International Journal of Wavelets, Multiresolution and Information Processing

In Global Positioning System (GPS), receivers use FFT-based convolvers to acquire the signals. This paper shows a robust substitute algorithm for calculating the convolution that is less sensitive to additive noise.

In this paper, we study the stability of two kinds of frames generated by nonlinear Fourier atoms. The first result is the Kadec type ¼-theorem. The second states that the nonlinear windowed Fourier atoms form a frame of L²(ℝ).

Medical images generally have low contrast and they get complex type of noise due to the use of various devices and applications of various algorithms. However, most of the denoising methods consider only additive noise or some special noise model dependent on their systems and conditions only. Such methods when applied to real medical images yield poor results.

The present work proposes a method for denoising of medical images using soft-thresholding in wavelet domain on multiple levels. We have developed a method to compute the threshold values for denoising of medical images, which depend on the median as well as the contrast ratio of the wavelet coefficients and also on the level number. We have performed experiments by adding various proportions of Gaussian, Salt-and-Pepper and Speckle noise, and found that the proposed method performs better for these cases. The method is efficient because the threshold values can be calculated directly and it is adaptive as these values depend on mean, median and standard deviation of wavelet coefficients of the particular image. The proposed method also gives a criterion for level-dependent thresholding. Application of the proposed method to Ultrasound, X-ray and MRI images is demonstrated in experiments. In the present work, we have also done studies on how to select the mother wavelet for a particular problem.

We introduce a general framework for consistent linear reconstruction in infinite-dimensional Hilbert spaces. We study stable reconstructions in terms of Riesz bases and frames, and generalize the notion of oblique dual frames to infinite-dimensional frames. As we show, the linear reconstruction scheme coincides with the so-called oblique projection, which turns into an ordinary orthogonal projection when adapting the inner product. The inner product of interest is, in general, not unique. We characterize the inner products and corresponding positive operators for which the new geometrical interpretation applies.

In this paper, a procedure for comparing the patterns of time series using wavelets is developed. Randomization tests based on the ratio of the sum of squared wavelet coefficients of pairs of time series at different scales are used. A simulation study using pairs of different types of time series using the Haar and Daubechies wavelets is carried out. The results reveal that the tests perform fairly well at scales where there are a sufficient number of wavelet coefficients. The tests are applied to a set of financial time series.

In this paper, we introduce a multiscale technique for the analysis of deformation phenomena of the Earth. Classically, the basis functions under use are globally defined and show polynomial character. In consequence, only a global analysis of deformations is possible such that, for example, the water load of an artificial reservoir is hardly to model in that way. Up till now, the alternative to realize a local analysis can only be established by assuming the investigated region to be flat.

In what follows, we propose a local analysis based on tools (Navier scaling functions and wavelets) taking the (spherical) surface of the Earth into account. Our approach, in particular, enables us to perform a zooming-in procedure. In fact, the concept of Navier wavelets is formulated in such a way that subregions with larger or smaller data density can accordingly be modelled with a higher or lower resolution of the model, respectively.

In this work, an effective method has been proposed for texture segmentation, which incorporates the best features of filter bank and statistical approaches. This technique combines the features of Gabor wavelets (filter based) and General Moments (statistical) approaches. The method has been successfully tested for various textures from Brodatz texture collection. The relative performance of this method against the conventional approaches has been analyzed using Fisher Criterion.

This paper discusses the definition of active and reactive power in wavelet domain. Different definitions for three-phase power may cause significant changes in the measurement equipment topology. The simple phase shift using the Akagi method between current and voltage for reactive power measurement is discussed. A new power quality analysis technique (pqAT) is proposed.

In this paper, we propose a wavelet-Taylor–Galerkin method for solving the two-dimensional Navier–Stokes equations. The discretization in time is performed before the spatial discretization by introducing second-order generalization of the standard time stepping schemes with the help of Taylor series expansion in time step. Wavelet-Taylor–Galerkin schemes taking advantage of the wavelet bases capabilities to compress both functions and operators are presented. Results for two-dimensional turbulence are shown.

An operator splitting type preconditioner is presented for fast solution of linear systems obtained by Galerkin discretization of the Burton and Miller formulation for the Helmholtz equation. Our approach differs from usual boundary element treatments of the three-dimensional scattering problem because we use a basis of biorthogonal wavelets. Such wavelets result in a sparse linear system and that facilitates preconditioning and makes matrix vector products cheap to form. In this Part I of our work, we implement a biorthogonal wavelet transform on a closed surface in three dimensions. Numerical results demonstrate the gains in efficiency that are already achievable with this convenient but non-optimal implementation.