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A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

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2 Author(s)
Vonesch, C. ; EPFL, Lausanne ; Unser, M.

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the -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.

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Image Processing, IEEE Transactions on  (Volume:17 ,  Issue: 4 )