Telescopes and imaging interferometers with sparsely filled apertures can be lighter weight and less expensive than conventional filled-aperture telescopes. However, their greatly reduced MTF's cause significant blurring and loss of contrast in the collected imagery. Image reconstruction algorithms can correct the blurring completely when the signal-to-noise ratio (SNR) is high, but only partially when the SNR is low. This paper compares both linear (Wiener) and nonlinear (iterative maximum likelihood) algorithms for image reconstruction under a variety of circumstances. These include high and low SNR, Gaussian noise and Poisson-noise dominated, and a variety of aperture configurations and degrees of sparsity. The quality metric employed to compare algorithms is image utility as quantified by the National Imagery Interpretability Rating Scale (NIIRS). On balance, a linear reconstruction algorithm with a power-law power-spectrum estimate performed best.