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A novel type2fuzzy adaptive filter is presented, which uses the concepts of type2fuzzy logic, for electrocardiogram signals denoising. Type2fuzzy adaptive filter is an information processor where both numerical and linguistic information are used as inputoutput pairs and fuzzy ifthen rules, respectively. The proposed approach is based on an iterative procedure to achieve acceptable information extraction in the case where the statistical characteristics of the inputoutput signals are unknown. The proposed filter is presented as a duallayered feedback system. Each layer has different function, the first layer being the type2fuzzy autoregressive filter model. The second layer being responsible for training the membership function parameters. The second layer adjusts the type2fuzzy adaptive filter parameters by using a teaching learningbased optimization algorithm (TLBO), which will allow the reaching of the required signal reconstruction by decreasing the criterion function. The proposed filter is validated and evaluated through some experimentations using the MITBIH ECGs databases where various artifacts were added to the ECGs signals; these included real and artificial noise. For comparison purposes, both model and nonmodelbased methods recently published are used. Furthermore, the effect of the proposed filter on the malformation of diagnostic features of the ECG was studied and compared with several benchmark schemes. The results show that the proposed method performs better denoising for all noise power levels and for a different criteria viewpoint.
ECG signal, ECG denoising, type2 fuzzy logic, optimization algorithm, TLBO
The purpose of an electrocardiogram (ECG) is to measure electrical potential changes in the heart over a specific time period. Particular cells in the heart produce electrical impulses that spread through the heart causing it to contract, thereby controlling the rate of the heart’s beating and causing these changes in the electrical potentials [14]. In the ECG, these electrical changes are measured through electrodes positioned on the chest. The electrical impulses are recorded in millivolts. Whilst the idealized heartbeat comprises several complexes, three of these complexes are frequently recorded and utilized in medical ECGs Terminology. These are the P complex, which measures the depolarization of the atrium, the QRS complex, which measures the depolarization of the ventricles, and the T wave, measuring the repolarization of the ventricles. However, the ECG signal frequently becomes contaminated by both internal and external noises. Whilst there are numerous sources of these noises, the ones of primary interest are instrument and Electromyogram (EMG) noises, electrode contact noise, motion artifacts and power line interference [5]. As such, it is necessary to carry out advanced digital processing of the ECG waveforms in order to use the ECG of an individual for identification and diagnosis purposes. Obviously, any noise that appears on the trace of the ECG can complicate diagnosis and identification analysis. Therefore, it is necessary to understand and cancel out the effects of noise from an ECG trace in order to extract the required identifying features of the trace itself. The required identification data can be masked by artifacts introduced by noise. Since its conception, outnumber of methods have been used to denoise ECG signals. The most widely used methods for ECG denoising are the nonmodelbased methods including a hybrid denoising scheme to enhance ECG signals by combining highorder synchro squeezing transform (FSSTH) with nonlocal means (NLM) [6], dualthreshold filter and discrete wavelet transform (ADTFDWT) [7], the empirical mode decomposition and genetic algorithm for adaptive denoising [8] and the adaptive Fourier decomposition (AFD) [9]. Other contributions in this subject are reported in Wang et al. study [1013] which have been widely used for ECG denoising. Alternatively, a modelbased method has been proposed, McSharry et al. use a threestate nonlinear dynamical model in Cartesian space for the generation of synthetic ECG signals. Indeed, several papers have used this model in order to denoise the ECG signal [14]. Hesar and Mohebbi [15] used this model with Bayesian filtering framework called the marginalized particleextended Kalman filter (MPEKF) for ECG denoising purposes. This model was extensively used by several researchers as reported by Sameni et al. [16, 17].
