Distance Measures for Reduced Ordering Based Vector Filters

Reduced ordering based vector filters have proved successful in removing long-tailed noise from color images while preserving edges and fine image details. These filters commonly utilize variants of the Minkowski distance to order the color vectors with the aim of distinguishing between noisy and noise-free vectors. In this paper, we review various alternative distance measures and evaluate their performance on a large and diverse set of images using several effectiveness and efficiency criteria. The results demonstrate that there are in fact strong alternatives to the popular Minkowski metrics

Adaptive hybrid Metropolis-Hastings samplers for DSGE models

Bayesian inference for DSGE models is typically carried out by single block random walk Metropolis, involving very high computing costs. This paper combines two features, adaptive independent Metropolis-Hastings and parallelisation, to achieve large computational gains in DSGE model estimation. The history of the draws is used to continuously improve a t-copula proposal distribution, and an adaptive random walk step is inserted at predetermined intervals to escape difficult points. In linear estimation applications to a medium scale (23 parameters) and a large scale (51 parameters) DSGE model, the computing time per independent draw is reduced by 85% and 65-75% respectively. In a stylised nonlinear estimation example (13 parameters) the reduction is 80%. The sampler is also better suited to parallelisation than random walk Metropolis or blocking strategies, so that the effective computational gains, i.e. the reduction in wall-clock time per independent equivalent draw, can potentially be much larger.Markov Chain Monte Carlo (MCMC); Adaptive Metropolis-Hastings; Parallel algorithm; DSGE model; Copula

Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study

Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced

Fuzzy metrics and fuzzy logic for colour image filtering

El filtrado de imagen es una tarea fundamental para la mayoría de los sistemas de visión por computador cuando las imágenes se usan para análisis automático o, incluso, para inspección humana. De hecho, la presencia de ruido en una imagen puede ser un grave impedimento para las sucesivas tareas de procesamiento de imagen como, por ejemplo, la detección de bordes o el reconocimiento de patrones u objetos y, por lo tanto, el ruido debe ser reducido. En los últimos años el interés por utilizar imágenes en color se ha visto incrementado de forma significativa en una gran variedad de aplicaciones. Es por esto que el filtrado de imagen en color se ha convertido en un área de investigación interesante. Se ha observado ampliamente que las imágenes en color deben ser procesadas teniendo en cuenta la correlación existente entre los distintos canales de color de la imagen. En este sentido, la solución probablemente más conocida y estudiada es el enfoque vectorial. Las primeras soluciones de filtrado vectorial, como por ejemplo el filtro de mediana vectorial (VMF) o el filtro direccional vectorial (VDF), se basan en la teoría de la estadística robusta y, en consecuencia, son capaces de realizar un filtrado robusto. Desafortunadamente, estas técnicas no se adaptan a las características locales de la imagen, lo que implica que usualmente los bordes y detalles de las imágenes se emborronan y pierden calidad. A fin de solventar este problema, varios filtros vectoriales adaptativos se han propuesto recientemente. En la presente Tesis doctoral se han llevado a cabo dos tareas principales: (i) el estudio de la aplicabilidad de métricas difusas en tareas de procesamiento de imagen y (ii) el diseño de nuevos filtros para imagen en color que sacan provecho de las propiedades de las métricas difusas y la lógica difusa. Los resultados experimentales presentados en esta Tesis muestran que las métricas difusas y la lógica difusa son herramientas útiles para diseñar técnicas de filtrado,Morillas Gómez, S. (2007). Fuzzy metrics and fuzzy logic for colour image filtering [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1879Palanci

Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems. In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion and Hamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms

Particle Learning and Smoothing

Particle learning (PL) provides state filtering, sequential parameter learning and smoothing in a general class of state space models. Our approach extends existing particle methods by incorporating the estimation of static parameters via a fully-adapted filter that utilizes conditional sufficient statistics for parameters and/or states as particles. State smoothing in the presence of parameter uncertainty is also solved as a by-product of PL. In a number of examples, we show that PL outperforms existing particle filtering alternatives and proves to be a competitor to MCMC.Comment: Published in at http://dx.doi.org/10.1214/10-STS325 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust online signal extraction from multivariate time series

We introduce robust regression-based online filters for multivariate time series and discuss their performance in real time signal extraction settings. We focus on methods that can deal with time series exhibiting patterns such as trends, level changes, outliers and a high level of noise as well as periods of a rather steady state. In particular, the data may be measured on a discrete scale which often occurs in practice. Our new filter is based on a robust two-step online procedure. We investigate its relevant properties and its performance by means of simulations and a medical application. --Multivariate time series,signal extraction,robust regression,online methods