20 September 2007 A fast iterative thresholding algorithm for wavelet-regularized deconvolution
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We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is sufficiently general to cover arbitrary choices of wavelet bases (non-orthonormal or redundant). The resulting procedure alternates between the following two steps: 1. a wavelet-domain Landweber iteration with subband-dependent step-sizes; 2. a denoising operation with subband-dependent thresholding functions. The subband-dependent parameters allow for a substantial convergence acceleration compared to the existing optimization method. Numerical experiments demonstrate a potential speed increase of more than one order of magnitude. This makes our "fast thresholded Landweber algorithm" a viable alternative for the deconvolution of large data sets. In particular, we present one of the first applications of wavelet-regularized deconvolution to 3D fluorescence microscopy.
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Cédric Vonesch, Cédric Vonesch, Michael Unser, Michael Unser, "A fast iterative thresholding algorithm for wavelet-regularized deconvolution", Proc. SPIE 6701, Wavelets XII, 67010D (20 September 2007); doi: 10.1117/12.733532; https://doi.org/10.1117/12.733532

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