It has been proved that Fuzzy systems are universal approximators, i.e., that an arbitrary continuous function can be approximated within any given precision. To be more precise, it has been proven that a system represented by fuzzy rules can approximate any real system given by its inputoutput data, with any given accuracy. The construction of the fuzzy system encompasses two steps [18]: The first one is concerned with the construction of the fuzzy system model’s structure. Several contributions in this subject are reported in the papers [1923]. The second step is the identification of the constructed fuzzy system model’s parameters using a set of inputoutput data pairs. Many methods have been discussed in the literature to identify such parameters including gradient descent, nonlinear least squares, and Kalman filter [1823]. Chafaa et al. [18] have proposed an efficient approach to construct automatically a TakagiSugeno fuzzy models where the free parameters were adjusted using the Kalman filter algorithm twice. dos Santos Coelho and Herrera [20] developed a method for identifying a TakagiSugeno fuzzy model based on the chaotic particle Swarm optimization algorithm combined with an efficient GustafsonKessel clustering algorithm. Fuzzy Wiener model was proposed by Li and Yang [21] to identify chaotic systems, where the model’s parameters were tuned using a particle swarm optimization algorithm. Abiyev et al. [22] in their work presented a new Type2Fuzzyneuro system to detect equalizing timevarying channels and detect timevarying systems, where the identification step was achieved using clustering and gradient algorithms.
Type2 fuzzy sets are extension of the ordinary type1 fuzzy sets, which are defined by membership functions which are themselves fuzzy. The major advantage of type2 fuzzy systems is that they can produce reasonable outputs when ambiguity and imprecision occur. Fuzzy logic systems have many sources of uncertainty, such as (1) uncertainties of their inputs (uncertainties in the premise membership functions); (2) uncertainties of their outputs (uncertainties in the consequence membership functions) and (3) linguistic uncertainties, where the significance of the terms used in the antecedent and consequence parts may means different things to various people.
Metaheuristic algorithms are well suited for solving difficult problem of optimization where they are used successfully. They are often applied to several fields in different areas. In such algorithms, the optimal solution is obtained by parallel processing in the population. These techniques are frequently inspired by biological or biogeographical mechanisms. In this investigation, Teaching LearningBased Optimization (TLBO), is used in order to tune the type2 fuzzy filter free parameters adaptively. The TLBO algorithm is inspired by the teachinglearning process and based on the effect of the teacher on the students in the classroom.
Efficiency of combining metaheuristic optimization methods and fuzzy logic have been exhaustively analyzed and reported by Olivas et al. [2427]. This investigation proposes an effective electrocardiogram signal filtering method based on type2fuzzy logic and Teaching Learning BasedOptimization algorithm. Four stages are needed to construct the proposed TLBO based type2 fuzzy adaptive filter. (1) In the first stage we define the initial membership functions of the filter input and output which must cover the entire input space. (2) In the second stage we construct a set of tunable type2fuzzy rules based on numerical information extracted from training inputoutput data pairs. (3) In the third stage, the rules of the filter are constructed. (4) and last, in the fourth step we update the free parameters of the filter using the TLBO algorithm.
The free parameters of type2 fuzzy filter to be tuned by the TLBO algorithm are the Gaussian centres and widths of the type2 fuzzy premise membership functions and the consequence intervals. This approach is evaluated through intensive computer experimentations using MITBIH ECGs database. It is envisaged that this method will successfully deal with white Gaussian (WG) noises and the real noises (MA and EM) that are taken from the MITBIH noise stress test database [28]. By comparing the results of this method with those of other benchmark methods (FSSTHNLM, ADTFDWT, AFD, EEMD, and MPEKF), it can be seen statistically that the proposed technique has a significant performance improvement.
The rest of this paper is structured as follows: after section1; section 2 presents an overview of the type2 fuzzy system and TLBO algorithm. Section 3 outlines the proposed technique. Simulations and discussions are presented in section 4. Section 5 concludes the paper.
