Realization of 2D FIR filters using generalized polyphase structure combined with singular-value decomposition

In this paper, a realization scheme that combines the singular-value decomposition (SVD) and the generalized polyphase (GP) structure is proposed for 2D linear-phase FIR filters. With a small number of extra additions, a high-order 2D FIR filter is converted to several lower-order 2D subfilters. These subfilters are then realized using the SVD, yielding a parallel implementation structure for each 2D subfilter which consists of a number of 1D short-tap FIR filters. Due to the energy compaction of the SVD and the frequency-selective property of the GP structure, the number of parallel branches in each 2D subfilter is significantly reduced without introducing a large error. It is also shown that the various symmetries of 2D filters, such as the quadrantal symmetry and the central symmetry, are well preserved in the proposed GP-SVD structure