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Block coders are among the most common compression tools available for still images and video sequences. Their low computational complexity along with their good performance make them a popular choice for compression of natural images. Yet, at low bit-rates, block coders introduce visually annoying artifacts into the image. One approach that alleviates this problem is to downsample the image, apply the coding algorithm, and interpolate back to the original resolution. In this paper, we consider the use of optimal decimation and interpolation filters in this scheme. We first consider only optimization of the interpolation filter, by formulating the problem as least-squares minimization. We then consider the joint optimization over both the decimation and the interpolation filters, using the variable projection method. The experimental results presented clearly exhibit a significant improvement over other approaches.