A Rational-dilation Wavelet Transform with Signal Dependent Dilation Factor

This paper presents a fast and effective method for the selection of the least number of scales able to represent significant information of a signal. To this aim, atoms interference in the time-scale wavelet domain is used to represent distinct configurations of transform coefficients; the goal is to find those scales where transform coefficients change their configura- tion. The selected set of scales cannot provide a dyadic partition of the frequency domain. The rational dilation wavelet transform is a exible tool that allows us to change the dilation parameter at each step of the decomposition. Preliminary experimental results prove that a multiscale transform with adaptive scale parameter allows us to reach better de- noising results than the dyadic decomposition in terms of PSNR, using a smaller number of scales and a negligible additional computational effort.