Data-Driven Multivariate Signal Denoising Using Mahalanobis Distance

Rehman, Naveed ur; Khan, Bushra; Naveed, Khuram

doi:10.1109/lsp.2019.2932715

Cited by 30 publications

(22 citation statements)

References 21 publications

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“…The proposed approach is also fundamentally and significantly different from our previous work related to multivariate denoising [14] that utilizes the properties of MD measure to extend interval thresholding operation within single-channel EMD to multivariate EMD. In [14], an analytical relation between the stationary points of MD measure and derivatives of individual input data channels is given that justifies the extension of interval thresholding at multiple scales (obtained via MEMD) to multichannel data. On the other hand, this work exploits the (EDF) statistics of squared-MD (or quadratic transformation) to define a novel multivariate GoF test that is subsequently applied at multiple scales obtained from DWT to perform multivariate denoising.…”

Section: Introductionmentioning

confidence: 87%

“…This method, called MEMD-IT in the sequel, is a straight forward multichannel extension of [13] where IT was used to extract oscillatory signal parts from the intrinsic mode functions (IMF) of univariate EMD. Similarly, [14] presents a new multivariate signal denoising method that performs interval thresholding on Mahalanobis distances (MDs) corresponding to the multivariate IMFs of MEMD. The main result in that paper is a theorem that underpins the extension of interval thresholding procedure on MD by providing an analytical relation between the stationary points of MD and derivatives of individual input data channels.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet based multivariate signal denoising using Mahalanobis distance and EDF statistics

Naveed,

Rehman

2020

Preprint

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A multivariate signal denoising method is proposed which employs a novel multivariate goodness of fit (GoF) test that is applied at multiple data scales obtained from discrete wavelet transform (DWT). In the proposed multivariate GoF test, we first utilize squared Mahalanobis distance (MD) measure to transform input multivariate data residing in M-dimensional space R M to a single-dimensional space of positive real numbers R+, i.e., R M → R+, where M > 1. Owing to the properties of the MD measure, the transformed data in R+ follows a distinct distribution. That enables us to apply the GoF test using statistic based on empirical distribution function (EDF) on the resulting data in order to define a test for multivariate normality. We further propose to apply the above test locally on multiple input data scales obtained from discrete wavelet transform, resulting in a multivariate signal denoising framework. Within the proposed method, the reference cumulative distribution function (CDF) is defined as a quadratic transformation of multivariate Gaussian random process. Consequently, the proposed method checks whether a set of DWT coefficients belong to multivariate reference distribution or not; the coefficients belonging to the reference distribution are discarded. The effectiveness of our proposed method is demonstrated by performing extensive simulations on both synthetic and real world datasets.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Wavelet based multivariate signal denoising using Mahalanobis distance and EDF statistics

Naveed,

Rehman

2020

Preprint

Self Cite

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“…R ECENT advances in multi-sensor and data acquisition technology have facilitated routine recordings of multivariate or multichannel data sets, e.g., electroencephalogram (EEG), sofar signal [1]. Noise, which broadly refers to unwanted artifacts, is an inherent part of such data and must be removed to improve the accuracy of related signal processing systems.…”

Section: Introductionmentioning

confidence: 99%

An Improved Multivariate Synchrosqueezing Wavelet Transform Denoising Method Using Subspace Projection

2020

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In recent years, the development of multi-sensor has emphasized the need to directly process multi-channel (multivariate) data. In this paper, a novel multivariate synchrosqueezing wavelet transform denoising method combined with subspace projection (SWT-SP) is proposed. One of the key points of this method is to obtain an optimal orthogonal matrix which can project a multivariate observation signal to a signal subspace occupied by a clean signal and an orthogonal noise subspace occupied by noise. Furthermore, the high dimensional time-frequency representation based on the synchrosqueezing transform realizes the multichannel signal information fusion, and the subspace projection makes full use of the spatial diversity characteristics of the observed signal. Finally, signal energy produces the aggregation effect in the former dimension space, which improves the signal-to-noise ratio(SNR) of signals in the signal subspace. The performance of this algorithm for standard multichannel denoising is verified on both real-world data and synthetic signals. The reconstructed signal obtained the improvement of the highest SNR by about 6 dB under different conditions.

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“…It uses a sifting process, similar to EMD, for decomposition of multivariate signals into multidimensional IMFs. Since its inception, the method has found cross disciplinary applications in wide ranging fields including biomedical signal classification and related applications [14], [15], fault diagnosis in machines [10], data fusion x25b, process control [16] and data denoising [17].…”

Section: Introductionmentioning

confidence: 99%

FPGA based design for online computation of Multivariate EMD (MEMD)

Gul¹,

Siddiqui²,

Rehman³

2020

Preprint

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Multivariate or multichannel data have become ubiquitous in many modern scientific and engineering applications, e.g., biomedical engineering, owing to recent advances in sensor and computing technology. Processing these data sets is challenging owing to: i) their large size and multidimensional nature, thus requiring specialized algorithms and efficient hardware designs for on-line and real-time processing; ii) the nonstationary nature of data arising in many real life applications demanding new extensions of standard multiscale non-stationary signal processing tools. In this paper, we address the former issue by proposing a fully FPGA based hardware architecture of a popular multi-scale and multivariate signal processing algorithm, termed as multivariate empirical mode decomposition (MEMD). MEMD is a data-driven method that extends the functionality of standard empirical mode decomposition (EMD) algorithm to multichannel or multivariate data sets. Since its inception in 2010, the algorithm has found wide spread applications spanning different engineering related fields. Yet, no parallel FPGA based hardware design of the algorithm is available for its on-line and real-time processing. Our proposed architecture for MEMD uses fixed point operations and employs cubic spline interpolation within the sifting process. Finally, examples of decomposition of multivariate synthetic and real world biological signals are provided.

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Data-Driven Multivariate Signal Denoising Using Mahalanobis Distance

Cited by 30 publications

References 21 publications

Wavelet based multivariate signal denoising using Mahalanobis distance and EDF statistics

Wavelet based multivariate signal denoising using Mahalanobis distance and EDF statistics

An Improved Multivariate Synchrosqueezing Wavelet Transform Denoising Method Using Subspace Projection

FPGA based design for online computation of Multivariate EMD (MEMD)

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