Effects of random noise on bispectra of fractal objects

Effects of random noise on the scaling property of bispectra of Cantor sets are compared with that of the corresponding power spectra by means of computer simulations. Additive and multiplicative random noises obeying Gaussian probability densities with different values of the mean and the standard deviation were tested. After suitable band-averaging operations, in many cases the bispectra were found to give a better estimation for the fractal dimension of objects than the power spectra. By introducing a modified band-averaging operation, the bispectrum was shown to give a correct fractal dimension in all cases under consideration.