Variational Semi-blind Sparse Deconvolution with Orthogonal Kernel Bases and its Application to MRFM
This work addresses image reconstruction in scenarios with imperfect PSF knowledge, such as in magnetic resonance force microscopy (MRFM), but it is incremental as it builds on existing Bayesian and sparse deconvolution techniques.
The authors tackled the problem of semi-blind deconvolution for image reconstruction and point spread function (PSF) estimation when the PSF is partially known, using a variational Bayesian method with an explicit sparsity prior, and demonstrated that it outperforms mismatched non-blind algorithms and compares favorably with previous MCMC methods.
We present a variational Bayesian method 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. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM).