Publications of Francesco Carravetta

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IASI Research Report n. 671  (Previous    Next)  

Francesco Carravetta

Nearest-neighbour modelling of reciprocal chains

ABSTRACT
This paper focuses on the class of finite-states, discrete-index, reciprocal processes (reciprocal chains). Such a class of processes seems to be a suitable setup in many applications, and in particular it appears well suited for image-processing. While addressing this issue, the aim is twofold: theoretic and practical. As to the theoretic purpose, some new results are provided: first, a general stochastic realization result is provided for reciprocal chains endowed with a known, but no matter how it is, distribution. Such model has the form of a fixed-degree nearest-neighbour polynomial model. Next, the polynomial model is shown to be exactly linearizable, which means it is equivalent to a nearest-neighbour linear model in a different set of variables. The latter model results to be formally identical to the Levi-Frezza-Krener linear model of a Gaussian reciprocal process, although actually nonlinear respect to the chain's values. As far as the practical purpose is concerned, in order to yield an example of application an estimation issue is addressed: a suboptimal (polynomial-optimal) solution is derived for the smoothing problem of a reciprocal chain partially observed under non-Gaussian noise. To this purpose, two kinds of boundary conditions (Dirichelet and Cyclic), specifying the reciprocal chain on a finite interval, are considered, and in both cases the model is shown to be well-posed, in a 'wide-sense'. Under this view, some well known representation results about Gaussian reciprocal processes, in a sense, extend to a 'non-Gaussian' case by reason of the present paper. Key words: Reciprocal processes, Markov chains, Markov fields, Smoothing algorithms, Stochastic realization, Nearest-neighbour models.
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