Bayesian signal processing

Affiliation: Istituto di Scienza e Tecnologie dell'Informazione "Alessandro Faedo", Area della Ricerca del CNR di Pisa

Duration: 16 hours

Period: April 18 - May 3, 2005

Place: Dipartimento di Ingegneria dell'Informazione: Elettronica, Informatica, Telecomunicazioni, via G. Caruso, meeting room, ground floor

Credits: 4

Final test: yes

Contacts: Prof. Fulvio Gini

Aims

Bayesian data analysis methods have become increasingly important in many fields such as economics, bioinformatics, computer science in the last decade. In particular, Bayesian approach has received an ever increasing momentum in the field of signal processing and classical statistical signal processing has been revolutionised into Bayesian signal processing. This change has been reflected immediately to applications such as image segmentation, audio restoration and machine vision with great success. This course aims to equip interested graduate students with the necessary theoretical background and the technical tools and also to present them various applications where Bayesian data analysis had and would have important potentials. Latest developments in the Bayesian field such as particle filters will also be presented which are hoped to lead to new research ideas in the classroom.

Syllabus

Bayes theorem, classical versus Bayesian statistics, Bayesian philosophy (1 hour)
MAP estimation, Bayesian risk estimator, Bayesian detection (1 hour)
Single parameter models, multiparameter models (1 hour)
Hierarchical models (1 hour)
Numerical Bayesian techniques (1 hour)
Bayesian importance sampling
Markov Chain Monte Carlo (MCMC) (2 hours)
Metropolis algorithm
Metropolis-Hastings
Gibbs sampling
Bayesian image processing (2 hours)
Markov random fields
MCMC
Segmentation
Filtering
...
Bayesian dynamical models (3 hours)
Kalman filtering
Extended Kalman Filter
Unscented Kalman Filter
Particle filters
Applications (3 hours)
Telecom
Bioinformatics
Computer vision
...
Case study: source separation of astronomy images (1 hour)