Related papers: Decomposing non-stationary signals with time-varyi…
One of the goals of neuroscience is to study interactions between different brain regions during rest and while performing specific cognitive tasks. The Multivariate Bayesian Autoregressive Decomposition (MBMARD) is proposed as an intuitive…
Structural Health Monitoring (SHM) plays an indispensable role in ensuring the longevity and safety of infrastructure. With the rapid growth of sensor technology, the volume of data generated from various structures has seen an…
Sparse random mode decomposition (SRMD) is a novel algorithm that constructs a random time-frequency feature space to sparsely approximate spectrograms, effectively separating modes. However, it fails to distinguish adjacent or overlapped…
Embedded deformation nodes based formulation has been widely applied in deformable geometry and graphical problems. Though being promising in stereo (or RGBD) sensor based SLAM applications, it remains challenging to keep constant speed in…
In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…
Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of…
Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a…
Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years,…
Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…
To capture the slowly time-varying spectral content of real-world time-series, a common paradigm is to partition the data into approximately stationary intervals and perform inference in the time-frequency domain. However, this approach…
In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
The ability to detect anomalies in time series is considered highly valuable in numerous application domains. The sequential nature of time series objects is responsible for an additional feature complexity, ultimately requiring specialized…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
Vibration signals have been increasingly utilized in various engineering fields for analysis and monitoring purposes, including structural health monitoring, fault diagnosis and damage detection, where vibration signals can provide valuable…
We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one…
Neural data analysis has increasingly incorporated causal information to study circuit connectivity. Dimensional reduction forms the basis of most analyses of large multivariate time series. Here, we present a new, multitaper-based…
Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM),…
Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by…
Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time…