Redefined Block-Lifting-Based Filter Banks With Efficient Reversible Nonexpansive Convolution

This paper redefines a block-lifting structure of M-channel (M ∈ N, M ≥ 2) filter banks and proposes an efficient reversible nonexpansive convolution at the boundaries for lossy-to-lossless image coding. The previous studies left two problems. One is that the conventional lifting-based filter banks (FBs) are restricted to having equal analysis/synthesis filter lengths. We derive block-lifting-based FBs (BLFBs) with not only equal analysis/synthesis filter lengths but also the longer synthesis filter lengths than those of the analysis banks. The other problem is that the conventional lifting-based FBs without the linear-phase property, such as BLFBs, cannot implement the conventional smooth nonexpansive convolution at the boundaries because of the rounding error in each lifting. We solve the boundary problem by using an efficient reversible nonexpansive convolution derived from a nonexpansive convolution for nonlinear-phase FBs with paraunitariness. We show that the redefined BLFBs with the efficient reversible nonexpansive convolution perform well at lossy-to-lossless image coding.