2D Non-Separable Block-Lifting Structure and Its Application to $M$ -Channel Perfect Reconstruction Filter Banks for Lossy-to-Lossless Image Coding

We propose a 2D non-separable block-lifting structure (2D-NSBL) that is easily formulated from the 1D separable block-lifting structure (1D-SBL) and 2D non-separable lifting structure (2D-NSL). The 2D-NSBL can be regarded as an extension of the 2D-NSL, because a two-channel 2D-NSBL is completely equivalent to a 2D-NSL. We apply the 2D-NSBL to M-channel (M=2
ⁿ
, n ∈ N) perfect reconstruction filter banks (PRFBs). The 2D-NSBL-based PRFBs outperform 1D-SBL-based PRFBs at lossy-to-lossless coding, whose image quality is scalable from lossless data to high compressed lossy data, because their rounding errors are reduced by merging many rounding operations.