We here establish and exploit the result that 2D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least square problems and generalized Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-square estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators.

Semi-local Hurst estimation is considered for random fields where the regularity varies in a piecewise manner. The recently developed generalised lasso is exploited to propose a spatially regularised Hurst estimator. Dual-tree complex wavelets are used to formulate the usual log-spectrum regression problem and an interlaced penalty matrix is constructed to form a 2-d fused lasso constraint on the double-indexed parameters. We thus extend a regularity-based denoising approach and demonstrate the utility of our method with experiments.

Abstract The goal of this paper is to highlight the particularities of Worldwide Interoperability for Microwave Access (WiMAX) traffic from a long‐range dependence perspective. The application presented in this paper consists in the estimation of the quality of base stations (BS) positioning in the architecture of a WiMAX network. Analysing the traffic of the considered WiMAX network, with an original data mining methodology based on long‐range dependence, we determine which BS have a correct position in the topology of the network and which BS have an incorrect position. These BS must be repositioned when the next session of the network maintenance will take place.

The SOund Navigation And Ranging (SONAR) images are perturbed by speckle noise. This paper presents a new denoising method in the wavelet domain, which tends to reduce the speckle, preserving the structural features and the textural information of the scene. Shift invariance associated with good directional selectivity is important for the use of a wavelet transform (WT) in denoising of SONAR images. In this paper, we propose the use of a variant of hyperanalytic WT, which is quasi-shift invariant and has good directional selectivity in association with a maximum a posteriori filter named bishrink. This filter makes a very good treatment of the contours. The corresponding denoising algorithm is simple and fast. Its performance was proved on images perturbed by synthesized speckle noise and on real SONAR images.

An effective denoising method for ECG signals affected by real sources of noise is proposed in this paper. The method is based on a maximum a-posteriori (MAP) filtering in the diversity-enhanced wavelet domain, under realistic a-priori assumptions regarding the statistical properties of the wavelet coefficients of the ECG signal. In order to evaluate the performance of the method, we studied the signal-to-noise ratio (SNR) improvement factor and the degree of the denoising influence on the automatic signal segmentation procedures. The method was tested in both synthetic and real noise conditions and it showed very promising results