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Variational Bayesian image reconstruction with an uncertainty model for measurement localization

We propose a general data acquisition model with volatile random displacement of measured samples. Discrepancies between recorded and true positions of the original data is due to the nature of measured data or the acquisition device itself. A reconstruction method based on the Variational Bayesian inference is proposed, which estimates the original data from samples acquired with the acquisition model, and its relation to Jensen's inequality is discussed. A model variant of 2D image reconstruction is analyzed in detail. Further, we outline a relation between the proposed method and the classic deconvolution problem, and illustrate superiority of the Variational Bayesian approach in the case of small number of samples.