Related papers: Wavelet Based Cross Correlations with Applications
Detecting anomalous edges in dynamic graphs is an important task in many applications over evolving triple-based data, such as social networks, transaction management, and epidemiology. A major challenge with this task is the absence of…
We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…
In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…
Due to the inherent complexity, temporal patterns in real-world time series often evolve across multiple intertwined scales, including long-term periodicity, short-term fluctuations, and abrupt regime shifts. While existing literature has…
This work shows the use of a two-dimensional Gabor wavelets in image processing. Convolution with such a two-dimensional wavelet can be separated into two series of one-dimensional ones. The key idea of this work is to utilize a Gabor…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
Unsupervised deep learning has recently demonstrated the promise of producing high-quality samples. While it has tremendous potential to promote the image colorization task, the performance is limited owing to the high-dimension of data…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
This book chapter describes how spectral correlations in scattered light fields can be utilized for high-precision time-of-flight sensing. The chapter should serve as a gentle introduction and is intended for computational imaging…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
The problem of known signal detection in Additive White Gaussian Noise is considered. In this paper a new detection algorithm based on Discrete Wavelet Transform pre-processing and threshold comparison is introduced. Current approaches…
Our previous multiscale graph basis dictionaries/graph signal transforms -- Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen Transform (HGLET); Natural Graph Wavelet Packets (NGWPs); and their relatives -- were…
Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with…
In previous work with Ken Wharton, it was proposed that Bell correlations are a special sort of selection artefact, explained by a combination of (i) collider bias and (ii) a boundary constraint on the collider variable. This requires no…
We introduce the mode connectivity as a measure of the number of eigenmodes of a wave equation connecting two points at a given frequency. Based on numerical simulations of scattering of electromagnetic waves in disordered media, we show…
Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of…
We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only…