心电文献.rar_ECG QRS_ecg analysis_行业发展研究下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/624fc05374bc5c0105516772/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624fc05374bc5c0105516772/bg1.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">Biomedical Signal Processing and Control 69 (2021) 102903</div><div class="t m0 x2 h3 y3 ff1 fs0 fc1 sc0 ls0 ws0">Available online 28 June 2021</div><div class="t m0 x2 h3 y4 ff1 fs0 fc1 sc0 ls0 ws0">1746-8094/© 2021 Elsevier Ltd. All rights reserved.</div></div><div class="t m0 x2 h4 y5 ff2 fs1 fc1 sc0 ls0 ws0">A denoising performance comparison based on ECG Signal Decomposition </div><div class="t m0 x2 h4 y6 ff2 fs1 fc1 sc0 ls0 ws0">and local means ltering </div><div class="t m0 x2 h5 y7 ff2 fs2 fc1 sc0 ls0 ws0">Mohamed Sraitih , Younes Jabrane</div><div class="t m1 x3 h6 y8 ff2 fs3 fc2 sc0 ls0 ws0">* </div><div class="t m0 x2 h7 y9 ff3 fs4 fc1 sc0 ls0 ws0">MSC Lab, ENSA Cadi Ayyad University, Marrakech, Morocco </div><div class="t m0 x2 h8 ya ff2 fs5 fc1 sc0 ls1 ws0">ARTICLE INFO </div><div class="t m0 x2 h7 yb ff3 fs4 fc1 sc0 ls0 ws0">Keywords: </div><div class="t m0 x2 h7 yc ff2 fs4 fc1 sc0 ls0 ws0">ECG denoising </div><div class="t m0 x2 h7 yd ff2 fs4 fc1 sc0 ls0 ws0">EMD </div><div class="t m0 x2 h7 ye ff2 fs4 fc1 sc0 ls0 ws0">EEMD </div><div class="t m0 x2 h7 yf ff2 fs4 fc1 sc0 ls0 ws0">DWT </div><div class="t m0 x2 h7 y10 ff2 fs4 fc1 sc0 ls0 ws0">SWT </div><div class="t m0 x2 h7 y11 ff2 fs4 fc1 sc0 ls0 ws0">non-local means </div><div class="t m0 x2 h7 y12 ff2 fs4 fc1 sc0 ls0 ws0">local means </div><div class="t m0 x4 h8 ya ff2 fs5 fc1 sc0 ls1 ws0">ABSTRACT </div><div class="t m0 x4 h3 y13 ff2 fs0 fc1 sc0 ls0 ws0">The electrocardiogram (ECG) signal is popular and extensively used as a diagnostic tool for revealing several </div><div class="t m0 x4 h3 y14 ff2 fs0 fc1 sc0 ls0 ws0">diseases related to the heart. Unfortunately, its sensitive to noises from various sources. Denoising these noises </div><div class="t m0 x4 h3 y15 ff2 fs0 fc1 sc0 ls0 ws0">remains a hard and major challenge task, although there are some existing methods for denoising, they remain </div><div class="t m0 x4 h3 y16 ff2 fs0 fc1 sc0 ls0 ws0">limited to a few types of noises with signicant distortion after the ltering process. In this paper, we investi-</div><div class="t m0 x4 h3 y17 ff2 fs0 fc1 sc0 ls0 ws0">gated a hybrid system that can deal with different types of noises, with different levels of SNR, conserving all the </div><div class="t m0 x4 h3 y18 ff2 fs0 fc1 sc0 ls0 ws0">signal features with the minimum distortion. The hybrid system consists of a decomposition method followed by </div><div class="t m0 x4 h3 y19 ff2 fs0 fc1 sc0 ls0 ws0">local means (LM) ltering. The best candidates used for the signal decomposition are the Empirical Mode </div><div class="t m0 x4 h3 y1a ff2 fs0 fc1 sc0 ls0 ws0">Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), Discrete Wavelet Transform (DWT), </div><div class="t m0 x4 h3 y1b ff2 fs0 fc1 sc0 ls0 ws0">and Stationary Wavelet Transform (SWT). To demonstrate the effectiveness of the proposed method, several real </div><div class="t m0 x4 h3 y1c ff2 fs0 fc1 sc0 ls0 ws0">ECG recordings and synthetic ECG infected by a different type of noise (i.e., baseline wander, muscle artifacts, </div><div class="t m0 x4 h3 y1d ff2 fs0 fc1 sc0 ls0 ws0">electrode motion, mix noise, white noise, colored noise) with different levels of signal to noise ratios (24, 18, 6, 0, </div><div class="t m0 x4 h3 y1e ff4 fs0 fc1 sc0 ls0 ws0">− 6) dB are used in our numerical analysis. The performance evaluation of our proposed system is made using the </div><div class="t m0 x4 h3 y1f ff2 fs0 fc1 sc0 ls0 ws0">following metrics: SNR improvement, signal-to-noise and distortion ratio (SINAD), the approximate entropy, and </div><div class="t m0 x4 h3 y20 ff2 fs0 fc1 sc0 ls0 ws0">the fuzzy entropy. The experimental results emphasized that the Ensemble Empirical Mode Decomposition </div><div class="t m0 x4 h3 y21 ff2 fs0 fc1 sc0 ls0 ws0">(EEMD) followed by local means (LM) outperforms all the comparison methods, in terms of all the metrics used, </div><div class="t m0 x4 h3 y22 ff2 fs0 fc1 sc0 ls0 ws0">with few exceptions where the Empirical Mode Decomposition (EMD) followed by local means (LM) and Discrete </div><div class="t m0 x4 h3 y23 ff2 fs0 fc1 sc0 ls0 ws0">Wavelet Transform (DWT) followed by local means (LM) performed well. </div><div class="t m0 x2 h9 y24 ff5 fs6 fc1 sc0 ls0 ws0">1. Introduction </div><div class="t m0 x5 h9 y25 ff2 fs6 fc1 sc0 ls0 ws0">The electrical activity generated during and after activation of the </div><div class="t m0 x2 h9 y26 ff2 fs6 fc1 sc0 ls0 ws0">different parts of the heart is measured by electrodes attached to the skin </div><div class="t m0 x2 h9 y27 ff2 fs6 fc1 sc0 ls0 ws0">and transformed into a signal. The recording of the electrical activity </div><div class="t m0 x2 h9 y28 ff2 fs6 fc1 sc0 ls0 ws0">presented as an electrocardiogram (ECG). This technique is well known </div><div class="t m0 x2 h9 y29 ff2 fs6 fc1 sc0 ls0 ws0">and extremely used for diagnosing various types of diseases related to </div><div class="t m0 