Accelerated Wavelet-Regularized Deconvolution for 3-D Fluorescence Microcopy

Modern deconvolution algorithms are often specified as minimization problems involving a non-quadratic regularization functional. When the latter is a wavelet-domain $ℓ _{ 1 }$ -norm that favors sparse solutions, the problem can be solved by a simple iterative shrinkage/thresholding algorithm (ISTA). This approach provides state-of-the-art results in 2-D, but is harder to deploy in 3-D because of its slow convergence. In this paper, we propose an acceleration scheme that turns wavelet-regularized deconvolution into a competitive solution for 3-D fluorescence microscopy. A significant speed-up is achieved though a synergistic combination of subband-adapted thresholds and sequential TwIST updates. We provide a theoretical justification of the procedure together with an experimental evaluation, including the application to real 3-D fluorescence data.