| On Wavelet Compression of Self-Similar Processes (2008) | |||||||||||||||
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| Self-similar stochastic processes are stochastic counterparts of deterministic fractals. Statistical properties of those processes are the same regardless of the resolution in which they are observed. Many natural images have parts that closely resemble one another even when viewed at different resolutions. This simple observation has led to thorough investigations of self-similarity properties in image modelling and applications. Numerous papers have dealt with appropriateness and applications of self-similarity and its close counterpart ”scale-invariance ” in natural and medical image processing. Fractional Brownian motion (fBm) is a self-similar non-stationary Gaussian process originally proposed to model power-law behavior of power spectrum of long-range dependant (LRD) natural processes. The first attempts to rigourously quantify the information theoretic properties of fBm has just been started. Multi-scale nature of wavelets make them natural candidates for analysis and synthesis of fractional Brownian motions. Even though the fBm itself is not stationary, its wavelet transform turns out to be stationary at each scale and at synchronous time | |||||||||||||||
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