UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2024-11-23 11:47
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Conference: Bucharest University Faculty of Physics 2008 Meeting


Section: Electricity and Biophysics


Title:
Bayesian Neural Networks for Digital Image Restoration


Authors:
Radu Mutihac


Affiliation:
Universitatea din Bucuresti, Facultatea de Fizica


E-mail


Keywords:
Artificial neural networks, Bayesian statistics, Digital image processing.


Abstract:
The shape of any positive, additive image can be directly identified with a probability distribution. Any probabilistic treatment depends on knowledge of the point spread function of the imaging system and assumptions on noise, image statistics, and priors. A neuromorphic approach requires only relevant training examples where true scenes are known, irrespective of our inability or bias to express prior distributions. Trained artificial neural networks (ANNs) are much faster image restoration means, especially in the case of strong implicit priors in data Bayesian statistics provides a unifying and self-consistent framework for data modeling. Bayesian modeling deals naturally with uncertainty in data explained by marginalization in predictions of other variables. ANNs can be conceptualized as highly flexible multivariate regression and multiclass classification non-linear models. However, over-flexible ANNs may discover non-existent correlations in data. Data overfitting and poor generalization are alleviated by incorporating the principle of Occam’s razor, which controls model complexity and set the preference for simple models. Bayesian inference satisfies the likelihood principle in the sense that inferences depend only on the probabilities assigned to data that were measured and not on the properties of some admissible data that had never been acquired. Neuromorphic and Bayesian modeling may apparently look like extremes of the data modeling spectrum. ANNs are non-linear parallel computational devices endowed with gradient descent algorithms trained by example to solve prediction and classification problems. In contrast, Bayesian statistics is based on coherent inference and clear axioms. Yet both approaches aim to create models in agreement with data. Bayesian decision theory provides intrinsic means to model ranking. Bayesian inference for ANNs can be implemented numerically by deterministic methods involving Gaussian approximations or by Monte-Carlo methods.