Four-channel lifting-householder-based Hadamard transform

This study presents a class of four-channel multiplierless reversible Hadamard transforms (HTs), called lifting-Householder-based HT (LiftH²T), for various signal processing and communication applications. This class is obtained by using a lifting-Householder factorization of a particular 4 × 4 symmetric orthogonal matrix and its application to a four-channel HT. In spite of the simple multiplierless structure with only nine adders, one shifter, and three process steps, it basically outperforms the integer HT (IntHT) and lifting-based HT (LiftHT) in the JPEG XR standard at lossy-to-lossless image coding, thanks to its considering the dynamic range and having less rounding error.