Fast Wavelet-Regularized Image Deconvolution

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 $l _{ 1 }$ -regularization may become tractable for the deconvolution of large datasets, e.g. in fluorescence microscopy.