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

Abstract

This paper presents a novel technique of factorization for 2-D non-separable quaternionic paraunitary filter banks (2-D NS Q-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 $(8 \times 24 Q$-PUFB one-dimensional coding gain is $CG_{1D}\,= 9.38$ dB) and 2D non-separable Q-PUFB $(8 \times 242\mathrm{D}$-NS Q-PUFB, multidimensional coding gain is $CG_{MD}\,= 17.15$ dB) 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.