Shift invariance associated with good directional selectivity is important for the use of a wavelet transform (WT) in many fields of image processing. Generally, complex wavelet transforms, e.g., the double-tree complex WT (DTCWT), have these useful properties. In this paper, we propose the use of a recently introduced implementation of such a WT, namely, the hyperanalytic WT (HWT), in association with filtering techniques already used with the discrete WT (DWT). The result is a very simple and fast image denoising algorithm. Some simulation results and comparisons prove the performance obtained using the new method.

This paper deals with a wavelet based forecasting method for WiMAX traffic time series. It is based on an algorithm composed by a few steps. One of these steps is the computation of the Stationary Wavelet Transform, SWT. This transform has two parameters: the mother wavelet which generates the decomposition and the number of decomposition levels. The aim of this paper is to propose a strategy for the selection of the first parameter. Our work is centered on the following wavelet families Daubechies, Coiflet, Symmlet, Biorthogonal and Reverse Biorthogonal. Some simulation results prove the efficiency of the proposed selection method.

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.

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.