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

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)

tttmtt nDsHy ,:1

1t t t t x A x v

Applications we have worked on

• Source separation

• Speckle filtering in synthetic aperture radar images

Astrophysical source separationAstrophysical source separation

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Original sources : CMB Galactic Syncrotron Galactic Dust

Observed maps: 30 Ghz 70 Ghz 143 Ghz

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SAR speckle filtering

Preliminary results with a special case of Particle filter

SAR image 5 looks

Particle FilterGamma Filter

Optical image

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