On Wavelet Compression of Self-Similar Processes

Self-similar stochastic processes are stochastic counterparts of deterministic fractals. Fractional Brownian motion (fBm) is a self-similar nonstationary Gaussian process originally proposed to model power-law behavior of power spectrum of long-range dependant (LRD) natural processes. Multiscale nature of wavelets make them natural candidates for analysis and synthesis of fractional Brownian motions. Despite wavelet compression being the method of choice for image compression, the performance of wavelet compression schemes are investigated for compressing fractional Brownian motions. Theoretical rate-distortion function of fBm is explicitly derived.