This paper focuses on the deblurring and denoising of Poisson noise contaminated images acquired with a new imaging technique producing large 3D data sets: Light Sheet Fluorescence Microscopy. This paper details the optimization algorithm used, which is based on the Alternating Direction Method of Multipliers, and its efficient implementation using GPU hardware. In practice, a 3D 100 million voxel image is deconvolved in five minutes, which is at least 25 times faster than a state-of-the-art MATLAB implementation.