Adaptive scale selection for Multiscale image Denoising

Adaptive transforms are required for better signal analysis and processing. Key issue in finding the optimal expansion basis for a given signal is the representation of signal information with very few elements of the basis. In this context a key role is played by the multiscale transforms that allow signal representation at different resolutions. This paper presents a method for building a multiscale transform with adaptive scale dilation factors. The aim is to promote sparsity and adaptiveness both in time and scale. To this aim interscale relationships of wavelet coefficients are used for the selection of those scales that measure significant changes in signal information. Then, a wavelet transform with variable dilation factor is defined accounting for the selected scales and the properties of coprime numbers. Preliminary experimental results in image denoising by Wiener filtering show that the adaptive multiscale transform is able to provide better reconstruction quality with a minimum number of scales and comparable computational effort with the classical dyadic transform.