The performance of an imaging system is limited by optical aberrations, which cause blurriness in the resulting image. Digital correction techniques, such as deconvolution, have limited ability to correct the blur, since some spatial frequencies in the scene are not measured adequately due to the aberrations (‘zeros’ of the system transfer function). Our work proves that the addition of a random mask to an imaging system removes its dependence on aberrations, resulting in no systematic zeros in the transfer function and consequently less sensitivity to noise during deconvolution. In simulation, we show that this strategy improves image quality over a range of aberration types, aberration strengths, and signal-to-noise ratios.