2.1 Type2 fuzzy adaptive filter
As mentioned previously, the concepts of fuzzy logic [2933] was extended to type2 fuzzy logic. In our work, Type2 fuzzy logic will be used to design adaptive filters. The proposed filter combines the set of inputoutput measurement pairs with a set of fuzzy IfThen rules. The benefits of using a type2fuzzy adaptive filter are its nonlinear nature and simple design. This simplicity allows human experts to incorporate linguistic information into the filter. When there is no linguistic information available, the type2 fuzzy adaptive filters can be redefined as nonlinear adaptive filters. The parameters of the membership functions are tuned with an adaptive procedure to characterize the IfThen rules through the use of some criterion function.
A duallayered feedforward network structure can be used to represent the type2 fuzzy adaptive filter [3436]. Therefore, it will be possible to train the type2 fuzzy adaptive filter to determine the required inputoutput relationship through the use of some learning algorithms, such as the TLBO in this investigation. Within this study, the type2 fuzzy adaptive filter's input $([x(k), x(k1), \ldots, x(kn+1)])$ is equal to the previous output, therefore the new input $x_{n}$ becomes $y_{n1} .$ Hence, at the sampling instant $k,$ the role of the type2 fuzzy adaptive filter is to filter the measured signal $\mathrm{y}(k)$ to obtain a smooth estimate $\hat{y}(k)$.
2.1.1 Type2 fuzzy logic system structure
Typen fuzzy sets were first proposed by Zadeh in 1975. They are characterized by membership functions that range over fuzzy type(n1) sets. In 1999, Karnik and Mendel have introduced some definitions, mechanisms, and algorithms for the type2 fuzzy sets [37]. The membership function of the type2 fuzzy set is itself a type1 fuzzy set.
Type2 fuzzy systems are hyperefficient compared to the type1 fuzzy systems, specifically in the presence of the ambiguity, uncertainty, and noisy data [3843]. Fuzzy systems are able to approximate any unknown function or nonlinear system using a set of inputoutput data. Any type2 fuzzy system is composed of five modules: a fuzzifier, a rule base, an inference engine, a type reducer, and a deffuzzifier (see Figure 1). Typereducer block is used to carry out the typereduction operation, which is an extension of the type1 defuzzification. This block produces type1 sets from type2 output sets. The typereduced set must be defuzzified to obtain crisp outputs.
The rule base of the type2 fuzzy system is a set of IfThen rules. These rules describe the relationship between the inputoutput spaces, and can be expressed as [44]:
Rule $^{i}$ : If $x_{1}$ is $\tilde{F}_{1}^{i}$ and,..., and $x_{n}$ is $\tilde{F}_{n}^{i}$ Then $y^{i}$ is $\tilde{G}^{i}$ (1)
where,
$x_{j}$: are premise variables;
$\tilde{F}_{j}^{i}$: are type2 fuzzy membership functions of the premise sets with j= 1, 2, …, n, and n is the number of regressors;
$y_{i} \in Y$: is the i^{th} output;
$\tilde{G}^{i}$: are type2 fuzzy sets of the consequences with i=1, 2, …, N, where N is the number of IfThenrules in the rule base.
The type reduction block is introduced to map the type2 fuzzy outputs of the inference engine to type1fuzzy sets. Among the most important methods for type reduction operations are KarnikMendel algorithm and WuMendel uncertainty bounds, which are based on the estimation of the centroid. There are other techniques proposed in the literature for the purpose of enhancing the robustness, performance, and time execution, such as the MEKM algorithm [45], the EKM algorithm, the EIASC, and many others reported by Tai et al. [46]. In our investigation the conventional KarnikMendal center of sets is used which is written as [47]:
$Y \cos \left(Y^{1}, \ldots, Y^{N R}, W^{1}, \ldots, W^{N R}\right)$$=\int_{y^{1}}^{0} \ldots \int_{Y^{N R}}^{0} \int_{w^{1}}^{0} \int_{w^{N R}}^{0} \frac{\frac{1}{\sum_{i=1}^{N R} w^{i} y^{i}}}{\sum_{i=1}^{N R} w^{i}}=\left[y_{1}, y_{r}\right]$ (2)
where, Ycos is the interval set bounded by two points y_{1}and y_{r}, $y^{i} \in Y^{i}=\left[y_{l}^{i}, y_{r}^{i}\right]$, Y^{i} is the centroid of the type2 interval consequent set G^{i }and $w^{i} \in W^{i}=\left[\underline{w}^{i}, \bar{w}^{i}\right]$ is the firing interval.
