Fractional M-band dual tree complex wavelet transform for digital watermarking

In this paper, a novel digital watermarking scheme using fractional M-band dual tree complex wavelet transform (Fr-M-band-DT-CWT) is proposed. High frequency channels have wide bandwidth and low frequency channels have narrow bandwidth. These characteristics are suitable for analysing low frequency signal, but not for relatively high frequency signal. The images often contain many edges, which may cause rich middle and high frequency components in the 2-band wavelet domain. Therefore, the ordinary 2-band dual tree complex wavelet transform (DT-CWT) is not well-suited for analysing the image. So, the M-band DT-CWT with the FrFT called Fr-M-band-DT-CWT is proposed in this paper to address this problem. Further, we integrate the Fr-M-Band-DT-CWT with singular value decomposition (SVD) in order to enhance the performance. Experimental results of the proposed watermarking scheme are compared with the previously available watermarking algorithms, fractional Fourier transform (FrFT), fractional wavelet transform (FrWT). Further, the proposed watermark extraction scheme is also tested on different attacks. The results of the present investigations show that the proposed watermarking scheme is superior as compared to other existing watermarking schemes.