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A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

C. Vonesch, M. Unser

Proceedings of the Fifth IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'08), Paris, French Republic, May 14-17, 2008, pp. 1351-1354.



Wavelet-domain ℓ1-regularization is a promising approach to deconvolution. The corresponding variational problem can be solved using a “thresholded Landweber” (TL) algorithm. While this iterative procedure is simple to implement, it is known to converge slowly. In this paper, we give the principle of a modified algorithm that is substantially faster. The method is applicable to arbitrary wavelet representations, thus generalizing our previous work which was restricted to the orthonormal Shannon wavelet basis.

Numerical experiments show that we can obtain up to a 10-fold speed-up with respect to the existing TL algorithm, while providing the same restoration quality. We also present an example with real data that demonstrates the feasibility of wavelet-domain regularization for 3D deconvolution microscopy.


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