A directional and shift-invariant transform based on M-channel rational-valued cosine-sine modulated filter banks

This paper proposes a directional and shift-invariant transform based on M-channel rational-valued cosine-sine modulated filter banks (R-CSMFBs) for the practical implementation on hardware devices. M-channel CSMFBs can be easily designed by the modulation of a prototype filter and achieve a good stopband attenuation. In addition, in our previous work, the directionality and the shift-invariance of CSMFBs have been theoretically clarified. Thus, they can be an alternative choice of the dual-tree complex wavelet transform (DTCWT) which is one of the most popular directional and shift-invariant transforms. In this paper, it is shown that the proposed lifting-based structure of the R-CSMFB can also achieve rich directional selectivity and the shift-invariance even if the lifting coefficients are rounded to rational values. Finally, the R-CSMFB can provide better stopband attenuation and image denoising performance than that of the conventional M-channel rational-valued DTCWT in the simulation.