In general, the reconstructed image in coded aperture imaging is affected by the source configuration. Fenimore's balanced convolution method in conjunction with the uniformly redundant array can remove the interference due to the source configuration. As an extension of Fenimore's balanced convolution method, we present general conditions for designing an unbiased mean estimator for a far-field coded aperture imaging system with a random binary mask. As part of the general conditions, we propose decoding arrays whose elements are variable with respect to source directions. We also show that the unbiased mean estimator from Fenimore's balanced convolution method is a special case of the general conditions. We also present a practical example of designing restoring arrays for a coded aperture system with a random mask.