Multiscale representations: fractals, self-similar random processes and wavelets
نویسندگان
چکیده
2 Principles 4 2.1 Fractals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Definition and history . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Fractal dimension . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Hölder exponent and singularity spectrum . . . . . . . . . . . . . 6 2.2 Self-similar random processes . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Definition and history . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Brownian motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3 Fractional Brownian motion . . . . . . . . . . . . . . . . . . . . . 9 2.2.4 Multi-fractional Brownian motion . . . . . . . . . . . . . . . . . 10 2.3 Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.1 Definition and history . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 Continuous wavelet transform . . . . . . . . . . . . . . . . . . . . 13 2.3.3 Orthogonal wavelet transform . . . . . . . . . . . . . . . . . . . . 16
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