Figure 1. Type2 fuzzy logic system structure
2.1.2 Parameter update rules
The determination of the unknown parameters of the antecedent and the consequent parts of the type2fuzzy IfThen rules is crucial to design the type2–fuzzy adaptative filter. The input space in the antecedent parts is decomposed into a set of type2 fuzzy regions, while the consequence parts are decomposed into regions which are automatically determined. The ambiguity in the Gaussian type2 membership functions can be attributed to the center (mean) and the standard deviation. In this investigation, the Gaussian type2 fuzzy membership functions were chosen due to their ability to uniformly estimate continuous functions, and to their ability to universal approximation [48]. Figure 2 represents the Gaussian type2 fuzzy membership function where the uncertainty is associated with the center (mean) and with the standard deviation (width). The Gaussian membership function can be expressed mathematically as:
$\tilde{\mu}(x)=\exp \left(\frac{1}{2} \frac{(xc)^{2}}{\sigma^{2}}\right)$ (3)
where,
c: the center (mean) of the membership function;
$\sigma$: the width (standard deviation) of the membership function;
x: is the data.
In this paper, uncertainty is considered both on the center (mean) $c=\left[c_{1}, c_{2}\right]$ and on the standard deviation $\sigma=\left[\sigma_{1}, \sigma_{2}\right]$, where $c_{1}, \sigma_{1}$ and $c_{2}, \sigma_{2}$ are the lower and upper bounds of the uncertainty interval, respectively.
Figure 2. Gaussian type2 fuzzy membership function with: (a) uncertain standard deviation; (b) uncertain center (mean)
2.2 Teacherlearningbased optimization algorithm
Rao [49] have proposed a new evolutionary algorithm labeled TLBO (Teaching Learning Based Optimization), which is inspired by the education process at school. This optimization algorithm is based on the impact of the teacher on the learners in the classroom. This optimization algorithm uses a population of solutions which contains a possible solution (feasible solution) of the optimization problem under consideration. Basically, this population is a group of learners. Several subjects given to the learners can be considered to be the design variables which are the parameters associated with the objective function of the optimization problem. Learner’s result is analogs to the fitness value of the feasible solution of the optimization problem.
TLBO algorithm is divided into two phases: “Teacher phase” and “learner phase” which are described below:
2.2.1 Teacher phase
Learning of the learners form the teacher is considered to be the first phase of the TLBO algorithm, where the teacher is considered as the highly learned and skilled person in society. For simulations, we assume that there are ‘m’ number of subjects (design variables, $j=1,2, \ldots, m$), ‘n’ number of learners (population size, $k=1,2, \ldots, n$) and $M_{j}^{i}$ be the mean results of the students in a particular subject ‘j’ at any teachinglearning cycle ($i=0,1,2 \ldots, I_{n}$). A Teacher is the most experienced, knowledgeable, and highly learned person in society. To simulate this concept, the best learner (feasible solution) in the entire population is considered as a teacher. Let $X_{j}^{i}$ be the best feasible solution of the population at the $i^{t h}$ teachinglearning cycle and $X_{T, j}^{i}$ denotes the $j^{t h}$ design variable in the best feasible solution of the population at the $i^{t h}$ teachinglearning cycle or the result of the teacher in subject $j$ ". The difference between the result of the teacher and the mean result of the learners in subject $j$ ' can be expressed as:
$D_{j}^{i}=r\left(X_{T, i}^{i}T_{F} M_{j}^{i}\right)$ (4)
where,
$X_{T, j}^{i}$ is the result of the best student in subject $^{\prime} j^{\prime} \cdot r$ is a random number in the range [0,1]. $T_{F}$ is the teaching factor which decides the value of the mean to be changed, the value of $T_{F}$ can be either 0 or 1. $T_{F}$ is not a parameter of the TLBO algorithm, and is not given as an input to the algorithm and its value is randomly decided by the algorithm using the following equation:
$T F=$ round $[1+$ rand (0,1)$\{21\}]$ (5)
Based on the difference between the result of the teacher and the mean result of the learners in subject ‘j’ ($D_{j}^{i}$), the existing solution is updated in the teacher phase according to the following expression:
$X_{n e w, k, j}^{i}=X_{o l d, k, j}^{i}+D_{j}^{i}$ (6)
$X_{n e w, k}^{k}$ is accepted if it gives better function value than $X_{\text {old}, k}^{k}$. All the accepted feasible solutions are maintained and these become the input to the student phase. The student phase depends upon the teacher phase.
