Two-dimensional non-separable block-lifting-based M-channel biorthogonal filter banks

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