The lack of complete spatial incoherence of the optical field in the object plane of an imaging system results in a nonlinear relationship between the object and image intensity distributions. The problem of correcting such nonlinear distortions (which are quadratic and have a nonzero spread) by using post-detection image processing is addressed. A minimum mean-square-error linear filter is determined and its performance assessed by computer-simulated examples. Results of restoring images in a Kohler illumination system are obtained for different source sizes (i.e., different degrees of spatial coherence) and for different pupil sizes. Limits in which linearity is approached are determined.