x2 h9 y2a ff2 fs6 fc1 sc0 ls0 ws0">the heart. The signal is formed in PQRST waves representing each part of </div><div class="t m0 x2 h9 y2b ff2 fs6 fc1 sc0 ls0 ws0">the activity inside the heart. Hence, the morphology and heart rate got </div><div class="t m0 x2 h9 y2c ff2 fs6 fc1 sc0 ls0 ws0">from the ECG signal reveals the cardiac health of the body. Badly, the </div><div class="t m0 x2 h9 y2d ff2 fs6 fc1 sc0 ls0 ws0">signal is sensitive to noises that come basically from certain types of </div><div class="t m0 x2 h9 y2e ff2 fs6 fc1 sc0 ls0 ws0">equipment or the patient. The noises presented in the literature are </div><div class="t m0 x2 h9 y2f ff2 fs6 fc1 sc0 ls0 ws0">classied as; baseline wander which makes noises at 0–0.5 Hz with an </div><div class="t m0 x2 h9 y30 ff2 fs6 fc1 sc0 ls0 ws0">amplitude of 15% of overall ECG amplitude due to the respiratory </div><div class="t m0 x2 h9 y31 ff2 fs6 fc1 sc0 ls0 ws0">movement, power line interference that performs a random component </div><div class="t m0 x2 h9 y32 ff2 fs6 fc1 sc0 ls0 ws0">at 60 Hz or 50 Hz ± 0.2 Hz produced by the power supply, electromy-</div><div class="t m0 x2 h9 y33 ff2 fs6 fc1 sc0 ls0 ws0">ography (EMG) produce a noise up to 10% of a regular peak-to-peak ECG </div><div class="t m0 x6 h9 y24 ff2 fs6 fc1 sc0 ls0 ws0">amplitude and frequency up to 10 kHz around 50 ms because of the </div><div class="t m0 x6 h9 y34 ff2 fs6 fc1 sc0 ls0 ws0">electrical activity from the muscle contractions, Electrode motion arti-</div><div class="t m0 x6 h9 y25 ff2 fs6 fc1 sc0 ls0 ws0">facts causes long distortions at 100–500 ms due to the patient move-</div><div class="t m0 x6 h9 y26 ff2 fs6 fc1 sc0 ls0 ws0">ments that affect the electrode skin impedance, and Electrodes contact </div><div class="t m0 x6 h9 y27 ff2 fs6 fc1 sc0 ls0 ws0">noise manifest 1 Hz frequency noise because of the improper contact of </div><div class="t m0 x6 h9 y28 ff2 fs6 fc1 sc0 ls0 ws0">electrodes with skin. These noises can change the morphology of the </div><div class="t m0 x6 h9 y29 ff2 fs6 fc1 sc0 ls0 ws0">signal and make the diagnosis and the interpretation of the signal a hard </div><div class="t m0 x6 h9 y2a ff2 fs6 fc1 sc0 ls0 ws0">task. Consequently, a pre-processing technique should be performed </div><div class="t m0 x6 h9 y2b ff2 fs6 fc1 sc0 ls0 ws0">before analyzing the signal and extracting features for diagnosis or de-</div><div class="t m0 x6 h9 y2c ff2 fs6 fc1 sc0 ls0 ws0">cision making. </div><div class="t m0 x7 h9 y2d ff2 fs6 fc1 sc0 ls0 ws0">The remains of this paper are organized as follows: in the next sec-</div><div class="t m0 x6 h9 y2e ff2 fs6 fc1 sc0 ls0 ws0">tion, a literature review is presented. Section 3, we describe the theo-</div><div class="t m0 x6 h9 y2f ff2 fs6 fc1 sc0 ls0 ws0">retical foundation. Then in Section 4, the proposed methodology is </div><div class="t m0 x6 h9 y30 ff2 fs6 fc1 sc0 ls0 ws0">detailed. In Section 5 a Proof of concept is explained. Section 6 spreads </div><div class="t m0 x6 h9 y31 ff2 fs6 fc1 sc0 ls0 ws0">The conducted experiments and results. Finally, we conclude the paper </div><div class="t m0 x6 h9 y32 ff2 fs6 fc1 sc0 ls0 ws0">in Section 7. </div><div class="c x0 y35 w2 h0"><div class="t m0 x8 h3 y36 ff2 fs0 fc1 sc0 ls0 ws0">* Corresponding author. </div><div class="t m0 x5 h3 y37 ff3 fs0 fc1 sc0 ls0 ws0">E-mail addresses: mohamed.sraitih@ced.uca.ma (M. Sraitih), y.jabrane@uca.ma (Y. Jabrane). </div><div class="t m0 x9 h9 y38 ff2 fs6 fc1 sc0 ls0 ws0">Contents lists available at ScienceDirect </div></div><div class="t m0 xa ha y39 ff2 fs7 fc1 sc0 ls0 ws0">Biomedical Signal Processing and Control </div><div class="t m0 xb hb y3a ff7 fs6 fc1 sc0 ls0 ws0">journal homepage: www.elsevier.com/locate/bspc </div><div class="c x0 y35 w2 h0"><div class="t m0 x2 h3 y3b ff2 fs0 fc2 sc0 ls0 ws0">https://doi.org/10.1016/j.bspc.2021.102903 </div><div class="t m0 x2 h3 y3c ff2 fs0 fc1 sc0 ls0 ws0">Received 27 April 2021; Received in revised form 6 June 2021; Accepted 19 June 2021 </div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a></div><div class="pi" data-data='{"ctm":[1.612697,0.000000,0.000000,1.612697,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624fc05374bc5c0105516772/bg2.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 xc hc y3d ff8 fs8 fc1 sc0 ls0 ws0">Biomedical Signal Processing and Control 69 (2021) 102903</div><div class="t m0 xd hc y3e ff1 fs8 fc1 sc0 ls0 ws0">2</div></div><div class="t m0 x2 h9 y3f ff5 fs6 fc1 sc0 ls0 ws0">2. Literature review </div><div class="t m0 x5 h9 y40 ff2 fs6 fc1 sc0 ls0 ws0">At present, there are numerous techniques to lter and pre-process </div><div class="t m0 x2 h9 y41 ff2 fs6 fc1 sc0 ls0 ws0">ECG signals. The basic lters in the literature are the high-pass and </div><div class="t m0 x2 h9 y42 ff2 fs6 fc1 sc0 ls0 ws0">low-pass lters, it uses approximation functions such as; Butterworth </div><div class="t m0 x2 h9 y43 ff2 fs6 fc1 sc0 ls0 ws0">lter [1–3], Elliptic lter (Cauer), The Chebyshev type 1 and 2 lters </div><div class="t m0 x2 h9 y44 ff2 fs6 fc2 sc0 ls0 ws0">[4], Bessel lter [5] and recommended especially for baseline wander. </div><div class="t m0 x2 h9 