We develop two likelihood based approaches to semiparametrically estimate the time-inhomogeneous diffusion process: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selection methods. Separate bandwidths are used for dr...

In this paper, the problem of identifying a hidden Markov model (HMM) with general state space, e.g. a partially observed diffusion process, is considered. A particle implementation of the recursive maximum likelihood estimator for a parameter in the transition kernel of the Markov chain is presented. The key assumption is that the derivative of the transition kernel w.r.t. the parameter has a ...

In this paper we design a smoothing filter for texture+depth images based on anisotropic diffusion. Our proposed filter is linear and allows to generate a scale space of the texture image which preserves internal image structure (i.e. it does not smooth through object boundaries). Moreover, we show experimentally that our filter demonstrates better stability under camera position changes in suc...

In this article, we develop a linear theory for optimal filtering of complex turbulent signals with model errors through linear autoregressive models. We will show that when the autoregressive model parameters are chosen such that they satisfy absolute stability and consistency conditions of at least order-2 of the classical multistep method for solving initial value problems, the filtered solu...

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

The goal of the present paper is to provide an overview of the commonly used nonlinear diffusion methods and to discuss their properties in the framework of ancient engraving enhancement. In [12] we proposed a directional diffusion method as a scale space transformation. The directional filter is based on a classical diffusion filter including a global orientation information. In this article w...

A very low voltage 9th order linear phase baseband switched capacitor (SC) filter has been designed to be used as part of a cellular GSM (Global System Mobile) receiver. A Gaussian-to-6dB filter of the order of seven is chosen and a second order function is added to reduce the group delay variations around. The filter uses a fully differential topology to increase the dynamic range and reduce t...

We present an R package bssm for Bayesian non-linear/non-Gaussian state space modelling. Unlike the existing packages, allows easy-to-use approximate inference based on Gaussian approximations such as Laplace approximation and extended Kalman filter. The accommodates also discretely observed latent diffusion processes. is fully automatic, adaptive Markov chain Monte Carlo (MCMC) hyperparameters...