2.2.2 Learner phase
It is the second part of the TLBO algorithm where learners increase their knowledge by interaction among themselves. A learner interacts randomly with other students for enhancing his or her knowledge. A learner (u) learns new things if the other learner (v) has more knowledge than him or her. The learning philosophy of this phase is simulated as below:
Randomly select two students u and v, where their feasible solutions are $X_{u}^{i}$ and $X_{v}^{i}$, respectively and then:
if $F\left(X_{u}^{i}\right)>F\left(X_{v}^{k}\right)$
$X_{n e w_{S P}, u, j}^{i}=X_{u, j}^{i}+r\left(X_{u, j}^{i}X_{v, j}^{i}\right)$
else $X_{n e w, u}^{i}=X_{n e w, u}^{i}$
end if
where,
F(x): is a fitness function that is used to find the fitness value of a feasible solution;
$X_{n e w_{S P}, u, j}^{i}$: is the j^{th} design variable of the modified feasible solution in student phase at i^{th} teachinglearning cycle and it is accepted if it gives a better function value as follows:
If $F\left(X_{\text {new } S P, u}^{i}\right)>F\left(X_{\text {new }, u}^{i}\right)$
$X_{\text {new}, u}^{i}=X_{\text {new } S P, u}^{k}$
else $X_{n e w, u}^{i}=X_{n e w, u}^{i}$
end if
Figure 3 shows the proposed TLBObased type2 fuzzy adaptive filter framework:
Figure 3. Proposed framework of the TLBO based type2fuzzy adaptive filter
To construct the TLBO basedtype2 fuzzy adaptive filter, the following phases are used:
Phase 1: Consider N type2 fuzzy sets $F_{i}^{l}$ for all input space intervals $\left[C_{i}, C_{i}+\right]$ having Gaussian type2 fuzzy membership functions as:
$\mu_{F_{i}^{l}}\left(x_{i}, \mu_{P_{i}^{l}}\right)=\exp \left(\frac{1}{2}\left(\frac{\mu_{P}^{l}m_{i}^{l}\left(x_{i}\right)}{\sigma_{m_{i}}^{l}}\right)^{2}\right)$ (7)
where, $\mu_{F_{i}^{l}}$ and $\mu_{P_{i}^{l}}$ are the upper and the lower bounds of the Gaussian membership function, respectively, with $\mu_{P_{i}^{l}} \in[0,1]$; $\sigma_{m_{i}^{l}}$ is the standard deviation of the upper membership function; $m_{i}^{l}\left(x_{i}\right)$ is the mean of the upper membership function, which is characterized by Gaussian membership function with mean $M$ and standard deviation $\sigma_{x}$ as follows:
$m_{i}^{l}\left(x_{i}\right)=\exp \left(\frac{1}{2}\left(\frac{x_{i}M_{i}^{l}}{\sigma_{i}^{l}}\right)^{2}\right)$ (8)
where, $l=1,2, \ldots, N, i=1,2, \ldots, n ;$ the filter's input is represented as $x_{i}=x(kI+1),$ the center of the $i^{t h}$ membership function in the $l^{t h}$ rule is represented as $m_{i}^{l},$ and the width of the $i^{t h}$ membership function in the $l^{t h}$ rule is represented as $\sigma_{m_{i}^{l}}$. Within this study the free parameters $m_{i}^{l}$ and $\sigma_{m_{i}^{l}}$ will be tuned using the evolutionary algorithm TLBO. The Gaussian type2 fuzzy membership function (Eq. (7)) was chosen over triangular, trapezoidal or other shapes because it is a universal approximator that is able to uniformly estimate any continuous function in a compact set [36]. Nevertheless, when this type of network employs the other membership function types, verification of the universal approximation capability is difficult. Additionally, in order to complete function approximation, a large number of rules are required.
