A wavelet-based approach to local fractal dimension estimation of SAR images of the sea surface is presented. Fractal analysis is considered as a tool for image texture characterization which can play a fundamental role to automatically detect oil slicks, and possibly distinguish them from natural surface films. A fractional Brownian motion (fBm) model is assumed for the clean sea surface. FBm processes have been proved to be suitable to describe signals backscattered by many natural surfaces, particularly by the sea surface within a certain range of scales. By using the properties of the average power spectra of fBm's, it is possible to estimated the fractal dimension, as demonstrated on synthetic fBm realizations. In this paper, a redundant wavelet representation is applied for estimating the local fractal dimension of the sea surface. By using this technique, which allows to operate at the original image resolution, all discontinuities of the fractal sea surface can be detected and accurately localized. Experimental results on true SAR images show that without considering the backscatter coefficient for calculating the fractal dimension, but only textural features, it is possible to detect oil slicks and man-made objects on the sea surface.