Wavelet based multivariate signal denoising using Mahalanobis distance and EDF statistics

Khuram Naveed, Naveed Ur Rehman*

*Corresponding author af dette arbejde

    Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

    Abstract

    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 RM to a single-dimensional space of positive real numbers R+ , i.e., RM→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
    OriginalsprogEngelsk
    Artikelnummer9234624
    TidsskriftIEEE Transactions on Signal Processing
    Vol/bind68
    Sider (fra-til)5997-6010
    Antal sider14
    ISSN1053-587X
    DOI
    StatusUdgivet - okt. 2020

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