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A fast algorithm for the 4×4 discrete Krawtchouk transform

WithJ.S. Wu, C.F. Yang, H.Z. Shu, L. Wang & L. Senhadji

Recently, research effort has been paid to the fast computation of the small fixed 4×4-, 8×8-point discrete orthogonal transforms, for example (Lee & Cho 1992, Nakagaki & Mukundan 2006, Nakagaki & Mukundan 2007, Ishwar et al. 2008, Zhu et al. 2009, Bouguezel et al. 2013, Cintra et  al. 2014). (Lee & Cho 1992) proposed a 4×4 DCT algorithm to serve the base case for the recursive computation of two-dimensional (2-D) DCT. Nakagaki and Mukundan derived a fast algorithm for the computation of 4×4 DTT (Nakagaki & Mukundan 2006, Nakagaki & Mukundan 2007). Inspired by the research work presented in (Lee & Cho 1992, Nakagaki & Mukundan 2006, Nakagaki  & Mukundan 2007), we propose in this letter a fast 4×4 DKT algorithm which could be used as the building-block for the DKT computation.