y45 ff2 fs6 fc1 sc0 ls0 ws0">Above and beyond these basic methods, other techniques are used such </div><div class="t m0 x2 h9 y46 ff2 fs6 fc1 sc0 ls0 ws0">as adaptive lters [6–9], Wiener lter [10], Kalman lter [11,12], </div><div class="t m0 x2 h9 y47 ff2 fs6 fc1 sc0 ls0 ws0">moving average [13,14], and quadratic lter [15], and other techniques. </div><div class="t m0 x2 h9 y48 ff2 fs6 fc1 sc0 ls0 ws0">The adaptive lters are described as self-designing lters based on al-</div><div class="t m0 x2 h9 y49 ff2 fs6 fc1 sc0 ls0 ws0">gorithms (Least Mean Square (LMS)) that adjust the weights of the </div><div class="t m0 x2 h9 y4a ff2 fs6 fc1 sc0 ls0 ws0">adaptive lter to minimize the error. Wiener lter uses the statistical </div><div class="t m0 x2 h9 y4b ff2 fs6 fc1 sc0 ls0 ws0">components for noise removing processes like source signal or secondary </div><div class="t m0 x2 h9 y4c ff2 fs6 fc1 sc0 ls0 ws0">recorded ECG signal. The Kalman lter predicts the state with a dynamic </div><div class="t m0 x2 h9 y4d ff2 fs6 fc1 sc0 ls0 ws0">model and regulates the ltering with an observation model, which </div><div class="t m0 x2 h9 y4e ff2 fs6 fc1 sc0 ls0 ws0">reduces the error covariance of the estimator. The median lter or a </div><div class="t m0 x2 h9 y4f ff2 fs6 fc1 sc0 ls0 ws0">moving average lter comprises a shifting time window where the </div><div class="t m0 x2 h9 y50 ff2 fs6 fc1 sc0 ls0 ws0">central sample of each time window is changed by the median of sample </div><div class="t m0 x2 h9 y51 ff2 fs6 fc1 sc0 ls0 ws0">values in the window. These lters are used to remove the white noise, </div><div class="t m0 x2 h9 y52 ff2 fs6 fc1 sc0 ls0 ws0">baseline wander, and in some cases the EMG components and electrodes </div><div class="t m0 x2 h9 y53 ff2 fs6 fc1 sc0 ls0 ws0">motion artifacts. A notch lter is recommended to remove the power line </div><div class="t m0 x2 h9 y54 ff2 fs6 fc1 sc0 ls0 ws0">interference [16]. These methods revealed can be implemented directly </div><div class="t m0 x2 h9 y55 ff2 fs6 fc1 sc0 ls0 ws0">or in form of nite impulse response FIR [17] and innite impulse </div><div class="t m0 x2 h9 y56 ff2 fs6 fc1 sc0 ls0 ws0">response IIR [18–21]. Furthermore, the signal can be pre-processed and </div><div class="t m0 x2 h9 y57 ff2 fs6 fc1 sc0 ls0 ws0">ltered in the time domain as well as in the frequency domain, using the </div><div class="t m0 x2 h9 y58 ff2 fs6 fc1 sc0 ls0 ws0">Fourier transforms but it provides only spectral information in the fre-</div><div class="t m0 x2 h9 y59 ff2 fs6 fc1 sc0 ls0 ws0">quency domain [22], causing losses in the information about the time </div><div class="t m0 x2 h9 y5a ff2 fs6 fc1 sc0 ls0 ws0">domain proprieties and vice versa. To overcome this issue, Short Time </div><div class="t m0 x2 h9 y5b ff2 fs6 fc1 sc0 ls0 ws0">Fourier Transform (STFT) provides a representation of the signal in both </div><div class="t m0 x2 h9 y5c ff2 fs6 fc1 sc0 ls0 ws0">time and frequency domains using the moving window function [23]. In </div><div class="t m0 x2 h9 y5d ff2 fs6 fc1 sc0 ls0 ws0">this technique, it is needed to operate with a stable window size on the </div><div class="t m0 x2 h9 y5e ff2 fs6 fc1 sc0 ls0 ws0">other hand; it does not allow multi-resolution information on the signal. </div><div class="t m0 x2 h9 y5f ff2 fs6 fc1 sc0 ls0 ws0">The wavelet transform serves a multi-resolution property to produce </div><div class="t m0 x2 h9 y60 ff2 fs6 fc1 sc0 ls0 ws0">both time and frequency domain information, together through variable </div><div class="t m0 x2 h9 y61 ff2 fs6 fc1 sc0 ls0 ws0">window size. This approach of decomposing the signals into sub- </div><div class="t m0 x2 h9 y62 ff2 fs6 fc1 sc0 ls0 ws0">elements have become popular for noise ltering and reduction and </div><div class="t m0 x2 h9 y63 ff2 fs6 fc1 sc0 ls0 ws0">successfully used for the ECG signals ltering process from noises like </div><div class="t m0 x2 h9 y64 ff2 fs6 fc1 sc0 ls0 ws0">power line interference, baseline wandering, and high-frequency noise </div><div class="t m0 x2 h9 y65 ff2 fs6 fc2 sc0 ls0 ws0">[24–26], in addition to its extension such as continuous wavelet trans-</div><div class="t m0 x2 h9 y66 ff2 fs6 fc1 sc0 ls0 ws0">form (CWT) [27,28], discrete wavelet transform (DWT), which is usu-</div><div class="t m0 x2 h9 y67 ff2 fs6 fc1 sc0 ls0 ws0">ally handled by implementing soft or hard thresholds on the gotten DWT </div><div class="t m0 x2 h9 y68 ff2 fs6 fc1 sc0 ls0 ws0">coefcients, [29,28], Stationary Wavelet Transform (SWT) [30]. [31] </div><div class="t m0 x2 h9 y69 ff2 fs6 fc1 sc0 ls0 ws0">introduced a new signal analysis method called empirical mode </div><div class="t m0 x2 h9 y6a ff2 fs6 fc1 sc0 ls0 ws0">decomposition (EMD), the EMD was effectively used for cleaning the </div><div class="t m0 x2 h9 y6b ff2 fs6 fc1 sc0 ls0 ws0">ECG signal [32–36], as well as its extension named The ensemble </div><div class="t m0 x2 h9 y6c ff2 fs6 fc1 sc0 ls0 ws0">empirical mode decomposition (EEMD) which resolves the mode mixing </div><div class="t m0 x2 h9 y6d ff2 fs6 fc1 sc0 ls0 ws0">issue in EMD, [37,38]. </div><div class="t m0 x2 h9 y6e ff5 fs6 fc1 sc0 ls0 ws0">3. Theoretical