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We present a variational Bayesian method of joint image reconstruction andpoint spread function (PSF) estimation when the PSF of the imaging device isonly partially known. To solve this semi-blind deconvolution problem, priordistributions are specified for the PSF and the 3D image. Joint imagereconstruction and PSF estimation is then performed within a Bayesianframework, using a variational algorithm to estimate the posteriordistribution. The image prior distribution imposes an explicit atomic measurethat corresponds to image sparsity. Importantly, the proposed Bayesiandeconvolution algorithm does not require hand tuning. Simulation resultsclearly demonstrate that the semi-blind deconvolution algorithm comparesfavorably with previous Markov chain Monte Carlo (MCMC) version of myopicsparse reconstruction. It significantly outperforms mismatched non-blindalgorithms that rely on the assumption of the perfect knowledge of the PSF. Thealgorithm is illustrated on real data from magnetic resonance force microscopy(MRFM).

Variational Semi-blind Sparse Deconvolution with Orthogonal Kernel Bases and its Application to MRFM