  We apply the wavelet transform modulus maxima (WTMM) method to the analysis
of simulated MBE-grown surfaces. In contrast to the structure function approach
commonly used in the literature, this new method permits an investigation of
the complete singularity spectrum. We focus on a kinetic Monte-Carlo model with
Arrhenius dynamics, which in particular takes into consideration the process of
thermally activated desorption of particles. We find a wide spectrum of Hoelder
exponents, which reflects the multiaffine surface morphology. Although our
choice of parameters yields small desorption rates (< 3 %), we observe a
dramatic change in the singularity spectrum, which is shifted towards smaller
Hoelder exponents. Our results offer a mathematical foundation of anomalous
scaling: We identify the global exponent alpha_g with the Hoelder exponent
which maximizes the singularity soectrum.
