Theory and Design of Two-Dimensional Filter Banks

Abstr:aet. There has boen considerable interest in the design of mullidimensional (MO) fill ~ banU. MD filler banbi find applicalion in subband coding of images l\IId vidcod3l.a. MO filter banks can be designed by cascading one-dimensionaJ (1 0) filter banks in the form ofa lree SlTUaure. In Ihis case, the individuallinalysis l\IId synlhestS fillers are separ.abIe and the filler bank is called. sepanble tiller bank. MD filter banks with non~1efillers offer more f1c~ibilily and usually provide beller perform:lnte. Nonecheless. their design is considerably more difficute!han scparabIe filter banbi. The purpo&e of chis p8pCl " is 10 provide an overview of developmenlS in!his tield 00 the design Icchniqucs for MO tiller banks. Il'IOSIly lwo-dirnensional (20) titeer banks. In some image coding applicalions. the 20 two-channel filler banks are of &:real importance. panicularly tile filler bank wilh dilUl1Ond-shaped filtcr5. We will present several design leclIIIiqucs for tile 2D two-channcl nonseparable tilter banks. As lhe design of MD filters are IlOI as Inlttable as thai of 10 fillL'rs, we seck design l«hniqucs thai do IlOI mvoh-e dlrecl opIimiUllion of MD filters. To racililale this. lransronn::uions lhal tum a separable MD tilter bank into a nonsep.:tr:lble one are developed. Abo. lJansformalions of 10 filter banks 10 MD tilter banks are invesligated. We will n,:view some: desIgns of MD tilter banks using transfOfllUltions. In lhe OOl\teJlt or I D filter bank design. the cosine modul:ued filler bank (CMFB) is well·known for its design and implernentatlondJicicncy. All the analysis tillers are rosine modolaled \"C1'Sions of a prototype tiller. 'The design cost of the tilter bank i