Semi-blind Sparse Image Reconstruction with Application to MRFM
This work addresses image reconstruction in magnetic resonance force microscopy, where sparsity is natural, but it is incremental as it builds on prior semi-blind methods.
The paper tackled the image deconvolution problem with a partially known convolution kernel, using a Bayesian Metropolis-within-Gibbs sampling framework for sparse images, and demonstrated superior performance over existing semi-blind algorithms on real MRFM data.
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.