We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain
regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization
framework of Daubechies et al.; it is sufficiently general to cover arbitrary choices of wavelet bases
(non-orthonormal or redundant). The resulting procedure alternates between the following two steps:
1. a wavelet-domain Landweber iteration with subband-dependent step-sizes;
2. a denoising operation with subband-dependent thresholding functions.
The subband-dependent parameters allow for a substantial convergence acceleration compared to the existing
optimization method. Numerical experiments demonstrate a potential speed increase of more than one order of
magnitude. This makes our "fast thresholded Landweber algorithm" a viable alternative for the deconvolution
of large data sets. In particular, we present one of the first applications of wavelet-regularized deconvolution to
3D fluorescence microscopy.