Fisica statistica

# Phase Transitions of Generalized Sparse Gaussian Prior in Bayesian Image Modeling

## by Kazuyuki Tanaka (GSIS, Tohoku University, Sendai, Japan)

Europe/Rome
Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

### Aula Conversi

#### Dip. di Fisica - Edificio G. Marconi

Description
In the Bayesian image modeling, a generalized sparse Gaussian prior probability distribution is one of very useful priors. Our prior includes sparsity in each interaction term between every pair of neighbouring nodes in Markov random fields. The sparsity is based on the $L_p$ norm ($0<p<2$). It corresponds to one of $L_{p}$-norm total variations in the regularization problem. In this talk, we show some phase transitions by applying the loopy belief propagation to the prior. In the loopy belief propagation, the present prior exhibits not only second-order phase transition but also first-order transition in a region of strong sparseness.