Recuperación de imágenes usando modelos auto-regresivos condicionales: CAR e IAR

This article performs Bayesian estimation of Gaussian Markov random fields. In particular, it is proposed to perform a spatial dependency analysis by means of a graph that characterizes the observed intensities of an image with a model widely used in spatial statistics and geostatistics known as the conditional autoregressive model (CAR). This model is useful for obtaining multivariate joint distributions from a random vector based on univariate conditional specifications. These conditional specifications are based on the Markov properties, so that the conditional distribution of a component of the random vector depends only on a set of neighbors, defined by the graph. Conditional autoregressive models are particular cases of random Markov fields and are used as a priori distributions, which, combined with the information contained in the sample data (likelihood function), induce a a posteriori distribution on which the estimate is based. The CAR model has a particular case called IAR, in which the a priori distribution is not proper, in this article both models are applied making a comparison between them. All model parameters are estimated in a completely Bayesian environment, using the Metropolis-Hastings algorithm. The complete estimation procedures are illustrated and compared using various artificial examples. For these experiments, the CAR model and the IAR model performed very favorably with homogeneous images Este artículo realiza la estimación Bayesiana de campos aleatorios gausianos de Markov. En particular, se propone realizar un análisis de dependencia espacial por medio de un grafo que caracteriza las intensidades observadas de una imagen con un modelo ampliamente utilizado en estadística espacial y geoestadística conocido como modelo autorregresivo condicional (CAR por sus siglas en inglés). Este modelo es útil para obtener distribuciones conjuntas multivariadas de un vector aleatorio basado en especificaciones condicionales univariadas. Estas especificaciones condicionales se basan en las propiedades de Markov, de modo que la distribución condicional de un componente del vector aleatorio depende solo de un conjunto de vecinos, definido por el grafo. Los modelos autorregresivos condicionales son casos particulares de campos aleatorios de Markov y se utilizan como distribuciones a priori, que combinadas con la información contenida en los datos de la muestra (función de verosimilitud), inducen una distribución a posteriori en las que se basa