Continuous wavelet transforms arising from the quasiregular representation of a semidirect product group G = R ⋊ H have been studied by various authors. Recently the attention has shifted from the irreducible case to include more general dilation groups H , for instance cyclic (more generally: discrete) or one-parameter groups. These groups do not give rise to irreducible square-integrable repr...

A wavelet, in the generalized sense, is a vector in the Hilbert space, Hπ , of a unitary representation, π, of a locally compact group, G, with the property that the wavelet transform it defines is an isometry of Hπ into L2(G). We study the image of this transform and how that image varies as the wavelet varies. We obtain a version of the Peter-Weyl Theorem for the class of groups for which the...

We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform on L 1 \L 2 (R d). These inversion formulas turn out to be local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R > 0 about a point x to within error , we can nd () > 0 such that this can be accomplished by knowing t...

In the present paper we have reported a wavelet based time-frequency multiresolution analysis of an ECG signal. The ECG (electrocardiogram), which records hearts electrical activity, is able to provide with useful information about the type of Cardiac disorders suffered by the patient depending upon the deviations from normal ECG signal pattern. We have plotted the coefficients of continuous wa...

SAR images of the sea often show backscatter patterns linked to the horizontal structure of the Marine Atmospheric Boundary Layer (MABL) at the interface with the sea surface. In general, their dimensions are spread over a wide range of length scales, presenting spatial periodicity as well as intermittence. With the aim to isolate such backscatter structures, the two-dimensional Continuous Wave...

The 2-D continuous wavelet transform has been applied to a number of problems in astrophysics. We survey quickly some of these, then focus on two new applications. The first one is the automatic detection and analysis of special objects from the solar corona in the data taken by the EIT instrument aboard the SoHO satellite. The second problem is the detection of gamma sources in the Universe, t...

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted Lp-spa...

Crackles are one of the most important physical signs in clinical medicine. They have an explosive pattern in time domain, with a rapid onset and short duration. The timing, repeatability, and shape of crackles are important parameters for diagnosis. Therefore, automatic detection of crackles and their classification as fine and coarse crackles have important clinical value. Since the multireso...

Datasets are usually compared using cross-correlation, often using a moving window to calculate the correlation as a function of time or space. However, signals can be considered as being composed of sinusoids which possess amplitudes, frequencies and phases. All these three attributes can be computed at each point in time, and then used as the basis of a cross-correlation method. By using all ...

It is well known that for irreducible, square-integrable representations of a locally compact group, there exist so-called admissible vectors which allow the construction of generalized continuous wavelet transforms. In this paper we discuss when the irreducibility requirement can be dropped, using a connection between generalized wavelet transforms and Plancherel theory. For unimodular groups ...