We consider the image reconstruction problem when the original image is assumed to be sparse and when partial
knowledge of the point spread function (PSF) is available. In particular, we are interested in recovering the
magnetization density given magnetic resonance force microscopy (MRFM) data, and we present an iterative
alternating minimization algorithm (AM) to solve this problem. A smoothing penalty is introduced on allowable
PSFs to improve the reconstruction. Simulations demonstrate its performance in reconstructing both the image
and unknown point spread function. In addition, we develop an optimization transfer approach to solving a
total variation (TV) blind deconvolution algorithm presented in a paper by Chan and Wong. We compare the
performance of the AM algorithm to the blind TV algorithm as well as to a TV based majorization-minimization
algorithm developed by Figueiredo et al.
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