Phase 2: Construct a set of adjustable type2fuzzy rules using the numerical information of the training inputoutput data pairs:
$R^{l}:$ If $x_{i}$ is $F_{1}^{l}$ and, ..., and $x_{n}$ is $F_{n}^{l}$ Then $\hat{y}=\bar{Y}^{l} l=1,2, \ldots, N$ (9)
$\hat{y}$: the desired output;where,
$F_{i}^{l}$'s: type2 fuzzy sets of the antecedent;
$\bar{Y}^{i}$'s: type2 fuzzy sets of the consequent having a singleton type2 membership function $\mu_{\bar{Y}} l$;
There will be a change of the membership function parameters of $\mu_{F_{i}^{l}}$ and $\mu_{\bar{Y}} l$ during the adaptation process.
Phase 3: Through the use of the fundamental KarnikMendel center of sets type reduction [47] and the centroid defuzzification, the type2 fuzzy filter is constructed around the set of N rules.
Phase 4: Adjustment of the filter’s parameters by TLBO algorithm so that the fitness function error e between the type2 fuzzy adaptive filter output $\hat{y}$ and the noisy ECG signal y attains its minimum value (see Figure 3). The filter parameters that are trained are the consequence intervals $\bar{Y}^{l}$ and the Gaussian center of the premise membership functions $\mu_{F_{i}^{l}}$.
The objective function that is used throughout the investigation (TLBO optimization cost function) is the Mean Square Error (MSE) expressed as follows:
$M S E=\frac{\sum_{k=1}^{N}\left(y_{k}\hat{y}_{k}\right)}{N}=\frac{\sum_{k=1}^{N} e_{k}^{2}}{N}$ (10)
where, $y_{k}$ is the actual measure, $\hat{y}_{k}$ is its estimate, and $N$ is the length of the data.
proposed method to filter ECG signals. For this purpose, 200 signal segments of real ECG signals from different subjects are selected from the MITBIH database [50, 51]. The suggested method was simulated with $N=40$ rules. Therefore, the filter was structured using a set of 40 rules with $40 \times 3=120$ adjustable parameters. consequently, there was two regressors to every rule and one consequence interval $(2 \times 40$ antecedent parameters and $1 \times 40$ consequence parameters). The type2 fuzzy adaptive filter's initial input vector $x$ is set as $x=\left[x_{1}, x_{2}\right]^{T}=[0,0]^{T} .$ The effectiveness of the proposed approach will be fully investigated by assessing its performance in some noisy environments. These include the typical noises associated with ambulatory ECG recordings, which involve MA and EM. These are individually selected from the MITBIH stress data [28]. In addition, the proposed method will be also tested with artificially generated white Gaussian noise, which will be added to the original ECG segments with a number of input $S N R$ levels. In general, evaluation of signal denoising methods usually involves a measure of similarity between the denoised signal and the original signal. In order to assess the obtained type2 fuzzy filter output fit, four of the frequently used criteria from other experimental studies have been applied.
