This paper addresses the problem of joint image reconstruction and point spread function PSF) estimation when the PSF of
the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for
the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework,
using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic
measure that corresponds to image sparsity. Simulation results demonstrate that the semi-blind deconvolution algorithm
compares favorably with previous Markov chain Monte Carlo MCMC) version of myopic sparse reconstruction. It also
outperforms non-myopic algorithms that rely on perfect knowledge of the PSF. The algorithm is illustrated on real data from
magnetic resonance force microscopy MRFM).
We propose a solution to the image deconvolution problem where the convolution operator 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 uncertainty in a high dimensional space. Specifically,
we assume the image is sparse corresponding to the natural sparsity of magnetic resonance force microscopy
(MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of
our Bayesian myopic algorithm is superior to previously proposed algorithms such as the alternating minimization
(AM) algorithm for sparse images. We illustrate our myopic algorithm on real MRFM tobacco virus data.
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