foundation </div><div class="t m0 x5 h9 y6f ff2 fs6 fc1 sc0 ls0 ws0">In recent times, the hybrid schemes especially those using decom-</div><div class="t m0 x2 h9 y70 ff2 fs6 fc1 sc0 ls0 ws0">position methods have been anticipated and used for denoising the ECG </div><div class="t m0 x2 h9 y71 ff2 fs6 fc1 sc0 ls0 ws0">signals as well as to lter multi-types of noises and to improve the </div><div class="t m0 x2 h9 y72 ff2 fs6 fc1 sc0 ls0 ws0">denoising performance [39,40,7,3]. A various hybrid schemes have been </div><div class="t m0 x2 h9 y73 ff2 fs6 fc1 sc0 ls0 ws0">proposed [41,42,40] proposed a combination of DWT and Neural Net-</div><div class="t m0 x2 h9 y74 ff2 fs6 fc1 sc0 ls0 ws0">works (NN) to minimize the noise in ECG, in other scheme, [8] a com-</div><div class="t m0 x2 h9 y75 ff2 fs6 fc1 sc0 ls0 ws0">bination of WT decomposition with adaptive ltering as well as in [43], </div><div class="t m0 x2 h9 y76 ff2 fs6 fc1 sc0 ls0 ws0">by using the EMD with adaptive switching mean ltering. [39] sug-</div><div class="t m0 x2 h9 y77 ff2 fs6 fc1 sc0 ls0 ws0">gested a combination of the EMD decomposition method with moving </div><div class="t m0 x2 h9 y78 ff2 fs6 fc1 sc0 ls0 ws0">average lter, as well as in [38] where the authors used EMD and EEMD </div><div class="t m0 x2 h9 y79 ff2 fs6 fc1 sc0 ls0 ws0">with improved adaptive lter and in [40] with BLMS adaptive lter. </div><div class="t m0 x2 h9 y7a ff2 fs6 fc1 sc0 ls0 ws0">These methods have been shown to be a powerful tool for denoising ECG </div><div class="t m0 x2 h9 y7b ff2 fs6 fc1 sc0 ls0 ws0">signals and provide better performances than conventional methods. </div><div class="t m0 x5 h9 y7c ff2 fs6 fc1 sc0 ls0 ws0">The Non local means (NLM) was originally used in image denoising </div><div class="t m0 x2 h9 y7d ff2 fs6 fc1 sc0 ls0 ws0">to address the problem of images degradation by Buades et al. [44]. The </div><div class="t m0 x6 h9 y3f ff2 fs6 fc1 sc0 ls0 ws0">method denoised the image by averaging patches from various regions </div><div class="t m0 x6 h9 y7e ff2 fs6 fc1 sc0 ls0 ws0">in images that have similar spatial structures, and this process is based </div><div class="t m0 x6 h9 y40 ff2 fs6 fc1 sc0 ls0 ws0">on the fact that the images usually have repeated patterns. Tracey and </div><div class="t m0 x6 h9 y41 ff2 fs6 fc1 sc0 ls0 ws0">Miller [45] adopted the NLM method to the ECG signal denoising by the </div><div class="t m0 x6 h9 y42 ff2 fs6 fc1 sc0 ls0 ws0">same concepts. The experiment results established that the NLM method </div><div class="t m0 x6 h9 y43 ff2 fs6 fc1 sc0 ls0 ws0">has improved the signal-to-noise ratio, which was highly similar to the </div><div class="t m0 x6 h9 y44 ff2 fs6 fc1 sc0 ls0 ws0">wavelet-based methods denoising, besides a signicant distortion </div><div class="t m0 x6 h9 y45 ff2 fs6 fc1 sc0 ls0 ws0">reduction of the denoised waveform. The computation cost of the NLM </div><div class="t m0 x6 h9 y46 ff2 fs6 fc1 sc0 ls0 ws0">method is high because of its complexity, but it is easier to implement </div><div class="t m0 x6 h9 y47 ff2 fs6 fc1 sc0 ls0 ws0">than the Wavelet transform and EMD denoising methods. [46] used </div><div class="t m0 x6 h9 y48 ff2 fs6 fc1 sc0 ls0 ws0">neighborhood ltering implementations instead of the sliding window </div><div class="t m0 x6 h9 y49 ff2 fs6 fc1 sc0 ls0 ws0">scheme in a way to improve the performance of the NLM method as well </div><div class="t m0 x6 h9 y4a ff2 fs6 fc1 sc0 ls0 ws0">as in [47], where the authors used principal components analysis (PCA) </div><div class="t m0 x6 h9 y4b ff2 fs6 fc1 sc0 ls0 ws0">to achieve dimensionality reduction. </div><div class="t m0 x7 h9 y4c ff2 fs6 fc1 sc0 ls0 ws0">More recently, Qian et al. [48] introduced a new approach as a fast </div><div class="t m0 x6 h9 y4d ff2 fs6 fc1 sc0 ls0 ws0">ECG signal denoising method, called as Local Means (LM) method, </div><div class="t m0 x6 h9 y4e ff2 fs6 fc1 sc0 ls0 ws0">which is basically a “local search” or local form of the NLM method, in </div><div class="t m0 x6 h9 y4f ff2 fs6 fc1 sc0 ls0 ws0">addition to a simple method to determine the standard deviation of </div><div class="t m0 x6 h9 y50 ff2 fs6 fc1 sc0 ls0 ws0">additive white Gaussian noise in the ECG signal. The author also sug-</div><div class="t m0 x6 h9 y51 ff2 fs6 fc1 sc0 ls0 ws0">gested that the neighborhood half-width M which is a key parameter of </div><div class="t m0 x6 h9 y52 ff2 fs6 fc1 sc0 ls0 ws0">the NLM method is considered not to be limited to more than several </div><div class="t m0 x6 h9 y53 ff2 fs6 fc1 sc0 ls0 ws0">heartbeats which means a “non-local” search, and less than one heart-</div><div class="t m0 x6 h9 y54 ff2 fs6 fc1 sc0 ls0 ws0">beat that means a “local search”, and the authors reported that the </div><div class="t m0 x6 h9 y55 ff2 fs6 fc1 sc0 ls0 ws0">computation cost will be reduced as M decreases. Interestingly, as the </div><div class="t m0 x6 h9 y56 ff2 fs6 fc1 sc0 ls0 ws0">neighborhood width M is less than one heartbeat in ECG signal which </div><div class="t m0 x6 h9 y57 ff2 fs6 fc1 sc0 ls0 ws0">means “local search”, the approach resulted in about 2 orders of </div><div class="t m0 x6 h9 y58 