A novel algorithm for the decomposition of non-stationary multidimensional and multivariate signals

• URL: http://arxiv.org/abs/2412.00553v1
• Date: Sat, 30 Nov 2024 18:40:56 GMT
• Title: A novel algorithm for the decomposition of non-stationary multidimensional and multivariate signals
• Authors: Roberto Cavassi, Antonio Cicone, Enza Pellegrino, Haomin Zhou,
• Abstract summary: Empirical Mode Decomposition (EMD) method and its variants, such as Iterative Filtering (IF) have emerged as effective nonlinear approaches. Fast Iterative Filtering (FIF) algorithm was developed, and further extensions, such as Multidimensional FIF (MvFIF) and Multidimensional FIF (FIF2) have been proposed to handle higher-dimensional data. MdMvFIF is capable of extracting Intrinsic Mode Functions (IMFs) from complex signals that vary in both space and time, overcoming limitations found in prior methods.
• Score: 4.4342107931214265
• License:
• Abstract: The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory components we can enhance the understanding and processing of the data, unveiling hidden information contained in them. Traditional methods, such as Fourier analysis and wavelet transforms, which are effective in handling mono-dimensional stationary signals struggle with non-stationary data sets and they require, this is the case of the wavelet, the selection of predefined basis functions. In contrast, the Empirical Mode Decomposition (EMD) method and its variants, such as Iterative Filtering (IF), have emerged as effective nonlinear approaches, adapting to signals without any need for a priori assumptions. To accelerate these methods, the Fast Iterative Filtering (FIF) algorithm was developed, and further extensions, such as Multivariate FIF (MvFIF) and Multidimensional FIF (FIF2), have been proposed to handle higher-dimensional data. In this work, we introduce the Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) technique, an innovative method that extends FIF to handle data that vary simultaneously in space and time. This new algorithm is capable of extracting Intrinsic Mode Functions (IMFs) from complex signals that vary in both space and time, overcoming limitations found in prior methods. The potentiality of the proposed method is demonstrated through applications to artificial and real-life signals, highlighting its versatility and effectiveness in decomposing multidimensional and multivariate nonstationary signals. The MdMvFIF method offers a powerful tool for advanced signal analysis across many scientific and engineering disciplines.

Related papers

• Phase-Based Approaches for Rapid Construction of Magnetic Fields in NV Magnetometry [9.378134074181768]
  This paper looks into estimating the magnetic field from the Optically Detected Magnetic Resonances (ODMR) signal. Mapping the shifts of ODMR signals to phase estimation, a computationally efficient approaches are proposed. Results show a significant reduction in computational time with the proposed method over existing methods.
  arXiv  Detail & Related papers  (2024-08-17T08:58:27Z)
• Multi-Source and Test-Time Domain Adaptation on Multivariate Signals using Spatio-Temporal Monge Alignment [59.75420353684495]
  Machine learning applications on signals such as computer vision or biomedical data often face challenges due to the variability that exists across hardware devices or session recordings. In this work, we propose Spatio-Temporal Monge Alignment (STMA) to mitigate these variabilities. We show that STMA leads to significant and consistent performance gains between datasets acquired with very different settings.
  arXiv  Detail & Related papers  (2024-07-19T13:33:38Z)
• Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution [13.298472586395276]
  We present an arbitrary-scale super-resolution (SR) method to enhance the resolution of scientific data. We conduct extensive experiments on diverse datasets from different domains.
  arXiv  Detail & Related papers  (2024-05-20T17:39:29Z)
• Physics-informed and Unsupervised Riemannian Domain Adaptation for Machine Learning on Heterogeneous EEG Datasets [53.367212596352324]
  We propose an unsupervised approach leveraging EEG signal physics. We map EEG channels to fixed positions using field, source-free domain adaptation. Our method demonstrates robust performance in brain-computer interface (BCI) tasks and potential biomarker applications.
  arXiv  Detail & Related papers  (2024-03-07T16:17:33Z)
• Unmixing Optical Signals from Undersampled Volumetric Measurements by Filtering the Pixel Latent Variables [5.74378659752939]
  Latent Unmixing is a new approach which applies a band-pass filter to the latent space of a multi-spectralal neural network. It enables better isolation and quantification of individual signal contributions, especially in the context of undersampled distributions. We showcase the method's practical use in experimental physics through two test cases that highlight the versatility of our approach.
  arXiv  Detail & Related papers  (2023-12-08T20:34:37Z)
• Transform Once: Efficient Operator Learning in Frequency Domain [69.74509540521397]
  We study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time. This work introduces a blueprint for frequency domain learning through a single transform: transform once (T1)
  arXiv  Detail & Related papers  (2022-11-26T01:56:05Z)
• Disentangling multiple scattering with deep learning: application to strain mapping from electron diffraction patterns [48.53244254413104]
  We implement a deep neural network called FCU-Net to invert highly nonlinear electron diffraction patterns into quantitative structure factor images. We trained the FCU-Net using over 200,000 unique dynamical diffraction patterns which include many different combinations of crystal structures. Our simulated diffraction pattern library, implementation of FCU-Net, and trained model weights are freely available in open source repositories.
  arXiv  Detail & Related papers  (2022-02-01T03:53:39Z)
• Serial-EMD: Fast Empirical Mode Decomposition Method for Multi-dimensional Signals Based on Serialization [7.206666825116138]
  Empirical mode decomposition (EMD) has developed into a prominent tool for adaptive, scale-based signal analysis. It is difficult for existing method and its variants to trade off the growth of data dimension and the speed of signal analysis. We present a novel signal-serialization method (serial-EMD) which decomposes multi-dimensional signals into a one-dimensional signal.
  arXiv  Detail & Related papers  (2021-06-22T03:56:08Z)
• Feature Weighted Non-negative Matrix Factorization [92.45013716097753]
  We propose the Feature weighted Non-negative Matrix Factorization (FNMF) in this paper. FNMF learns the weights of features adaptively according to their importances. It can be solved efficiently with the suggested optimization algorithm.
  arXiv  Detail & Related papers  (2021-03-24T21:17:17Z)
• Multilinear Compressive Learning with Prior Knowledge [106.12874293597754]
  Multilinear Compressive Learning (MCL) framework combines Multilinear Compressive Sensing and Machine Learning into an end-to-end system. Key idea behind MCL is the assumption of the existence of a tensor subspace which can capture the essential features from the signal for the downstream learning task. In this paper, we propose a novel solution to address both of the aforementioned requirements, i.e., How to find those tensor subspaces in which the signals of interest are highly separable?
  arXiv  Detail & Related papers  (2020-02-17T19:06:05Z)
• Theory inspired deep network for instantaneous-frequency extraction and signal components recovery from discrete blind-source data [1.6758573326215689]
  This paper is concerned with the inverse problem of recovering the unknown signal components, along with extraction of their frequencies. None of the existing decomposition methods and algorithms is capable of solving this inverse problem. We propose a synthesis of a deep neural network, based directly on a discrete sample set, that may be non-uniformly sampled, of the blind-source signal.
  arXiv  Detail & Related papers  (2020-01-31T18:54:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.