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Optimisation in Signal and Image Processing by Patrick Siarry

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Chapter 4

Information Criteria: Examples of Applications in Signal and Image Processing

4.1. Introduction and context

In this chapter we will focus on the sequence of N observations xN = (xl, ..., xN) on a stationary and random process consisting of a family of random variables X = {Xn}nimagesZ distributed according to the same unknown law θ. A model θk based on k free parameters will represent this process X. Determining the optimal estimation imagesk of θk in the maximum likelihood (ML) sense enables us to find imagesk which maximizes f(xNk) where f represents the conditional density probability of the observations xN when choosing the model θk. Finding imagesk which will minimize Lk) = −log f(xNk) and therefore images has the same effect.

Even though this criterion of estimation is expressed by a fixed number k, it might be tempting to use this criterion to carry out a simultaneous estimation of the model’s parameters and its number of free parameters, which in a written form can be expressed as follows: ...

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