ff2 fs6 fc1 sc0 ls0 ws0">magnitude lower computational cost than the NLM method because of </div><div class="t m0 x6 h9 y59 ff2 fs6 fc1 sc0 ls0 ws0">the “local search” and successfully denoised the ECG signal. Currently, </div><div class="t m0 x6 h9 y5a ff2 fs6 fc1 sc0 ls0 ws0">The Local Means (LM) has been successfully applied to denoise an ECG </div><div class="t m0 x6 h9 y5b ff2 fs6 fc1 sc0 ls0 ws0">signal with Additive White Gaussian noise [48]. However, Results of </div><div class="t m0 x6 h9 y5c ff2 fs6 fc1 sc0 ls0 ws0">denoising performance demonstrate that the LM method is better than </div><div class="t m0 x6 h9 y5d ff2 fs6 fc1 sc0 ls0 ws0">the NLM method especially in low SNR condition. </div><div class="t m0 x7 h9 y5e ff2 fs6 fc1 sc0 ls0 ws0">In this paper, in light of the above factors and inspired by the </div><div class="t m0 x6 h9 y5f ff2 fs6 fc1 sc0 ls0 ws0">advantage of LM over NLM, we propose an hybrid denoising strategy for </div><div class="t m0 x6 h9 y60 ff2 fs6 fc1 sc0 ls0 ws0">the ECG signal based on the decomposition method and local means </div><div class="t m0 x6 h9 y61 ff2 fs6 fc1 sc0 ls0 ws0">(LM). The proposed method starts by decomposing a noisy ECG signal </div><div class="t m0 x6 h9 y62 ff2 fs6 fc1 sc0 ls0 ws0">into a series of intrinsic mode functions (IMFs) using the EMD or the </div><div class="t m0 x6 h9 y63 ff2 fs6 fc1 sc0 ls0 ws0">EEMD, or into a set of detailed components and approximates compo-</div><div class="t m0 x6 h9 y64 ff2 fs6 fc1 sc0 ls0 ws0">nents of different scales using the DWT or the SWT. Then, the decom-</div><div class="t m0 x6 h9 y65 ff2 fs6 fc1 sc0 ls0 ws0">posed signal is ltered by the local means (LM). Finally, the denoised </div><div class="t m0 x6 h9 y66 ff2 fs6 fc1 sc0 ls0 ws0">ECG signal can be restored by reconstructing the ltered IMFs or the </div><div class="t m0 x6 h9 y67 ff2 fs6 fc1 sc0 ls0 ws0">detailed components and approximates components. Both the synthetic </div><div class="t m0 x6 h9 y68 ff2 fs6 fc1 sc0 ls0 ws0">and experimental ECG signals of the MIT-BIH database from physionet </div><div class="t m0 x6 h9 y69 ff2 fs6 fc1 sc0 ls0 ws0">have established the performance of the suggested approach on noise </div><div class="t m0 x6 h9 y6a ff2 fs6 fc1 sc0 ls0 ws0">reduction for ECG signals by measuring several metrics such as SNR </div><div class="t m0 x6 h9 y6b ff2 fs6 fc1 sc0 ls0 ws0">improvement, signal to noise and distortion ratio (SINAD), in addition to </div><div class="t m0 x6 h9 y6c ff2 fs6 fc1 sc0 ls0 ws0">the ltered ECG signal quality measurement using Approximate entropy </div><div class="t m0 x6 h9 y6d ff2 fs6 fc1 sc0 ls0 ws0">(ApEn) and Fuzzy entropy (fuzzyEnp), in form of extensive simulation </div><div class="t m0 x6 h9 y7f ff2 fs6 fc1 sc0 ls0 ws0">studies on real and random noise corrupted ECG signals as detailed in </div><div class="t m0 x6 h9 y80 ff2 fs6 fc2 sc0 ls0 ws0">Fig. 1. The methods we used for decomposition are the DWT, SWT, EMD, </div><div class="t m0 x6 h9 y81 ff2 fs6 fc1 sc0 ls0 ws0">and the best candidate is the EEMD. </div><div class="t m0 x6 h9 y82 ff5 fs6 fc1 sc0 ls0 ws0">4. Proposed methodology </div><div class="t m0 x7 h9 y83 ff2 fs6 fc1 sc0 ls0 ws0">For a given signal x with a set of additive noise n we have; v = x +n. </div><div class="t m0 x6 h9 y74 ff3 fs6 fc1 sc0 ls0 ws0">4.1. Discrete Wavelet Transform (DWT) and Stationary Wavelet </div><div class="t m0 x6 h9 y75 ff3 fs6 fc1 sc0 ls0 ws0">Transform (SWT) </div><div class="t m0 x7 h9 y77 ff2 fs6 fc1 sc0 ls0 ws0">The DWT operates on wavelets that are discretely sampled and are </div><div class="t m0 x6 h9 y78 ff2 fs6 fc1 sc0 ls0 ws0">calculated, after choosing the mother wavelet (Morlet, Daubechies, </div><div class="t m0 x6 h9 y79 ff2 fs6 fc1 sc0 ls0 ws0">Haar, etc), by-passing a signal through a collection of low-pass and high- </div><div class="t m0 x6 h9 y7a ff2 fs6 fc1 sc0 ls0 ws0">pass lters followed by down-sampling (by the factor of 2) in order to </div><div class="t m0 x6 h9 y7b ff2 fs6 fc1 sc0 ls0 ws0">decompose a signal into a set of detailed components produced by a </div><div class="t m0 x6 h9 y7c ff2 fs6 fc1 sc0 ls0 ws0">high-pass lter and approximates components produced by the low-pass </div><div class="t m0 x6 h9 y7d ff2 fs6 fc1 sc0 ls0 ws0">lter of different scales. The approximation coefcients represent the </div><div class="t m0 x2 h7 y84 ff3 fs4 fc1 sc0 ls0 ws0">M. Sraitih and Y. 