International Journal of Wavelets, Multiresolution and Information Processing

Empirical mode decomposition (EMD) is an adaptive and data-driven approach for analyzing multicomponent nonlinear and non-stationary signals. The mode-mixing problem is one of the most important topics for the improvement of the EMD algorithm. In this paper, we study the reasons of the mode mixing phenomenon. And then, we propose a new method to resolve this problem relying on the assumption that each IMF should be locally orthogonal to the others. We experiment on several signals, including simulated and real-life signals, to demonstrate the efficacy of the proposed method to resolve the mode mixing problem.

The Linear Time Frequency Analysis Toolbox is a MATLAB/Octave toolbox for computational time-frequency analysis. It is intended both as an educational and computational tool. The toolbox provides the basic Gabor, Wilson and MDCT transform along with routines for constructing windows (filter prototypes) and routines for manipulating coefficients. It also provides a bunch of demo scripts devoted either to demonstrating the main functions of the toolbox, or to exemplify their use in specific signal processing applications. In this paper we describe the used algorithms, their mathematical background as well as some signal processing applications.

The sentences in several different natural languages can be produced congruously and synchronous by the new generating system USGS = {↔, G_I|G_I = (T_I, N, B-R_ISU, C-tree_I, S, P_I, F_I), I = 0, 1, 2, …, n}, based on Semantic Language(SL) theory, all are legitimate and reasonable, where, B-R_ISU is the set of basic-R_ISU, C-tree_I is the set of category-trees, and F_I is the set of functions in I-natural language. The characteristic of this new generating system is unified, synchronous and one by one corresponding, based on semantic unit theory and that the number of rules is several millions.

We provide a space domain-oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itself is well-known in geomagnetic modeling, usually in terms of a spherical harmonic analysis or a wavelet analysis that is spherical harmonic-based. In contrast to these frequency-oriented methods, we use a more spatially-oriented approach in this paper. We derive integral representations with explicitly known convolution kernels. Regularizing these singular kernels allows a multiscale representation of the internal and external contributions to the magnetic field with locally supported wavelets. This representation is applied to a set of CHAMP data for crustal field modeling.

The extraction of affine invariant features plays an important role in many fields of computer vision. Contour-based wavelet methods are unapplicable to objects with several separable components. In this paper, a method is proposed by converting the object into a closed curve, which is called radial centroid curve (RCC). Point on this curve is the centroid of radial line segment from centroid of the object. It is shown that the RCC derived from the affine transformed object is the same affine transformed version as that of the original object. An affine invariant function (AIF) is constructed by applying stationary wavelet transform (SWT) to the derived RCC. This scheme is applicable to objects with several separable components. Several experiments have been conducted to evaluate the performance of the proposed method.

The compact supported, linear phase, perfect reconstruction, orthogonal 3-band wavelet with high vanishing moments is very useful in engineering. However, the construction of these systems is not a simple task. In this paper, we construct the 3-band wavelet system with those properties. In this approach, we first designate the scaling filter length which means compact support, then the vanishing moments is set beforehand in spectral factorization formulation. Consequently, the scaling filters with desirable properties are obtained by solving nonlinear equations which implies less parameters. Moreover, we proposed a lattice structure decomposition of polyphase matrix for 3-band wavelet system, which imposed with paraunitary property. With this method, the corresponding wavelet filters are constructed.

In this paper we are concerned with the continuous shearlet transform in arbitrary space dimensions where the shear operation is of Toeplitz type. In particular, we focus on the construction of associated shearlet coorbit spaces and on atomic decompositions and Banach frames for these spaces.

Let G be a locally compact group with a compact subgroup H. We define a square integrable representation of a homogeneous space G/H on a Hilbert space . The reconstruction formula for G/H is established and as a result it is concluded that the set of admissible vectors is path connected. The continuous wavelet transform on G/H is defined and it is shown that the range of the continuous wavelet transform is a reproducing kernel Hilbert space. Moreover, we obtain a necessary and sufficient condition for the continuous wavelet transform to be onto.

Vector-valued refinable interpolatory functions with multiplicity r are discussed in this paper. This kind of refinable functions have a sampling property like Shannon's sampling theorem, and corresponding matrix-valued refinable masks possess special structure. In the context of multiwavelets, some properties of multifilter banks related will be present. Based on these properties, it will be shown that there are no symmetric (or antisymmetric) vector-valued refinable functions with interpolatory property. In the practical application, multiwavelets are always required to possess a certain degree of smoothness, which is related to three different concepts: balancing order, approximation order and analysis-ready order. In the general case, three notions are different. But if the scaling function is interpolatory, three concepts will be verified to equal to each other. Finally, a complete characterization of multifilter banks {H, G} will also be given and it will be used to construct some new balanced multiwavelets with interpolatory property for case r = 2, corresponding to which, multifilter banks have rational coefficients.

As high-throughput molecular dynamics simulations of proteins become more common and the databases housing the results become larger and more prevalent, more sophisticated methods to quickly and accurately mine large numbers of trajectories for relevant information will have to be developed. One such method, which is only recently gaining popularity in molecular biology, is the continuous wavelet transform, which is especially well-suited for time course data such as molecular dynamics simulations. We describe techniques for the calculation and analysis of wavelet transforms of molecular dynamics trajectories in detail and present examples of how these techniques can be useful in data mining. We demonstrate that wavelets are sensitive to structural rearrangements in proteins and that they can be used to quickly detect physically relevant events. Finally, as an example of the use of this approach, we show how wavelet data mining has led to a novel hypothesis related to the mechanism of the protein γδ resolvase.