A method for evaluating image-recovery algorithms is presented, which is based on the numerical assessment of how well a specified visual task may be performed using the reconstructed images. A Monte Carlo technique is used to simulate the complete imaging process including the generation of scenes appropriate to the desired application, subsequent data taking, image recovery, and performance of the stated task based on the final image. The use of a pseudo-random simulation process permits one to assess the response of an image-recovery algorithm to many different scenes. Nonlinear algorithms are readily evaluated. The usefulness of this method is demonstrated through a study of the algebraic reconstruction technique (ART), which reconstructs images from their projections. In the imaging situation studied, it is found that the use of the nonnegativity constraint in ART can dramatically increase the detectability of objects in some instances, especially when the data consist of a limited number of noiseless projections.