Reversible Symmetric Nonexpansive Convolution: An Effective Image Boundary Processing for M-Channel Lifting-Based Linear-Phase Filter Banks

We present an effective image boundary processing for M-channel (M., M = 2) lifting-based linear-phase filter banks that are applied to unified lossy and lossless image compression (coding), i.e., lossy-to-lossless image coding. The reversible symmetric extension we propose is achieved by manipulating building blocks on the image boundary and reawakening the symmetry of each building block that has been lost due to rounding error on each lifting step. In addition, complexity is reduced by extending nonexpansive convolution, called reversible symmetric nonexpansive convolution, because the number of input signals does not even temporarily increase. Our method not only achieves reversible boundary processing, but also is comparable with irreversible symmetric extension in lossy image coding and outperformed periodic extension in lossy-to-lossless image coding.