Design and analysis of directional 2D nonseparable perfect reconstruction filter banks for subband coding of images and video signals
Chang-Lin Huang, Chen-Chang Lien · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
In this paper, we develop a directional 2-D non-separable filter bank which can perform the perfect reconstruction of the downsampled subband signals. The filter bank represents a union of two powerful image and video processing tools: directional decomposition and subband decomposition. This subband decomposition is implemented by: (1) shifting the input signal and the subband signals; (2) using a tree-structure diamond shape prefilter followed by downsampling on quincunx grids; and (3) applying four types parallelogram prefilters followed by four different downsampling matrices respectively. This paper addresses the design and implementation of two-channel filter banks for such applications. The two-band subsystem in the tree-structure filter bank is proved and analyzed to be able to provide perfect reconstruction of the downsampled subband signals. Our method is extremely computationally simple in designing the analysis/synthesis subfilters for the filter bank without using any nonlinearly constrained numerical optimization. Finally, we use conventional 1-D analysis/synthesis filters as prototype and then apply McClellan transform for the specific 2-D diamond shape and parallelogram shape sub-filters.