Semi-blind sparse image reconstruction with application to MRFM

Se Un Park (1) , Nicolas Dobigeon (2, 3) , Alfred O. Hero (1)

1 EECS - Department of Electrical Engineering and Computer Science
2 IRIT-SC - Signal et Communications
3 Toulouse INP - Institut National Polytechnique (Toulouse)

We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a high-dimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of our Bayesian semi-blind algorithm for sparse images is superior to previously proposed semi-blind algorithms such as the alternating minimization algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data.

Mots clés: Bayesian inference; Magnetic resonance force microscopy (MRFM) experiment; Markov chain Monte Carlo (MCMC) methods; Semi-blind (myopic) sparse deconvolution

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

Se Un Park, Nicolas Dobigeon, Alfred O. Hero. Semi-blind sparse image reconstruction with application to MRFM. IEEE Transactions on Image Processing, 2012, vol. 21, pp. 3838-3849. ⟨10.1109/TIP.2012.2199505⟩. ⟨hal-00729998⟩