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

TL;DR

This paper introduces a variational Bayesian semi-blind deconvolution method that jointly reconstructs images and estimates PSF with minimal tuning, outperforming traditional methods especially in MRFM applications.

Contribution

It presents a novel variational Bayesian approach for semi-blind deconvolution that effectively estimates PSF and image simultaneously without manual parameter tuning.

Findings

Outperforms previous MCMC-based methods in accuracy.

Significantly better than non-blind algorithms with mismatched PSF.

Successfully applied to real MRFM data.

Abstract

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).