Signalto noise output ration ($S N R_{\text {out}}$):
$S N R_{\text {output}}=10 \times \log \left(\frac{\sum_{k=1}^{N}\left(x_{k}\right)^{2}}{\sum_{k=1}^{N}\left(\hat{y}_{k}x_{k}\right)^{2}}\right)$ (11)
Mean Square Error ($M S E$):
$M S E=\frac{1}{N} \sum_{k=1}^{N}\left(\hat{y}_{k}x_{k}\right)^{2}$ (12)
The SNR improvement ($S N R_{i m p}$):
$S N R_{i m p}=S N R_{\text {output}}S N R_{\text {input}}$ (13)
The Root Mean Square Error (RMSE):
$R M S E=\sqrt{\frac{1}{N} \sum_{k=1}^{N}\left(\hat{y}_{k}x_{k}\right)^{2}}$ (14)
where, $x_{k}$ is the clean signal, $\hat{y}_{k}$ is its estimate and N is the length of the data.
4.1 Denoising
To evaluate the outcomes of the proposed technique, three types of noise are utilized (real and artificial noises) and added to the real ECG referenced 18177.dat, taken from the MITBIH database [51]. The denoising results for different noise types are shown in Figures 47.
The results show that with the addition of white Gaussian noise at 3dB SNR level, the denoised ECG signal is very close to the clean ECG morphology (see Figure 4). Meanwhile, Figure 5 shows that the denoised signal does not show any EMG artefacts with real MA noises at 3dB SNR level. Nevertheless, whilst the most troublesome noise is the EM, due to its ability to mimic ectopic beats, a very successful outcome is obtained with this experiment. Normally, undesired notches and EM noise are seen on the ST segment, and it is very difficult to remove them using simple bandpass filters; however, the proposed method is able to remove these motion artefacts (EM), as shown in Figure 6, whilst also preserving the signal’s diagnostic morphology information. In order to assess the proposed method’s efficiency to remove more complicated noises, all three noises (EM, MA and white Gaussian noise) are added to the same signal (18177.dat). Comparing the noised ECG with the denoised one, it can be seen that the proposed method produces a very smooth signal (see Figure 7).
In what follows, the recording 18177.dat is used to evaluate the effectiveness of the proposed technique under different $S N R$ input levels of real EM and MA, and artificial WGN noises where severe distortion occurs. Fuzzy filter output is assessed for each noise power case by using the criteria formulas (11)(14). The SNR_{output}, SNR_{imp}, MSE and RMSE generated by the proposed framework for WGN, MA and EM versus different SNR_{input}(0dB to 10dB) are shown in Figure 8. These results show that the method achieves positive results in all different noise environments for a number of SNR_{input}levels. This can be seen in Figure 8 where the slope of the different criteria, particularly the SNR_{output}, are not flat and there is an obvious increase of the SNR_{output} with a corresponding decrease in SNR_{input}. So, this confirms that the framework is capable of optimally filter the ECG signal even in the presence of artefacts such as WGN, MA, and EM and with severe distortions.
Next, the proposed type2 fuzzy adaptive filter is applied to a series of real ECG signals to further test the validity of the approach. The considered records are 100.dat, 103.dat, 200.dat and 208.dat taken from the MITBIH arrhythmia database. The noisy ECG signal is constructed by adding 5dB Gaussian white noise (taking into account the real existing noise in the records). Visual inspections of Figures 9, 10, 11 and 12 show the filtering efﬁciency.
4.2 Comparison
The performances of the introduced filter will be compared to the results obtained by recently published methods in ECG signal denoising. Tables 14 give detailed results obtained by comparing the proposed method with the adaptive dual threshold filter and discrete wavelet transform (ADTFDWT) method [7]. The results given by Jenkal et al. [7] were validated by the works of several authors who compared the ADTFDWT with the paralleltype fractional zerophase filtering (FZP) [10], the Reimann Liouville (RL) integrator [11], and the zerophase average window filter (AZP) [10]. The EMG artefact comparison results are shown in Table 1. The noises are simulated in the same manner as the experiment described in the study [7]. Denoising comparison of 5dB white Gaussian noise from the selected entries of the MITBIH arrhythmia database [41] is shown in Table 2. The original paper [7] compares its results with a number of different methods, including the adaptive dependent wavelet thresholding technique (ADWT) and the multiadaptive bionicwavelet transform (MABWT) [12]. Tables 3 and 4 show the results of the comparison between the proposed method and some benchmark methods at the same levels of WGN.
