The binDCT: fast multiplierless approximation of the DCT

This paper presents a family of fast biorthogonal block transforms called binDCT that can be implemented using only shift and add operations. The transform is based on a VLSI-friendly lattice structure that robustly enforces both linear phase and perfect reconstruction properties. The lattice coefficients are parameterized as a series of dyadic lifting steps providing fast, efficient, in place computation of the transform coefficients as well as the ability to map integers to integers. The new 8/spl times/8 transforms all approximate the popular 8/spl times/8 DCT closely, attaining a coding gain range of 8.77-8.82 dB, despite requiring as low as 14 shifts and 31 additions per eight input samples. Application of the binDCT in both lossy and lossless image coding yields very competitive results compared to the performance of the original floating-point DCT.