In this paper, it is shown how continuous Clifford Cl3,0-valued admissible wavelets can be constructed using the similitude group SIM(3), a subgroup of the affine group of R3. We express the admissibility condition in terms of a Cl3,0 Clifford Fourier transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how...

In this paper we propose a filter bank structure derived by using admissible wavelet packet transform. These filters have Mel scale spacing and have an advantage of easy implementation with higher resolution in time-frequency domain because of wavelet transform. The features are obtained by first calculating the energy in each filter band and then applying the Discrete Cosine Transform (DCT) to...

Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the computational possibility for the realization of this approach. We provide modified simpler explanation of the reconstruction formula, restricted on the practical cas...

A new type of analyzing wavelets which optimally match seismic wavelets (SW wavelets) is presented. It is proved that these wavelets are admissible. The advantages of the SW wavelets are shown for the seismic data processing and attributes analysis. By taking one of the SW wavelets as analyzing wavelet, a wavelet transform method (WT method) of calculating the instantaneous spectrum bandwidth (...

Many multivariate Gaussian models can conveniently be split into independent, block-wise problems. Common settings where this situation arises are balanced ANOVA models, balanced longitudinal models, and certain block-wise shrinkage estimators in nonparametric regression estimation involving orthogonal bases such as Fourier or wavelet bases. It is well known that the standard, least squares est...

In the standard scale space approach one obtains a scale space representation u : R R → R of an image f ∈ L2(R) by means of an evolution equation on the additive group (R,+). However, it is common to apply a wavelet transform (constructed via a representation U of a Lie-group G and admissible wavelet ψ) to an image which provides a detailed overview of the group structure in an image. The resul...

We consider the problem of recovering a structured sparse representation of a signal in an overcomplete time-frequency dictionary with a particular structure. For infinite dictionaries that are the union of a nice wavelet basis and a Wilson basis, sufficient conditions are given for the Basis Pursuit and (Orthogonal) Matching Pursuit algorithms to recover a structured representation of an admis...

We investigate a vector-valued version of the classical continuous wavelet transform. Special attention is given to the case when the analyzing vector consists of the first elements of the basis of admissible functions, namely the functions whose Fourier transform is a Laguerre function. In this case, the resulting spaces are, up to a multiplier isomorphism, poly-Bergman spaces. To demonstrate ...

Let Sp(n,R) be the symplectic group, and K∗ n its maximal compact subgroup. Then G = Sp(n,R)/K∗ n can be realized as the Siegel domain of type one. The square-integrable representation of G gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent s...