Synthesis filter bank optimization with lattice structure constraints in 2D separable image processing

In one-dimensional signal processing, the perfect reconstruction (PR) synthesis FB is not unique for a given analysis LP oversampled filter bank (FB). Optimal Design methods have been developed to choose the optimal noise reduction linear phase (LP) synthesis FB. This paper deals with the optimal design of LP synthesis FBs for separable 2D image processing. With the same analysis LP oversampled FB for row and column processing separately, we show that the optimal synthesis FBs for row and column processing are generally not the same. A design method is developed when the spectrum of the subband noises is known. Numerical examples are given to demonstrate the effectiveness of our results.