This paper presents a new technique for image reconstruction from a partial set of transform coefficients in DCT image coders. By utilizing the correlation between adjacent blocks and imposing smoothing constraints on the reconstructed image, the proposed algorithm produces an image which is maximally smooth among all the images with the same available coefficients. The optimal solution can be obtained either by a linear transformation or through an iterative process. The underlying principle of the algorithm is applicable to any unitary block-transform and is very effective for recovering the DC and other low frequency coefficients. Applications in DCT based still image codecs and video codecs using motion compensation have been considered. Simulation results with still images show that a very good reconstruction can be obtained even when DC and certain low frequencies are missing in many blocks.