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In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wa ...
We continue the analysis of the continuous wavelet transform on the 2-sphere, introduced in a previous paper. After a brief review of the transform, we define and discuss the notion of directional spherical wavelet, i.e., wavelets on the sphere that are se ...
Compact support is undoubtedly one of the wavelet properties that is given the greatest weight both in theory and applications. It is usually believed to be essential for two main reasons: (1) to have fast numerical algorithms, and (2) to have good time or ...
I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decompos ...
We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis ...
Statistical Parametric Mapping (SPM) is a widely deployed tool for detecting and analyzing brain activity from fMRI data. One of SPM's main features is smoothing the data by a Gaussian filter to increase the SNR. The subsequent statistical inference is bas ...
We provide an overview of spline and wavelet techniques with an emphasis on applications in pattern recognition. The presentation is divided in three parts. In the first one, we argue that the spline representation is ideally suited for all processing task ...
Wavelet transform is a powerful instrument in catching zero-dimensional singularities. Ridgelets are a powerful instrument in catching and representing mono-dimensional singularities in bidimensional space. In this paper we propose a hybrid video coder sch ...
A new method of physical activity monitoring is presented, which is able to detect body postures (sitting, standing, and lying) and periods of walking in elderly persons using only one kinematic sensor attached to the chest. The wavelet transform, in conju ...
A correlation function that compares each base in a DNA sequence to its various neighbours and which is subsequently processed by Fourier and wavelet transforms has been developed. The procedure has been applied to sequences from the human chromosome 22, t ...
