## A fast thresholded Landweber algorithm for waveletregularized multidimensional deconvolution (2008)

Venue: | IEEE Trans. Image Process |

Citations: | 20 - 4 self |

### BibTeX

@ARTICLE{Vonesch08afast,

author = {Cédric Vonesch and Student Member and Michael Unser},

title = {A fast thresholded Landweber algorithm for waveletregularized multidimensional deconvolution},

journal = {IEEE Trans. Image Process},

year = {2008},

pages = {539549}

}

### OpenURL

### Abstract

Abstract—We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the 1-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alternating between a Landweber iteration and a wavelet-domain soft-thresholding operation. While having the advantage of simplicity, they are known to converge slowly. By expressing the cost functional in a Shannon wavelet basis, we are able to decompose the problem into a series of subband-dependent minimizations. In particular, this allows for larger (subband-dependent) step sizes and threshold levels than the previous method. This improves the convergence properties of the algorithm significantly. We demonstrate a speed-up of one order of magnitude in practical situations. This makes wavelet-regularized deconvolution more widely accessible, even for applications with a strong limitation on computational complexity. We present promising results in 3-D deconvolution microscopy, where the size of typical data sets does not permit more than a few tens of iterations. Index Terms—Deconvolution, fast, fluorescence microscopy, iterative, nonlinear, sparsity, 3-D, thresholding, wavelets,

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