Imaging interferometry suffers from sparse Fourier measurements, and, at the visible wavelengths, a lack of phase information, creating a need for an image reconstruction algorithm. A support constraint is useful for optimization but is often not known a priori. The two-point rule for finding an object support from the autocorrelation is limited in usefulness by the sparsity and non-uniformity of the Fourier data and is insufficient for image reconstruction. Compactness, a common prior, does not require knowledge of the support. Compactness penalizes solutions that have bright pixels away from the center, favoring soft-edged objects with a bright center and darker extremities. With regards to imaging hard-edged objects such as satellites, a support constraint is desired but unknown and compactness may be unfavorable. Combining various techniques, a method of simultaneously estimating the object’s support and the object’s intensity distribution is presented. Though all the optimization parameters are in the image domain, we are effectively performing phase retrieval at the measurement locations and interpolation between the sparse data points.