EPFL | Biomedical Imaging Group | Regularized Deconvolution

Fast Wavelet-Regularized Image Deconvolution

C. Vonesch, M. Unser

Proceedings of the Fourth IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'07), Arlington VA, USA, April 12-15, 2007, pp. 608–611.

We present a modified version of the deconvolution algorithm introduced by Figueiredo and Nowak, which leads to a substantial acceleration. The algorithm essentially consists in alternating between a Landweber-type iteration and a wavelet-domain denoising step.

Our key innovations are 1) the use of a Shannon wavelet basis, which decouples the problem accross subbands, and 2) the use of optimized, subband-dependent step sizes and threshold levels.

At high SNR levels, where the original algorithm exhibits slow convergence, we obtain an acceleration of one order of magnitude. This result suggests that wavelet-domain l₁-regularization may become tractable for the deconvolution of large datasets, e.g. in fluorescence microscopy.

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