed. Scale-space varying pdf models, as opposite to scale varying models, are promoted. Promising methods following non-Bayesian approaches, like nonlocal (NL) filtering and total variation (TV) regularization, are reviewed and compared to spatial- and wavelet-domain Bayesian filters. Both established and new trends for assessment of despeckling are presented. A few experiments on simulated data and real COSMO-SkyMed SAR images highlight, on one side the costperformance tradeoff of the different methods, on the other side the effectiveness of solutions purposely designed for SAR heterogeneity and not fully developed speckle. Eventually, upcoming methods based on new concepts of signal processing, like compressive sensing, are foreseen as a new generation of despeckling, after spatial-domain and multiresolution-domain method

Audio source separation for music in low-latency and high-latency scenarios

Aquesta tesi proposa mètodes per tractar les limitacions de les tècniques existents de separació de fonts musicals en condicions de baixa i alta latència. En primer lloc, ens centrem en els mètodes amb un baix cost computacional i baixa latència. Proposem l'ús de la regularització de Tikhonov com a mètode de descomposició de l'espectre en el context de baixa latència. El comparem amb les tècniques existents en tasques d'estimació i seguiment dels tons, que són passos crucials en molts mètodes de separació. A continuació utilitzem i avaluem el mètode de descomposició de l'espectre en tasques de separació de veu cantada, baix i percussió. En segon lloc, proposem diversos mètodes d'alta latència que milloren la separació de la veu cantada, gràcies al modelatge de components específics, com la respiració i les consonants. Finalment, explorem l'ús de correlacions temporals i anotacions manuals per millorar la separació dels instruments de percussió i dels senyals musicals polifònics complexes.Esta tesis propone métodos para tratar las limitaciones de las técnicas existentes de separación de fuentes musicales en condiciones de baja y alta latencia. En primer lugar, nos centramos en los métodos con un bajo coste computacional y baja latencia. Proponemos el uso de la regularización de Tikhonov como método de descomposición del espectro en el contexto de baja latencia. Lo comparamos con las técnicas existentes en tareas de estimación y seguimiento de los tonos, que son pasos cruciales en muchos métodos de separación. A continuación utilizamos y evaluamos el método de descomposición del espectro en tareas de separación de voz cantada, bajo y percusión. En segundo lugar, proponemos varios métodos de alta latencia que mejoran la separación de la voz cantada, gracias al modelado de componentes que a menudo no se toman en cuenta, como la respiración y las consonantes. Finalmente, exploramos el uso de correlaciones temporales y anotaciones manuales para mejorar la separación de los instrumentos de percusión y señales musicales polifónicas complejas.This thesis proposes specific methods to address the limitations of current music source separation methods in low-latency and high-latency scenarios. First, we focus on methods with low computational cost and low latency. We propose the use of Tikhonov regularization as a method for spectrum decomposition in the low-latency context. We compare it to existing techniques in pitch estimation and tracking tasks, crucial steps in many separation methods. We then use the proposed spectrum decomposition method in low-latency separation tasks targeting singing voice, bass and drums. Second, we propose several high-latency methods that improve the separation of singing voice by modeling components that are often not accounted for, such as breathiness and consonants. Finally, we explore using temporal correlations and human annotations to enhance the separation of drums and complex polyphonic music signals

Detection of non-stationary dynamics using sub-space based representations, cyclic based and variability constraints

La siguiente Tesis de Maestría propone una metodología para el análisis de series de tiempo no-estacionarias con el propósito de filtrado y detección de ruido en reconocimiento de patrones. La metodología se encuentra dividida en dos etapas: el análisis de comportamientos no-estacionarios que recaen en procesos cíclicos y como diferentes componentes no-periódicos afectan el análisis de la señal. El segundo enfoque, está centrado en el problema de extracción de series de tiempo no-estacionarias que afectan procesos estacionarios. Ambos esquemas están basados en restricciones de (ciclo-)estacionariead y representaciones basadas en subespacios de manera que mediante la evaluación de las dinámicas de la señal sea posible identificar las componentes no-estacionarias indeseadas. Los resultados se muestran para cada enfoque de manera independiente por medio de datos sintéticos y reales, el desempeño obtenido muestra una gran capacidad de detección, rechazo y/o extracción de ruido y artefactos en series de tiempo (ciclo-)estacionarias usando restricciones de estacionariedad así como condiciones cíclicas basadas en la naturaleza de la señalAbstract : The present Master’s Thesis proposes a methodology for the non–stationary time-series analysis for filtering and noise rejection purposes in pattern recognition. The methodology is divided into two different approaches: the analysis of periodic non–stationary behavior that relies into a cyclic process and how additional non–cyclic non–stationarities disrupt and affect the signal processing. Second approach deals with the problem of non–stationary signal extraction that affects inherent weak stationary processes. Both frameworks of analysis take base on (cyclo-)stationary constraints and subspace based representations in order to assess and characterize the signals dynamics to facilitate the identification of the undesired non–stationary components. Results are shown over each approach with different real and synthetic data, the obtained performances show high rejection, detection and extraction capabilities for noise and artifacts in (cyclo)–stationary signals using external and internal based constraints of analysis and high separation capability for stationary signalsMaestrí

Independent component analysis for time series

El objetivo de esta tesis es aplicar el análisis de componentes independientes (ICA) sobre datos multivariantes de series temporales. También, se propone un nuevo procedimiento para predecir un vector de series temporales a partir de un número reducido de componentes independientesThe aim of this thesis is to analyze the performance of independent component analysis (ICA) when it is applied to a vector of non-Gaussian time series in order to find an "interesting" representation of the observations. First, we give an introduction to the ICA methodology and how it performs on estimating a set of non-Gaussian and statistically independent latent factors. Second, we review some basic ideas of multivariate time series analysis, paying special attention to well known dimension reduction techniques previously proposed in the literature. Third, we give an overview of the existing research that links ICA and time series data. Finally we outline the thesisSEJ2006-04957S2007-HUM-0413SEJ2007-64500ECO2009-1028

Advances in variational Bayesian nonlinear blind source separation

Linear data analysis methods such as factor analysis (FA), independent component analysis (ICA) and blind source separation (BSS) as well as state-space models such as the Kalman filter model are used in a wide range of applications. In many of these, linearity is just a convenient approximation while the underlying effect is nonlinear. It would therefore be more appropriate to use nonlinear methods. In this work, nonlinear generalisations of FA and ICA/BSS are presented. The methods are based on a generative model, with a multilayer perceptron (MLP) network to model the nonlinearity from the latent variables to the observations. The model is estimated using variational Bayesian learning. The variational Bayesian method is well-suited for the nonlinear data analysis problems. The approach is also theoretically interesting, as essentially the same method is used in several different fields and can be derived from several different starting points, including statistical physics, information theory, Bayesian statistics, and information geometry. These complementary views can provide benefits for interpretation of the operation of the learning method and its results. Much of the work presented in this thesis consists of improvements that make the nonlinear factor analysis and blind source separation methods faster and more stable, while being applicable to other learning problems as well. The improvements include methods to accelerate convergence of alternating optimisation algorithms such as the EM algorithm and an improved approximation of the moments of a nonlinear transform of a multivariate probability distribution. These improvements can be easily applied to other models besides FA and ICA/BSS, such as nonlinear state-space models. A specialised version of the nonlinear factor analysis method for post-nonlinear mixtures is presented as well.reviewe