A fast multiplierless block transform for image and video compression

In this paper, we present a family of fast biorthogonal block transforms called binDCT that can be implemented using only shift and add operations. All transforms are based on a VLSI-friendly lattice structure which 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 8×8 transforms approximate closely the popular 8×8 DCT, attaining coding gains from 8.77 to 8.82 dB, despite requiring a modest amount of computations: as low as 14 shifts and 31 additions per 8 input samples. Application of the novel transforms in both lossy and lossless image coding yields very competitive results compared to the performance of the original heating-point DCT