Lossless 2D discrete Walsh-Hadamard transform

The 64-point separable lossless two dimensional (2D) WHT is composed of the 8-point lossless one dimensional WHT. The latter is obtained by first decomposing the 8-point WHT into 2-point WHTs and then replacing every 2-point WHT by a ladder network. Since the coefficients in the ladder network then become real, the advantage of being multiplier-free vanishes. This paper therefore proposes a 64-point nonseparable lossless 2D WHT without multiplication as follows. First, the 64-point separable 2D WHT is decomposed into 4-point 2D WHTs. Second, every 4-point 2D WHT is replaced by a 2D ladder network which is multiplier-free. It is also shown that the transform coefficients of the proposed transform are closer to those of the 64-point lossy 2D WHT than those of the 64-point separable lossless 2D WHT