Adaptive Savitzky-Golay Filtering in Non-Gaussian Noise

John, A and Sadasivan, J and Seelamantula, CS (2021) Adaptive Savitzky-Golay Filtering in Non-Gaussian Noise. In: IEEE Transactions on Signal Processing, 69 . pp. 5021-5036.

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Abstract

A Savitzky-Golay (SG) filter, widely used in signal processing applications, is a finite-impulse-response low-pass filter obtained by a local polynomial regression on noisy observations in the least-squares sense. The problem addressed in this paper is one of optimal order (or filter length) selection of SG filter in the presence of non-Gaussian noise, such that the mean-squared-error (or risk) between the underlying clean signal and the SG filter estimate is minimized. Since mean-squared-error (MSE) depends on the unknown clean signal, direct minimization is impractical. We circumvent the problem within a risk-estimation framework, wherein, instead of minimizing the original MSE, an unbiased estimate of the MSE (which depends only on the noisy observations and noise statistics) is minimized in order to obtain the optimal order. The proposed method gives an unbiased estimate of the MSE considering SG filtering in the presence of additive noise following any distribution with finite first- and second-order statistics and independent of the signal. The SG filter's order and length are optimized by minimizing the unbiased estimate of MSE. The denoising performance of the optimal SG filter is demonstrated on real-world electrocardiogram (ECG) signals as well as signals from the WaveLab Toolbox under Gaussian, Laplacian, and Uniform noise conditions. The proposed denoising algorithm is superior to four benchmark algorithms in low-to-medium input signal-to-noise ratio (SNR) regions (-5 dB to 12.5 dB) in terms of the SNR gain. © 1991-2012 IEEE.

Item Type:	Journal Article
Publication:	IEEE Transactions on Signal Processing
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Adaptive filtering; Additive noise; Biomedical signal processing; Electrocardiography; Gaussian distribution; Impulse response; Low pass filters; Mean square error; Polynomial regression; Risk perception; Signal to noise ratio, De-noising algorithm; Electrocardiogram signal; Finite-impulse response; Local polynomial regression; Savitzky Golay Filtering; Savitzky-Golay filter; Second order statistics; Signal processing applications, Gaussian noise (electronic)
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	09 Mar 2023 06:25
Last Modified:	09 Mar 2023 06:25
URI:	https://eprints.iisc.ac.in/id/eprint/80882

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