A two-dimensional non-separable implementation of dyadic-valued cosine-sine modulated filter banks for low computational complexity

This paper aims to design a new two-dimensional (2D) non-separable implementation of dyadic-valued cosine-sine modulated filter banks (2D D-CSMFBs) for low computational complexity. CSMFBs satisfy rich directional selectivity (DS) and shift-invariance (SI), and they can be easily designed by the modulation of a prototype filter. In addition, our previous work introduced a one-dimensional (1D) D-CSMFBs (1D D-CSMFBs). By restricting real-valued filter coefficients to rational-valued ones, they can save computational cost while keeping DS and SI. The proposed 2D implementation in this paper can further reduce the computational cost by unifying the conventional 2D separable structure into a 2D non-separable one directly. Furthermore, experimental results of image non-linear approximation show that the proposed 2D D-CSMFBs are comparable or even better than the 1D D-CSMFBs.