The nonredundant contourlet transform (NRCT): A multiresolution and multidirection image representation

As a directional multiresolution image representation, the contourlet transform can efficiently capture curved and oriented geometrical structures in images. However, it has the drawback of a 4/3 redundancy in its oversampling ratio. This paper proposes an innovative framework of filter banks to achieve the same frequency partition as the contourlet transform, while eliminating its redundancy. The new image representation is called the nonredundant contourlet transform (NRCT). The proposed NRCT possesses two important properties: critical sampling and perfect reconstruction. Moreover, the NRCT is an extension of the wavelet transform. Numerical experiments are presented to demonstrate the potential of the NRCT for image compression.