The contrast and resolution of images obtained with optical microscopes can be improved by deconvolution and computational fusion of multiple views of the same sample, but these methods are computationally expensive for large datasets. Here we describe theoretical and practical advances in algorithm and software design that result in image processing times that are tenfold to several thousand fold faster than with previous methods. First, we show that an 'unmatched back projector' accelerates deconvolution relative to the classic Richardson-Lucy algorithm by at least tenfold. Second, three-dimensional image-based registration with a graphics processing unit enhances processing speed 10- to 100-fold over CPU processing. Third, deep learning can provide further acceleration, particularly for deconvolution with spatially varying point spread functions. We illustrate our methods from the subcellular to millimeter spatial scale on diverse samples, including single cells, embryos and cleared tissue. Finally, we show performance enhancement on recently developed microscopes that have improved spatial resolution, including dual-view cleared-tissue light-sheet microscopes and reflective lattice light-sheet microscopes.