Multiresolution estimation of fractal dimension from images affected by signal-dependent noise

A well-suited approach to calculate the fractal dimension of digital images stems from the power spectrum of a fractional Brownian motion: the ratio between powers at different scales is related to the persistence parameter H and, thus, to the fractal dimension D = 3 - H. The signal-dependent nature of the speckle noise, however, prevents from a correct estimation of fractal dimension from Synthetic Aperture Radar (SAR) images. Here, we propose and assess a novel method to obtain D based on the multiscale decomposition provided by the normalized Laplacian pyramid (NLP), which is a bandpass representation obtained by dividing the layers of an LP by its expanded baseband and is designed to force the noise to become signal-independent. Extensive experiments on synthetic fractal textures, both noise-free and noisy, corroborate the underlying assumptions and show the performances, in terms of both accuracy and confidence of estimation, of pyramid methods compared with the well-established method based on the wavelet transform. Preliminary results on true SAR images from ERS-1 look promising as well.