In astronomical imaging techniques, the relative level of the zero-frequency component of an image is usually unknown relative to all other components. This problem arises because the overall object brightness cannot easily be separated from background when viewing small, faint objects. This affects image interpretability and therefore is a problem that is ubiquitous in high-resolution astronomical imaging. Potential solutions to this problem include various interpolation techniques and image-constraint techniques. These approaches are described, and performance is evaluated with an optimal interpolator that accounts for sample density, signal-to-noise ratio, and the object's overall shape. Novel analytic expressions are obtained which provide insight into the limitations of any restoration approach, and practical means for achieving those limits.