Two-dimensional non-separable quaternionic paraunitary filter banks

This paper presents a novel technique of factorization for 2-D non-separable quaternionic paraunitary filter banks (2-D NSQ-PUFB). Two-dimensional factorization structures called “16in-16out” and “64in-64out” respectively for 4-channel and 8-channel $\boldsymbol{Q}$-PUFB based on the proposed technique are shown. The given structures can be mapped to parallel-pipeline processor architecture with a minimum latency time $2 (\boldsymbol{N}+1)$ quaternion multiplication operations, where $\boldsymbol{N}$ is transform order of the $Q$-PUFB. The latency of parallel-pipeline processing does not depend on the size of the original image in contrast to the conventional 2-D transform. The coding gains $\boldsymbol{CG_{MD}}$ of 2-D non-separable Q-PUFBs for the isotropic auto-correlation function model with the correlation factor $\boldsymbol{\rho}=0.95$ are the following: $\boldsymbol{C}\boldsymbol{G}_{MD}=13.4\ \text{dB}$ for “16in-16out” structure and $\boldsymbol{C}\boldsymbol{G}_{MD}=15.6\ \text{dB}$ for “64in-64out” structure.