Multidimensional Systems and Signal Processing
Two approximation methods to synthesize the power spectrum of fractional Gaussian noise
Computational Statistics & Data Analysis
A fractal-based relaxation algorithm for shape from terrain image
Computer Vision and Image Understanding
A note on fractal dimensions of biomedical waveforms
Computers in Biology and Medicine
Asymptotic decorrelation of between-scale wavelet coefficients of generalized fractional process
Digital Signal Processing
Locally constrained synthetic LoDs generation for natural terrain meshes
Future Generation Computer Systems
Empirical mode decomposition synthesis of fractional processes in 1D- and 2D-space
Image and Vision Computing
2D wavelet-based spectra with applications
Computational Statistics & Data Analysis
Local fractal and multifractal features for volumic texture characterization
Pattern Recognition
Effects of multiscale noise tuning on stochastic resonance for weak signal detection
Digital Signal Processing
Λ-neighborhood wavelet shrinkage
Computational Statistics & Data Analysis
A 2D wavelet-based multiscale approach with applications to the analysis of digital mammograms
Computational Statistics & Data Analysis
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Fractional Brownian motion (FBM) offers a convenient modeling for nonstationary stochastic processes with long-term dependencies and 1/f-type spectral behavior over wide ranges of frequencies. Statistical self-similarity is an essential feature of FBM and makes natural the use of wavelets for both its analysis and its synthesis. A detailed second-order analysis is carried out for wavelet coefficients of FBM. It reveals a stationary structure at each scale and a power-law behavior of the coefficients' variance from which the fractal dimension of FBM can be estimated. Conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed, consequences of discretization are considered, and some connections between the wavelet point of view and previous approaches based on length measurements (analysis) or dyadic interpolation (synthesis) are briefly pointed out