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Abstract-Recent work on block-based compression for low bit-rate coding has shown that employing a block coder within a sampling scheme where the image is downsampled prior to coding (and upsampled after the decoding stage) results in superior performance compared to standard block coding. In this paper, we explore the use of optimal decimation and interpolation filters in this coding scheme. We show that the problem of finding optimal filters for a general, unknown, "black-box" coder can be written as a separable least squares problem in two sets of variables. We then elegantly solve this optimization problem using the Variable Projection method. The experimental results presented clearly exhibit a significant improvement over existing approaches.