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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
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Overview
• introduction
• MCMC
• Particle filtering
• What we can offer
• What we look for
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Numerical Bayesian Techniques
• Bayesian methods frequently involve integrals of– Averaging– Marginalisation– Normalisation
which are difficult to evaluate.• Therefore numerical integration techniques are
adopted.
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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
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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
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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
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Applications we have worked on
• Source separation
• Speckle filtering in synthetic aperture radar images
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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
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Preliminary results with a special case of Particle filter
SAR image 5 looks
Particle FilterGamma Filter
Optical image
Copyright @ Gençağa et. al.
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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