Deconvolution with gaussian blur parameter and hyperparameters estimation

François Orieux (1) , Jean-François Giovannelli (1, 2) , Thomas Rodet (1)

1 L2S - Laboratoire des signaux et systèmes
2 IMS - Laboratoire de l'intégration, du matériau au système

This paper proposes a Bayesian approach for unsupervised image deconvolution when the parameter of the gaussian PSF is unknown. The parameters of the regularization parameters are also unknown and jointly estimated with the other parameters. The solution is found by inferring on a global a posteriori law for unknown object and parameters. The estimate is chosen in the sense of the posterior mean, numerically calculated by means of a Monte-Carlo Markov chain algorithm. The computation is efficiently done in Fourier space and the practicability of the method is shown on simulated examples. Results show high-frequencies restoration in the estimated image with correct estimation of the hyperparameters and instrument parameters.

Mots clés: Index Terms -High-dimensional sampling; Big Data; Gibbs sampling; Bayesian strategy; inverse problem

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

François Orieux, Jean-François Giovannelli, Thomas Rodet. Deconvolution with gaussian blur parameter and hyperparameters estimation. ICASSP 2010 - 35th IEEE International Conference on Acoustics, Speech and Signal Processing, Mar 2010, Dallas, TX, United States. pp.1350 - 1353, ⟨10.1109/ICASSP.2010.5495444⟩. ⟨hal-00546590⟩