title: Semi-blind sparse image reconstruction with application to MRFM.
abstract: 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.
authors.affiliation: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2122, USA. seunpark@umich.edu
authors.forename: Se Un
authors.initials: SU
authors.lastname: Park
authors.forename: Nicolas
authors.initials: N
authors.lastname: Dobigeon
authors.forename: Alfred O
authors.initials: AO
authors.lastname: Hero
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D009682:Magnetic Resonance Spectroscopy / Q000379:methods*; D008390:Markov Chains; D008853:Microscopy / Q000379:methods*; D015233:Models, Statistical; D009010:Monte Carlo Method