Related papers: Wavelet Based Cross Correlations with Applications
The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
We describe a simple automated method to extract and quantify transient heterogeneous dynamical changes from large datasets generated in single molecule/particle tracking experiments. Based on wavelet transform, the method transforms raw…
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…
Time series forecasting requires capturing patterns across multiple temporal scales while maintaining computational efficiency. This paper introduces AWGformer, a novel architecture that integrates adaptive wavelet decomposition with…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
It is shown that multiple representations (such as replicas or Hilbert transforms) of a random waveform can interfere constructively to form a compact pattern, akin to a wave packet, when the representations are created in synchrony with…
Classification of time series signals has become an important construct and has many practical applications. With existing classifiers we may be able to accurately classify signals, however that accuracy may decline if using a reduced…
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the…
This paper develops a novel statistical approach to characterize temporally localised cross-oscillatory interactions between channels in a functional brain network. Brain signals are generally nonstationary and the proposed framework uses…
We describe a new wavelet transform, for use on hierarchies or binary rooted trees. The theoretical framework of this approach to data analysis is described. Case studies are used to further exemplify this approach. A first set of…
This article combines wavelet analysis techniques with machine learning methods for univariate time series forecasting, focusing on three main contributions. Firstly, we consider the use of Daubechies wavelets with different numbers of…
Capturing high-frequency data concerning the condition of complex systems, e.g. by acoustic monitoring, has become increasingly prevalent. Such high-frequency signals typically contain time dependencies ranging over different time scales…
The polar wavelet transform (PWT) has been proven to be a powerful mathematical tool for signal and image processing in recent years. Due to the increasing demand for directional representations of signals in engineering, it is impossible…
Image enhancement is a technique that frequently utilized in digital image processing. In recent years, the popularity of learning-based techniques for enhancing the aesthetic performance of photographs has increased. However, the majority…
The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…
We use Daubechies' orthonormal compact wavelets as a variational basis for the $XY$ model in two and three dimensions. Assuming that the fluctuations of the wavelet coefficients are Gaussian and uncorrelated, minimization of the free energy…
Cloud detection is a specialized application of image recognition and object detection using remotely sensed data. The task presents a number of challenges, including analyzing images obtained in visible, infrared and multi-spectral…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients…