During their service life, marine pipelines continually accumulate damage as a result of the action of various environmental forces. Clearly, the development of robust techniques for early damage detection is very important to avoid the possible occurrence of a disastrous structural failure. Most of vibration-based damage detection methods require the modal properties that are obtained from mea...

Wavelet transforms are not capable of reconstructing curved images perfectly, hence we go for this new concept, called Contourlet Transform. It is a multiresolution and directional decomposition of a signal using a combination of Laplacian Pyramid (LP) and a Directional Filter Bank (DFB). The Contourlet transform has good approximation properties for smooth 2D functions and finds a direct discr...

We consider the continuous wavelet transform [Formula: see text] associated with the Weinstein operator. We introduce the notion of localization operators for [Formula: see text]. In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of [Formula: see text] on sets of finite measure. ...

We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we prove that the modulus of the wavelet transform uniquely determines the function up to a global phase. We show that the reconstruction operator is continuou...

Investigation of the dynamics of internal gravity waves often includes the interrelationship between wave amplitudes, wave speeds, and wavelengths. These relationships are commonly thought of as dispersion relations. Because internal gravity waves are the result of nonlinear dynamics dispersion relations are a challenge to obtain in a quantitative sense. Model data for internal gravity waves in...

In the present note we investigate norm and almost everywhere convergence of the inverse continuous wavelet transform in the variable Lebesgue space. Mathematics Subject Classification (2010): Primary 42C40, Secondary 42C15, 42B08, 42A38, 46B15.

In this paper we present the use of the Continuous Wavelet Transform and the subsequent energy distribution derived from the transform of Electrocardiogram (ECG) signals to analyse atrial electrical activity. The atrium produces a low amplitude wave in the ECG, which can often be overwhelmed by noise making it difficult to analyse by eye and therefore limiting the P wave as an indicator in card...

− The paper describes an unusual approach to diagnose standard ignition subsystem of fuel engines. All the information about real state conditions of the ignition coils and sparks is taken from simple measurement of power consumption transient of the electric control systems of engine. The transient is processed by continuous wavelet transformation (CWT). Result of the CWT is used for a classif...

A (‘oni1non assumpt,ion of the shape from texture problc~ri s that i i perceived imago mainly contains only one type of texture with the sanic’ surface orientation. Unfortuiiatelly. a natural image is often composed of more than onc: t,exures. In order t,o solve the shape from tcxturc problern in a practical manner, we need to segment, 3D textured images. In this paper, we propose a new algorit...