A fast thresholded Landweber algorithm for general wavelet bases: Application to 3D deconvolution microscopy

Wavelet-domain lscr₁-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 or- thonormal 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.