A new, universal approach to reconstructing transform-coded images is proposed. The method views the images as a probability mass function (pmf), allowing the retained coefficients of a transform (Karhunen-Loeve, discrete cosine, slant, etc.) to be thought of as averages of the basis functions over the pmf. This sets the stage for reconstructing the original images by using the maximum entropy principle (MEP) and the minimum relative entropy principle (MREP) with the retained coefficients as constraints in the extremizations. A formulation combining the two methods is also proposed, resulting in a reconstruction algorithm that is fast, proceeding in an iterative way using the estimate from each coefficient as a prior pmf for the next one via the MREP. The proposed approaches are illustrated with images compressed by discrete cosine transform coding, and the results are compared with standard reconstruction using the inverse discrete cosine transform.