Light-sheet fluorescence microscopy techniques commonly use deconvolution to remove the effect of the illumination beam shape on the image formation, reducing the effects of side lobes and increasing the contrast in three-dimensional imaging. Deconvolution requires knowledge of the optical transfer function of the system and can only be estimated or measured imperfectly. Furthermore, in biological samples the optical transfer function is degraded by the presence of phase aberrations, this implies that any a priori deconvolution applied to the sample will be to some degree incorrect since it does not account for this unknown phase error in the optical transfer function. By combining adaptive optics and computational processing in this microscope, it is shown that by introducing perturbations to the optical transfer function it is possible to estimate the object distribution and remove aberrations. © 2017 OSA.