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A commonly recognized weak point of the DCT-based transform coding is its blocking effects which become increasingly visible in the low bit-rate territory. In the first part of this paper, motivated by a recent work of Bruckstein, Elad, and Kimmel (BEK)  and by the progress from , we propose a combined adaptive technique that can be applied to a BEK type of transform coding system for performance improvement. In the second part of the paper, motivated by a recent work of Tsaig, Elad, Milanfar, and Golub (TEMG) , we investigate an averaging technique for the design of optimal interpolation filter that can be utilized in a TEMG type system framework for further performance improvement. Simulation results are presented to demonstrate the effectiveness of the two proposed methods.