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The well-known shrinkage technique is still relevant for contemporary signal processing problems over redundant dictionaries. We present theoretical and empirical analyses for two iterative algorithms for sparse approximation that use shrinkage. The general IT algorithm amounts to a Landweber iteration with nonlinear shrinkage at each iteration step. The… (More)

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… (More)

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… (More)

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