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<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624fc05374bc5c0105516772/bg3.jpg"><div class="c x0 y1 w0 h2"><div class="t m0 xc hc y3d ff8 fs8 fc1 sc0 ls0 ws0">Biomedical Signal Processing and Control 69 (2021) 102903</div><div class="t m0 xd hc y3e ff1 fs8 fc1 sc0 ls0 ws0">3</div></div><div class="t m0 x2 h9 y85 ff2 fs6 fc1 sc0 ls0 ws0">low-frequency part of the signal containing the main features and in-</div><div class="t m0 x2 h9 y86 ff2 fs6 fc1 sc0 ls0 ws0">formation. Detail coefcients are important to preserve the perfect </div><div class="t m0 x2 h9 y87 ff2 fs6 fc1 sc0 ls0 ws0">shape when reconstruction is processed. To achieve the multilevel of </div><div class="t m0 x2 h9 y88 ff2 fs6 fc1 sc0 ls0 ws0">decomposition, the output of the approximation coefcients are divided </div><div class="t m0 x2 h9 y89 ff2 fs6 fc1 sc0 ls0 ws0">into new approximation and details coefcients by the same process, the </div><div class="t m0 x2 h9 y8a ff2 fs6 fc1 sc0 ls0 ws0">outputs then used for signal ltering. The inverse wavelet transforms </div><div class="t m0 x2 h9 y8b ff2 fs6 fc1 sc0 ls0 ws0">(IDWT) or discrete wavelet rebuilding has an identical construction, but </div><div class="t m0 x2 h9 y8c ff2 fs6 fc1 sc0 ls0 ws0">the down-sampling is replaced by an up-sampling. The SWT is similar to </div><div class="t m0 x2 h9 y8d ff2 fs6 fc1 sc0 ls0 ws0">the classical discrete wavelet (DWT) except the signal is not sub-sampled </div><div class="t m0 x2 h9 y8e ff2 fs6 fc1 sc0 ls0 ws0">and instead; the lters are up-sampled at each level of decomposition. </div><div class="t m0 x2 h9 y8f ff2 fs6 fc1 sc0 ls0 ws0">The choice of a wavelet basis function represents a critical aspect in </div><div class="t m0 x2 h9 y90 ff2 fs6 fc1 sc0 ls0 ws0">denoising performance [49]. Daubechies 6 (D6) of the Daubechies </div><div class="t m0 x2 h9 y91 ff2 fs6 fc1 sc0 ls0 ws0">family are similar in shape to the QRS complex and their energy spec-</div><div class="t m0 x2 h9 y92 ff2 fs6 fc1 sc0 ls0 ws0">trum is concentrated around low frequencies Therefore, we selected Db6 </div><div class="t m0 x2 h9 y93 ff2 fs6 fc1 sc0 ls0 ws0">as a wavelet function for both methods DWT and SWT with decompo-</div><div class="t m0 x2 h9 y94 ff2 fs6 fc1 sc0 ls0 ws0">sition levels 12 and 4 respectively, in decomposing the ECG signal for </div><div class="t m0 x2 h9 y95 ff2 fs6 fc1 sc0 ls0 ws0">the ltering process in this paper. </div><div class="t m0 x2 h9 y96 ff3 fs6 fc1 sc0 ls0 ws0">4.2. Empirical mode decomposition EMD and enesmble EMD </div><div class="t m0 x5 h9 y97 ff2 fs6 fc1 sc0 ls0 ws0">Huang et al. [31]Proposed a new approach named the empirical </div><div class="t m0 x2 h9 y98 ff2 fs6 fc1 sc0 ls0 ws0">mode decomposition (EMD) to decompose the signal into multiple </div><div class="t m0 x2 h9 y99 ff2 fs6 fc1 sc0 ls0 ws0">components. Each component contains noise and effective information. </div><div class="t m0 x2 h9 y9a ff2 fs6 fc1 sc0 ls0 ws0">The multiple components considered as a sum of intrinsic mode func-</div><div class="t m0 x2 h9 y9b ff2 fs6 fc1 sc0 ls0 ws0">tions (IMFs). All the local maxima and minima dene an IMF, being </div><div class="t m0 x2 h9 y9c ff2 fs6 fc1 sc0 ls0 ws0">symmetrical regarding zero. Similar to the simple harmonic function </div><div class="t m0 x2 h9 y9d ff2 fs6 fc1 sc0 ls0 ws0">used in Fourier analysis, the IMF illustrates a basic oscillatory mode in </div><div class="t m0 x2 h9 y9e ff2 fs6 fc1 sc0 ls0 ws0">the EMD analysis. We can summarize the process of the EMD algorithm </div><div class="t m0 x2 h9 y9f ff2 fs6 fc1 sc0 ls0 ws0">as follows: </div><div class="t m0 xe h9 ya0 ff2 fs6 fc1 sc0 ls0 ws0">1. Identify all extrema of signal v(t); </div><div class="t m0 xe h9 ya1 ff2 fs6 fc1 sc0 ls0 ws0">2. Interpolate between minima (resp. maxima) with cubic spline, </div><div class="t m0 x5 h9 ya2 ff2 fs6 fc1 sc0 ls0 ws0">ending up with envelope emin(t) (resp. emax(t)) (the lower and </div><div class="t m0 x5 h9 ya3 ff2 fs6 fc1 sc0 ls0 ws0">upper envelopes); </div><div class="t m0 xe h9 ya4 ff2 fs6 fc1 sc0 ls0 ws0">3. Compute the mean m(t) = (emin(t) + emax(t))/2; </div><div class="t m0 xe h9 ya5 ff2 fs6 fc1 sc0 ls0 ws0">4. Extract the detail d(t) = v(t) - m(t); </div><div class="t m0 xe h9 ya6 ff2 fs6 fc1 sc0 ls0 ws0">5. Iterate on the residual m(t). </div><div class="t m0 x5 h9 ya7 ff2 fs6 fc1 sc0 ls0 ws0">If m(t) becomes a constant or monotonic function, the process of </div><div class="t m0 x2 h9 ya8 ff2 fs6 fc1 sc0 ls0 ws0">decomposing the signal into IMFs is terminated. At this point a certain </div><div class="t m0 x2 h9 ya9 ff2 fs6 fc1 sc0 ls0 ws0">number of N IMFS have been extracted, and the original signal can be </div><div class="t m0 x2 h9 yaa ff2 fs6 fc1 sc0 ls0 ws0">then reconstructed by superposing the obtained IMFs: </div><div class="t m0 x2 hd yab ff9 fs6 fc1 sc0 ls0 ws0">v(t) =</div><div class="t m0 xf he yac ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x10 hf yad ff9 fs9 fc1 sc0 ls0 ws0">N</div><div class="t m0 x11 h10 yae ff9 fs9 fc1 sc0 ls0 ws0">i=1</div><div class="t m0 x12 h11 yaf ff9 fs6 fc1 sc0 ls0 ws0">IMF</div><div class="t m0 x13 hf yb0 ff9 fs9 fc1 sc0 ls0 ws0">i</div><div class="t m0 x14 hd yaf ff4 fs6 fc1 sc0 ls0 ws0">(t)+r</div><div class="t m0 x15 hf yb0 ff9 fs9 fc1 sc0 ls0 ws0">N</div><div class="t m0 x16 h9 yaf ff4 fs6 fc1 sc0 ls0 ws0">(t), (1) </div><div class="t m0 x2 h9 yb1 ff2 fs6 fc1 sc0 ls0 ws0">where r</div><div class="t m0 x17 h12 yb2 ff3 fsa fc1 sc0 ls0 ws0">N</div><div class="t m0 x18 h9 yb3 ff4 fs6 fc1 sc0 ls0 ws0">(t) is the residue after the extraction of IMF</div><div class="t m0 x19 h12 yb2 ff3 fsa fc1 sc0 ls0 ws0">N </div><div class="t m0 x1a h9 yb3 ff2 fs6 fc1 sc0 ls0 ws0">and N is the </div><div class="t m0 x2 h9 yb4 ff2 fs6 fc1 sc0 ls0 ws0">number of IMFs, i.e. the signal is decomposed into (M-1) IMFs and one </div><div class="t m0 x2 