Computationally intensive methods Ercan E. Kuruoglu CNR – Istituto di Scienza e Tecnologie dell’Informazione Pisa, Italy Muscle Joint WP5-WP7 Focus Meeting, Rocquencourt, December 2005

introduction MCMC Particle filtering What we can offer Overview introduction MCMC Particle filtering What we can offer What we look for

Numerical Bayesian Techniques Bayesian methods frequently involve integrals of Averaging Marginalisation Normalisation which are difficult to evaluate. Therefore numerical integration techniques are adopted.

Alternative Statistics In most applications of statistical signal and image processing classical statistical measures, i.e. second order statistics is used Instead a wide variety of other statistics exists Higher order statistics Fractional lower order statistics Log statistics Extreme value statistics We would like to explore the potentials of log statistics and extreme values statistics in image, video and multimedia problems

Markov Chain Monte Carlo Samples from a pdf with clever Markov Chain moves Economic in terms of samples needed for describing a pdf Analytical difficulties are surpassed

Particle Filtering In various real life applications, the signal is non-stationary, and MCMC being a batch processing technique falls short of following non-stationarity Wiener filter Kalman filter linear observations (h) Gaussian observation noise (n) linear state process (f) Gaussian process noise (v)

Applications we have worked on Source separation Speckle filtering in synthetic aperture radar images

Astrophysical source separation

Original sources : CMB Galactic Syncrotron Galactic Dust Observed maps: 30 Ghz 70 Ghz 143 Ghz

SAR speckle filtering

Preliminary results with a special case of Particle filter Optical image SAR image 5 looks Gamma Filter Particle Filter Copyright @ Gençağa et. al.

What we would like to share with partners Expertise in MCMC and Particle filtering Expertise in extreme value statistics, alpha-stable models (impulsive and nonsymmetric data models Particle filtering code For model selection problems: Reversible Jump MCMC code