Semi-blind Sparse Image Reconstruction with Application to MRFM

TL;DR

This paper introduces a Bayesian semi-blind deconvolution method tailored for sparse images in MRFM, effectively handling partial PSF knowledge and outperforming existing algorithms in reconstructing real MRFM data.

Contribution

It presents a novel Bayesian semi-blind deconvolution approach that exploits PSF perturbations and sparsity, specifically designed for MRFM images, with superior performance over prior methods.

Findings

Outperforms previous semi-blind algorithms in MRFM image reconstruction

Effectively models PSF uncertainty using principal components

Demonstrated on real MRFM tobacco virus data

Abstract

We propose a solution to the image deconvolution problem where the convolution kernel 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 PSF uncertainty in a high dimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of our Bayesian semi-blind algorithm for sparse images is superior to previously proposed semi-blind algorithms such as the alternating minimization (AM) algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data.