Estimation of 2-D noisy fractional Brownian motion and its applications using wavelets

The two-dimensional (2-D) fractional Brownian motion (fBm) model is useful in describing natural scenes and textures. Most fractal estimation algorith ms for 2-D isotropic fBm images are simple extensions of the one-dimensiona l (1-D) fBm estimation method. This method does not perform well when the i mage size is small (say, 32 x 32), We propose a new algorithm that estimate s the fractal parameter from the decay of the variance of the wavelet coeff icients across scales. Our method places no restriction on the wavelets. Al so, it provides a robust parameter estimation for small noisy fractal image s. For image denoising, a Wiener filter is constructed by our algorithm usi ng the estimated parameters and is then applied to the noisy wavelet coeffi cients at each scale. We show that the averaged power spectrum of the denoi sed image is isotropic and is a nearly 1/f process, The performance of our algorithm is shown by numerical simulation for both the fractal parameter a nd the image estimation, Applications on coastline detection and texture se gmentation in noisy environment are also demonstrated.