h9 yb5 ff2 fs6 fc1 sc0 ls0 ws0">residual. </div><div class="t m0 x5 h9 yb6 ff2 fs6 fc1 sc0 ls0 ws0">Unfortunately, The EMD decomposition has the weakness of mode </div><div class="t m0 x2 h9 yb7 ff2 fs6 fc1 sc0 ls0 ws0">mixing, presented as a single IMF either containing signals of broadly </div><div class="t m0 x2 h9 yb8 ff2 fs6 fc1 sc0 ls0 ws0">unequal scales, or a signal of a similar scale existing in different IMF </div><div class="t m0 x2 h9 yb9 ff2 fs6 fc1 sc0 ls0 ws0">components. This leads to the mixing of higher-order segments with the </div><div class="t m0 x2 h9 yba ff2 fs6 fc1 sc0 ls0 ws0">lower order components. A new analysis approach called the ensemble </div><div class="t m0 x2 h9 ybb ff2 fs6 fc1 sc0 ls0 ws0">empirical mode decomposition (EEMD) alleviates the mode mixing </div><div class="t m0 x2 h9 ybc ff2 fs6 fc1 sc0 ls0 ws0">problem, by adding white noise to the signal to cover uniformly different </div><div class="t m0 x2 h9 ybd ff2 fs6 fc1 sc0 ls0 ws0">scales of the signal during the decomposition, then calculates the </div><div class="t m0 x2 h9 ybe ff2 fs6 fc1 sc0 ls0 ws0">average after many times decomposing. We can summarize this process </div><div class="t m0 x2 h9 ybf ff2 fs6 fc1 sc0 ls0 ws0">as: </div><div class="t m0 x1b h9 yc0 ff2 fs6 fc1 sc0 ls0 ws0">1. White noise is added to the acquired data v(t), y</div><div class="t m0 x1c h12 yc1 ff3 fsa fc1 sc0 ls0 ws0">n</div><div class="t m0 x1d h9 y85 ff4 fs6 fc1 sc0 ls0 ws0">= V</div><div class="t m0 x1e h12 yc1 ff3 fsa fc1 sc0 ls0 ws0">n</div><div class="t m0 x1f h9 y85 ff4 fs6 fc1 sc0 ls0 ws0">(t)+u(t) for n </div><div class="t m0 x7 h9 y86 ff4 fs6 fc1 sc0 ls0 ws0">= 1, 2, …,N, with N the ensemble number; </div><div class="t m0 x1b h9 y87 ff2 fs6 fc1 sc0 ls0 ws0">2. The data with added white noise is decomposed into IMFs; </div><div class="t m0 x1b h9 y88 ff2 fs6 fc1 sc0 ls0 ws0">3. Step 1 and step 2 are repeated many times with various white noise </div><div class="t m0 x7 h9 y89 ff2 fs6 fc1 sc0 ls0 ws0">set every time; </div><div class="t m0 x1b h9 y8a ff2 fs6 fc1 sc0 ls0 ws0">4. The (ensemble) average of corresponding IMFs of the decomposition </div><div class="t m0 x7 h9 y8b ff2 fs6 fc1 sc0 ls0 ws0">are obtained at the end by averaging the total i IMF related to K trials: </div><div class="t m0 x20 h11 yc2 ff9 fs6 fc1 sc0 ls0 ws0">IMF</div><div class="t m0 x21 hf yc3 ff9 fs9 fc1 sc0 ls0 ws0">aver</div><div class="t m0 x21 hf yc4 ff9 fs9 fc1 sc0 ls0 ws0">m</div><div class="t m0 x22 hd yc5 ff4 fs6 fc1 sc0 ls0 ws0">(t) =</div><div class="t m0 x23 h11 yc6 ff6 fs6 fc1 sc0 ls0 ws0">1</div><div class="t m0 x24 h11 yc7 ff9 fs6 fc1 sc0 ls0 ws0">N</div><div class="t m0 x25 he yc8 ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x26 hf yc9 ff9 fs9 fc1 sc0 ls0 ws0">N</div><div class="t m0 x27 h10 yca ff9 fs9 fc1 sc0 ls0 ws0">i=1</div><div class="t m0 x28 h11 yc5 ff9 fs6 fc1 sc0 ls0 ws0">IMF</div><div class="t m0 x29 hf yc3 ff9 fs9 fc1 sc0 ls0 ws0">n</div><div class="t m0 x29 hf yc4 ff9 fs9 fc1 sc0 ls0 ws0">m</div><div class="t m0 x2a h9 yc5 ff4 fs6 fc1 sc0 ls0 ws0">(t). (2) </div><div class="t m0 x7 h9 ycb ff2 fs6 fc1 sc0 ls0 ws0">The original signal can be then reconstructed by superposing the </div><div class="t m0 x6 h9 ycc ff2 fs6 fc1 sc0 ls0 ws0">extracted IMFs as previously. The results generated by the EEMD depend </div><div class="t m0 x6 h9 ycd ff2 fs6 fc1 sc0 ls0 ws0">on the decision of the ensemble quantity N and the amplitude of added </div><div class="t m0 x6 h9 yce ff2 fs6 fc1 sc0 ls0 ws0">noise A. The following relation should be satised as shown by [50]: </div><div class="t m0 x6 hd ycf ffc fs6 fc1 sc0 ls0 ws0">∊ =</div><div class="t m0 x2b h11 yd0 ff9 fs6 fc1 sc0 ls0 ws0">A</div><div class="t m0 x2c he yd1 ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x2c h11 yd2 ff9 fs6 fc1 sc0 ls0 ws0">N</div><div class="t m0 x2d hd yd1 ff4 fs6 fc1 sc0 ls0 ws0">√</div><div class="t m0 x2e h9 yd3 ffb fs6 fc1 sc0 ls0 ws0">, (3) </div><div class="t m0 x6 h9 yd4 ff2 fs6 fc1 sc0 ls0 ws0">where ∊ is the nal standard deviation of error measured as the differ-</div><div class="t m0 x6 h9 yd5 ff2 fs6 fc1 sc0 ls0 ws0">ence between the original signal and the sum of the IMFs resulting from </div><div class="t m0 x6 h9 yd6 ff2 fs6 fc1 sc0 ls0 ws0">the EEMD. Unlike the wavelet transforms, the EMD and EEMD decom-</div><div class="t m0 x6 h9 yd7 ff2 fs6 fc1 sc0 ls0 ws0">position does not require a selection of a basis function, except two </div><div class="t m0 x6 h9 yd8 ff2 fs6 fc1 sc0 ls0 ws0">parameters for EEMD, which are ∊ equals 0.2 as a ratio of the standard </div><div class="t m0 x6 h9 yd9 ff2 fs6 fc1 sc0 ls0 ws0">deviation, and the ensemble number N equals 70. </div><div class="t m0 x6 h9 yda ff3 fs6 fc1 sc0 ls0 ws0">4.3. Denoising method: non-local means ltering </div><div class="t m0 x7 h9 ydb ff2 fs6 fc1 sc0 ls0 ws0">The non-local means ltering has been adopted by several studies </div><div class="t m0 x6 h9 ydc ff2 fs6 fc2 sc0 ls0 ws0">[46,44,51,45] to increase the cleaning of the signal disturbed by noise. </div><div class="t m0 x6 h9 ydd ff2 fs6 fc1 sc0 ls0 ws0">The value of the estimated signal x at a site s is a