Some applications of the wavelet transform with signal-dependent dilation factor

Time-scale transforms play a fundamental role in the compact representation of signals and images [1]. Non linear time representation provided a significant contribution to the definition of more flexible and adaptive transforms. However, in many applications signals are better characterized in the frequency domain. In particular, frequency distribution in the frequency axis is strictly dependent on the signal under study. On the contrary, frequency axis partition provided by conventional transforms obeys more rigid rules. It would be then desirable to have a transform able to adapt to the frequency content of the signal under study, i.e. having a changing Q factor. The rational dilation wavelet transform [2, 3] (RDWT) is a flexible tool that allows to change the dilation factor at each step of the transformaswell as the analyzingwindowfunction, by maintaining the structure and properties of the classical wavelet transform, which is implemented through perfect reconstruction filter banks. Some examples concerning the way of selecting significant scales, i.e. central frequencies and bandwidths of the filter bank, in different applications, including image denoising, deblurring and fusion, will be shown. The properties of the corresponding adaptive transformwill be also discussed.