Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Gu, Jialiang; Lin, Peiru; Ling, Bingo Wing‐Kuen; Yang, Chuqi; Feng, Peng

doi:10.1049/iet-spr.2017.0432

Cited by 12 publications

(13 citation statements)

References 18 publications

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“…Therefore, the singular spectrum analysis components corresponding to the small eigenvalues are summed up together to obtain an approximated despiked electroencephalogram. This is unlike the conventional singular spectrum analysis based denoising methods [15][16][17] x m . Here, it is required to determine m * via a thresholding method.…”

Section: Proposed Spike Suppression Methodsmentioning

confidence: 98%

“…To suppress the spikes in the filtered electroencephalogram, the filtered electroencephalogram is required to decompose into various components and appropriate processing is applied to these components. Since the magnitudes of the spikes are large [4][5][6] and the singular spectrum analysis components are expressed as the magnitudes of the eigenvalues of the trajectory matrix [15][16][17], the singular spectrum analysis is an appropriate tool to decompose the filtered electroencephalogram into various components for suppressing the spikes.…”

Section: Proposed Spike Suppression Methodsmentioning

confidence: 99%

“…2.1. Review on the Singular Spectrum Analysis [15][16][17] The singular spectrum analysis is to represent a signal as the sum of the singular spectrum analysis components. The procedures for performing the singular spectrum analysis are as follows.…”

Section: Reviews On the Singular Spectrum Analysis And The Low-rank Dmentioning

confidence: 99%

“…On the other hand, the singular spectrum analysis components corresponding to the large eigenvalues are used for the reconstruction of the signal. Hence, they are summed up together to obtain the denoised signal [15][16][17]. However, as the spikes are with the large magnitudes and the singular spectrum analysis components corresponding to the spikes are usually corresponding to the large eigenvalues, the spikes are still corrupted in the denoised signal.…”

Section: Introductionmentioning

confidence: 99%

“…Since different approaches have their own advantages and disadvantages, this paper proposes an iterative joint singular spectrum analysis and low-rank decomposition approach for suppressing the spikes in an electroencephalogram. Unlike the conventional singular spectrum analysis based denoising methods [15][16][17], this paper sums up the singular spectrum analysis components corresponding to the small eigenvalues. Also, this paper does not completely discard the sparse component obtained by the low-rank decomposition.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Suppressing the Spikes in Electroencephalogram via an Iterative Joint Singular Spectrum Analysis and Low-Rank Decomposition Approach

Tian

Ling

Zhou

et al. 2020

Sensors

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The novelty and the contribution of this paper consists of applying an iterative joint singular spectrum analysis and low-rank decomposition approach for suppressing the spikes in an electroencephalogram. First, an electroencephalogram is filtered by an ideal lowpass filter via removing its discrete Fourier transform coefficients outside the δ wave band, the θ wave band, the α wave band, the β wave band and the γ wave band. Second, the singular spectrum analysis is performed on the filtered electroencephalogram to obtain the singular spectrum analysis components. The singular spectrum analysis components are sorted according to the magnitudes of their corresponding eigenvalues. The singular spectrum analysis components are sequentially added together starting from the last singular spectrum analysis component. If the variance of the summed singular spectrum analysis component under the unit energy normalization is larger than a threshold value, then the summation is terminated. The summed singular spectrum analysis component forms the first scale of the electroencephalogram. The rest singular spectrum analysis components are also summed up together separately to form the residue of the electroencephalogram. Next, the low-rank decomposition is performed on the residue of the electroencephalogram to obtain both the low-rank component and the sparse component. The low-rank component is added to the previous scale of the electroencephalogram to obtain the next scale of the electroencephalogram. Finally, the above procedures are repeated on the sparse component until the variance of the current scale of the electroencephalogram under the unit energy normalization is larger than another threshold value. The computer numerical simulation results show that the spike suppression performance based on our proposed method outperforms that based on the state-of-the-art methods.

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Section: Proposed Spike Suppression Methodsmentioning

confidence: 98%

Section: Proposed Spike Suppression Methodsmentioning

confidence: 99%

Section: Reviews On the Singular Spectrum Analysis And The Low-rank Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Suppressing the Spikes in Electroencephalogram via an Iterative Joint Singular Spectrum Analysis and Low-Rank Decomposition Approach

Tian

Ling

Zhou

et al. 2020

Sensors

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Underlying Trend Extraction via Joint Ensemble Intrinsic Timescale Decomposition Algorithm and Matching Pursuit Approach

Wang

Ling

2019

Circuits Syst Signal Process

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Performing fractional delay via fractional singular spectrum analysis

Zhou

Ling

Huang

et al. 2021

SIViP

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This paper proposes a fractional singular spectrum analysis (SSA) based method for performing the fractional delay. First, the input sequence is divided into two overlapping sequences with the first sequence being the input sequence without its last point and the second sequence being the input sequence without its first point. Then, the singular value decompositions (SVD) are performed on the trajectory matrices constructed based on these two sequences. Next, the designs of both the right unitary matrix and the left unitary matrix for generating the new trajectory matrix are formulated as the quadratically constrained quadratic programing problems. The analytical solutions of these quadratically constrained quadratic programing problems are derived via the SVD approach. Finally, the fractional SSA components are obtained by performing the diagonal averaging operation and the fractional delay sequence is obtained by summing up all the fractional SSA components together. Since the fractional SSA operations are nonlinear and adaptive, our proposed method is a kind of nonlinear and adaptive approach for performing the fractional delay. Besides, by discarding some fractional SSA components, the joint fractional delay operation and the denoising operation can be performed simultaneously.

show abstract

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Cited by 12 publications

References 18 publications

Suppressing the Spikes in Electroencephalogram via an Iterative Joint Singular Spectrum Analysis and Low-Rank Decomposition Approach

Suppressing the Spikes in Electroencephalogram via an Iterative Joint Singular Spectrum Analysis and Low-Rank Decomposition Approach

Underlying Trend Extraction via Joint Ensemble Intrinsic Timescale Decomposition Algorithm and Matching Pursuit Approach

Performing fractional delay via fractional singular spectrum analysis

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