weighted sum of values </div><div class="t m0 x6 h9 yde ff2 fs6 fc1 sc0 ls0 ws0">at other points t that are within the interval of some “search neighbor-</div><div class="t m0 x6 h9 ydf ff2 fs6 fc1 sc0 ls0 ws0">hood” N (s). </div><div class="t m0 x6 hd ye0 ffa fs6 fc1 sc0 ls0 ws0">x(s) =</div><div class="t m0 x2f h11 ye1 ff6 fs6 fc1 sc0 ls0 ws0">1</div><div class="t m0 x30 hd ye2 ff9 fs6 fc1 sc0 ls0 ws0">Z(s)</div><div class="t m0 x31 he ye3 ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x32 h10 ye4 ff9 fs9 fc1 sc0 ls0 ws0">t∈N(s)</div><div class="t m0 x33 h9 ye5 ff9 fs6 fc1 sc0 ls0 ws0">w(s, t)v(t), (4) </div><div class="t m0 x6 h9 ye6 ff2 fs6 fc1 sc0 ls0 ws0">where Z(s) =</div><div class="t m0 x34 he ye7 ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x35 h12 ye8 ff3 fsa fc1 sc0 ls0 ws0">t</div><div class="t m0 x24 h9 ye9 ff3 fs6 fc1 sc0 ls0 ws0">w(s, t)v(t) and the weights are [52]; </div><div class="t m0 x6 hd yea ff9 fs6 fc1 sc0 ls0 ws0">w(s, t) = exp</div><div class="t m0 x36 he yeb ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x34 he yec ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x35 h10 yed ff9 fs9 fc1 sc0 ls0 ws0">δ∈Δ</div><div class="t m0 x37 hd yee ff4 fs6 fc1 sc0 ls0 ws0">(v(s + δ) − v(t +δ))</div><div class="t m0 x38 hf yef ff6 fs9 fc1 sc0 ls0 ws0">2</div><div class="t m0 x39 h11 yf0 ff6 fs6 fc1 sc0 ls0 ws0">2L</div><div class="t m0 x3a hf yf1 ff6 fs9 fc1 sc0 ls0 ws0">Δ</div><div class="t m0 x3b h11 yf0 ff9 fs6 fc1 sc0 ls0 ws0">λ</div><div class="t m0 x2a hf yf2 ff6 fs9 fc1 sc0 ls0 ws0">2</div><div class="t m0 x3c he yf3 ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x3d hd yf4 ff4 fs6 fc1 sc0 ls0 ws0">≡ exp</div><div class="t m0 x3e he yf3 ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x3f h11 yf5 ff9 fs6 fc1 sc0 ls0 ws0">d</div><div class="t m0 x40 hf yf6 ff6 fs9 fc1 sc0 ls0 ws0">2</div><div class="t m0 x41 hd yf5 ff4 fs6 fc1 sc0 ls0 ws0">(s, t)</div><div class="t m0 x42 h11 yf7 ff6 fs6 fc1 sc0 ls0 ws0">2L</div><div class="t m0 x1c hf yf1 ff6 fs9 fc1 sc0 ls0 ws0">Δ</div><div class="t m0 x43 h11 yf0 ff9 fs6 fc1 sc0 ls0 ws0">λ</div><div class="t m0 x44 hf yf2 ff6 fs9 fc1 sc0 ls0 ws0">2</div><div class="t m0 x45 he yf3 ffa fs6 fc1 sc0 ls0 ws0"></div><div class="t m0 x1e h9 yf4 ffb fs6 fc1 sc0 ls0 ws0">, (5) </div><div class="t m0 x6 h9 yf8 ff9 fs6 fc1 sc0 ls0 ws0">λ is a bandwidth parameter, while Δ represents a local patch of samples </div><div class="t m0 x6 h9 yf9 ff2 fs6 fc1 sc0 ls0 ws0">surrounding s, containing L</div><div class="t m0 x2a h13 yfa ff6 fsa fc1 sc0 ls0 ws0">Δ </div><div class="t m0 x46 h9 yfb ff2 fs6 fc1 sc0 ls0 ws0">samples; a patch of the same shape also </div><div class="t m0 x6 h9 yfc ff2 fs6 fc1 sc0 ls0 ws0">surrounds t. d</div><div class="t m0 x47 h12 yfd ff2 fsa fc1 sc0 ls0 ws0">2 </div><div class="t m0 x48 h9 yfe ff2 fs6 fc1 sc0 ls0 ws0">illustrates the sum of the squared point-by-point differ-</div><div class="t m0 x6 h9 yff ff2 fs6 fc1 sc0 ls0 ws0">ence between samples of two patches which is centered on s and t. The </div><div class="t m0 x6 h9 y100 ff2 fs6 fc1 sc0 ls0 ws0">novelty of NLM is that the weighting w(s, t) depends on patch similarity, </div><div class="t m0 x6 h9 y101 ff2 fs6 fc1 sc0 ls0 ws0">not on the physical distance between the points s and t. Averaging </div><div class="t m0 x6 h9 y102 ff2 fs6 fc1 sc0 ls0 ws0">similar patches help to keep edges, in contrast to more typical ltering </div><div class="t m0 x6 h9 y103 ff2 fs6 fc1 sc0 ls0 ws0">(cf., convolutions by a Gaussian smoothing kernel). A notable effort has </div><div class="t m0 x6 h9 y104 ff2 fs6 fc1 sc0 ls0 ws0">been dedicated to fast NLM methods [51,47].In this study, We per-</div><div class="t m0 x6 h9 y105 ff2 fs6 fc1 sc0 ls0 ws0">formed local means (LM) ltering approach, which is a “local” form of </div><div class="t m0 x6 h9 y106 ff2 fs6 fc1 sc0 ls0 ws0">the NLM technique, proposed in [48], by adopting a fast NLM algorithm </div><div class="t m0 x6 h9 y107 ff2 fs6 fc1 sc0 ls0 ws0">employed in [46]. This method signicantly speeds NLM by reordering </div><div class="t m0 x6 h9 y108 ff2 fs6 fc1 sc0 ls0 ws0">operations to get rid of a xed loop. For a 1-D signal of dimension N, the </div><div class="t m0 x6 h9 y109 ff2 fs6 fc1 sc0 ls0 ws0">computational complexity of [46] is O (2 NM) versus O (L</div><div class="t m0 x1f h13 y10a ff6 fsa fc1 sc0 ls0 ws0">Δ </div><div class="t m0 x49 h9 y10b ff2 fs6 fc1 sc0 ls0 ws0">NM) for the </div><div class="t m0 x6 h9 y10c ff2 fs6 fc1 sc0 ls0 ws0">Buades algorithm[44]. </div><div class="t m0 x7 h9 y10d ff2 fs6 fc1 sc0 ls0 ws0">There are three criterias in the NLM method that need to be deter-</div><div class="t m0 x6 h9 y10e ff2 fs6 fc1 sc0 ls0 ws0">mined: The length N(s), dened as a neighborhood half-width M, the </div><div class="c x0 y35 w2 h0"><div class="t m0 x4a h3 y10f ff5 fs0 fc1 sc0 ls0 ws0">Fig. 1. the structure of the proposed approach. </div></div><div class="t m0 x2 h7 y84 ff3 fs4 fc1 sc0 ls0 ws0">M. Sraitih and Y. Jabrane </div><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a></div><div class="pi" data-data='{"ctm":[1.612697,0.000000,0.000000,1.612697,0.000000,0.000000]}'></div></div>