Geometric mode decomposition

Yu, Shi; Ma, Jianwei; Osher, Stanley

doi:10.3934/ipi.2018035

Cited by 19 publications

(19 citation statements)

References 39 publications

(53 reference statements)

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“…Again, ADMM is used to minimize Equation (2). Yu et al (2018), taking the inspiration from 2D-VMD, proposed a geometric mode decomposition (GMD) method that can represent the modes with directional and line-like geometric features. 2D-VMD performs well for scenarios where oscillation patterns exist.…”

Section: Theory Variational Mode Decompositionmentioning

confidence: 99%

“…Chen et al (2021) used a re-constrained VMD method to denoise three-component microseismic data. Another recent inspiration from the VMD framework is the geometric mode decomposition (GMD; Yu et al, 2018) that can optimally estimate the geometric features such as lines and parabolas on two-dimensional (2D) datasets. More specifically, Yu 2018) proposed a GMD method based on Fourier spectrum (GMD-F) for linear features and another GMD method based on radon transform for more complex features and applied these methods to seismic data for denoising, demultiple and interpolation problems.…”

Section: Introductionmentioning

confidence: 99%

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Using geometric mode decomposition for the background noise suppression on microseismic data

Abbasi

Jayaram

Akram³

et al. 2023

Geophysical Prospecting

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Microseismic datasets typically have relatively low signal‐to‐noise ratio waveforms. To that end, several noise suppression techniques are often applied to improve the signal‐to‐noise ratio of the recorded waveforms. We apply a linear geometric mode decomposition approach to microseismic datasets for background noise suppression. The geometric mode decomposition method optimizes linear patterns within amplitude–frequency modulated modes and can efficiently distinguish microseismic events (signal) from the background noise. This method can also split linear and non‐linear dispersive seismic events into linear modes. The segmented events in different modes can then be added carefully to reconstruct the denoised signal. The application of geometric mode decomposition is well suited for microseismic acquisitions with smaller receiver spacing, where the signal may exhibit either (nearly) linear or non‐linear recording patterns, depending on the source location relative to the receiver array. Using synthetic and real microseismic data examples from limited‐aperture downhole recordings only, we show that geometric mode decomposition is robust in suppressing the background noise from the recorded waveforms. We also compare the filtering results from geometric mode decomposition with those obtained from FX‐Decon and one‐dimensional variational mode decomposition methods. For the examples used, geometric mode decomposition outperforms both FX‐Decon and one‐dimensional variational mode decomposition in background noise suppression.

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Section: Theory Variational Mode Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Using geometric mode decomposition for the background noise suppression on microseismic data

Abbasi

Jayaram

Akram³

et al. 2023

Geophysical Prospecting

Self Cite

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show abstract

“…Given the attention that these methods received from the worldwide scientific community (Huang papers received so far more than 30000 citations based on Scopus) many other research groups started working on this topic and proposed their alternative approaches to signals decomposition. We recall the sparse TF representation [23,24], the Geometric mode decomposition [56], the Blaschke decomposition [14], the Empirical wavelet transform [22], the Variational mode decomposition [20], and similar techniques [44,36,42]. All of these methods are based on optimization with respect to an a priori chosen basis.…”

Section: Introductionmentioning

confidence: 99%

New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: the IMFogram algorithm

Cicone¹,

Li²,

Zhou³

2022

Preprint

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The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative time-frequency representations of a signal each with its advantages and limitations. In this work, following the success of nonlinear methods for the decomposition of signals into intrinsic mode functions (IMFs), we first provide more theoretical insights into the so-called Iterative Filtering decomposition algorithm, proving an energy conservation result for the derived decompositions. Furthermore, we present a new time-frequency representation method based on the IMF decomposition of a signal, which is called IMFogram. We prove theoretical results regarding this method, including its convergence to the spectrogram representation for a certain class of signals, and we present a few examples of applications, comparing results with some of the most well know approaches available in the literature.

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“…Furthermore, from the prospective of nonstationarities handling, they pose new challenges since they worsen the mode-splitting problem present in the EMD algorithm [45]. Over the years many alternative approaches to the EMD have been proposed, like, for instance, the sparse TF representation [22,23], the Geometric mode decomposition [46], the Empirical wavelet transform [21], the Variational mode decomposition [18], and similar techniques [36,30,35]. All these methods are based on optimization with respect to an a priori chosen basis.…”

Section: Introductionmentioning

confidence: 99%

Conjectures on spectral properties of ALIF algorithm

Barbarino,

Cicone

2020

Preprint

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A new decomposition method for nonstationary signals, named Adaptive Local Iterative Filtering (ALIF), has been recently proposed in the literature. Given its similarity with the Empirical Mode Decomposition (EMD) and its more rigorous mathematical structure, which makes feasible to study its convergence compared to EMD, ALIF has really good potentiality to become a reference method in the analysis of signals containing strong nonstationary components, like chirps, multipaths and whistles, in many applications, like Physics, Engineering, Medicine and Finance, to name a few.In [11], the authors analyzed the spectral properties of the matrices produced by the ALIF method, in order to study its stability. Various results are achieved in that work through the use of Generalized Locally Toeplitz (GLT) sequences theory, a powerful tool originally designed to extract information on the asymptotic behavior of the spectra for PDE discretization matrices. In this manuscript we focus on answering some of the open questions contained in [11], and in doing so, we also develop new theory and results for the GLT sequences.

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Geometric mode decomposition

Cited by 19 publications

References 39 publications

Using geometric mode decomposition for the background noise suppression on microseismic data

Using geometric mode decomposition for the background noise suppression on microseismic data

New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: the IMFogram algorithm

Conjectures on spectral properties of ALIF algorithm

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