Blind deconvolution for sparse molecular imaging

This paper considers the image reconstruction problem when the original image is assumed to be sparse and when limited information of the point spread function (PSF) is available. In particular, we are interested in reconstructing the magnetization density given magnetic resonance force microscopy (MRFM) image data, and an alternating iterative algorithm is presented to solve this problem. Simulations demonstrate its performance not only in the reconstruction of the original image, but also in the recovery of the partially known PSF. In addition, we suggest the introduction of a smoothing penalty on allowable PSFs to improve the reconstruction.