2-D non-separable integer implementation of paraunitary filter bank based on the quaternionic multiplier block-lifting structure

This paper presents a novel technique of factorization for 2-D non-separable quaternionic paraunitary filter banks (2-D NSQ-PUFB) based on the integer-to-integer invertible quaternionic multipliers. Two-dimensional factorization structures called "16in-16out" and "64in-64out" respectively for 4-channel and 8-channel Q-PUFB based on the proposed technique are shown. Comparison of the energy compaction level between the 2-D separable Q-PUFB based on the 1D Q-PUFB (8 x 24 Q-PUFB one-dimensional coding gain is CG(1D) = 9.38 dB) and 2D non-separable Q-PUFB (8 x 24 2D-NSQ-PUFB, multi-dimensional coding gain is CG(MD) = 17.15dB) for the Barbara image shows that the 2-D non-separable Q-PUFB generates a higher percentage of small-value coefficients, hence creates a significant increase in the number of zero trees. This holds the key to our coder's superior performance.