This survey comparison shows that the results obtained from the proposed filter are much better than those obtained from the other benchmark methods, namely the ADTFDWT, RL, AZP, FZP, ADWT, MABWT methods as detailed by Jenkal et al. [7]. Indeed, the results show that the proposed method shows an increased SNR improvement and a reduced mean square error (MSE). In order to generate further validity in our results, we also compared the proposed approach performance against another recently published method [9] that is based on the adaptive Fourier decomposition (AFD). In [9], the authors made comparisons of the AFD based method with a number of other EMD and EEMD based methods described by Chang et al. [13]. The results of the comparison between the AFD method and the proposed method are presented in Table 5. They show that again, the introduced method performs better in terms of MSE criterion (These results that are presented in Table 5 are calculated with signal magnitude that has been increased by 200 times from its original value).
Figure 4. (a) Typical filtering of the proposed method for the record 18177.dat; with an added WGN at 3dB SNR level (b) Zoomed segment of denoised ECG signal
Figure 5. (a) Typical filtering of the proposed for the Record 18177.dat; with muscle artifact (MA) at 3dB SNR level (b) Zoomed segment of denoised ECG signal
Figure 6. (a) Typical filtering of the proposed method for the Record 18177.dat; with electrode motion artifact (EM) at 3dB SNR level (b) Zoomed segment of denoised ECG signal
Figure 7. Typical filtering of the proposed method for the record 18177.dat with the three noises (WGN+MA+EM)
Figure 8. Measures performances of the proposed method versus different input SNRs for WGN, EM and AM noise: (a) SNR_{output}(b) SNR _{improvement} (c) MSE (d) RMSE
Figure 9. (a) Typical filtering of the proposed method for the Record 100.dat with WGN at 5dB SNR level (b) Zoomed segment of denoised ECG signal
Figure 10. (a) Typical filtering of the proposed method for the Record 103.dat with WGN at 5dB SNR level (b) Zoomed segment of denoised ECG signal
Figure 11. (a) Typical filtering of the proposed method for the Record 200.dat with WGN at 5dB SNR level (b) Zoomed segment of denoised ECG signal
Figure 12. (a) Typical filtering of the proposed method for the Record 208.dat with WGN at 5dB SNR level (b) Zoomed segment of denoised ECG signal
Table 1. Comparison of the denoising results of the EMG artefact in the record 115.dat
Criteria 
RL [11] 
AZP [10] 
FZP [10] 
ADTFDWT [7] 
Proposed Method 
SNRoutput 
6.830 
11.820 
13.680 
15.590 
29.220 
MSE 
0.07050 
0.02230 
0.01460 
0.01460 
0.00810 
Table 2. Comparison of the denoising results of the WGN noise at 5dB in some record taken from the MITBIH arrhythmia database
Record N° 
Criteria 
ADTFDWT [7] 
Proposed Method 
100.dat 
MSE 
0.0044 
0.00310 
RMSE 
0.0660 
0.05560 

SNRimp 
9.7000 
19.2200 

101.dat 
MSE 
0.0042 
0.00230 
RMSE 
0.0400 
0.04790 

SNRimp 
10.230 
19.6100 

103.dat 
MSE 
0.0058 
0.00280 
RMSE 
0.0760 
0.05290 

SNRimp 
9.1000 
19.6800 

113.dat 
MSE 
0.0088 
0.00190 
RMSE 
0.0930 
0.04350 

SNRimp 
9.3300 
21.0500 

115.dat 
MSE 
0.0122 
0.00730 
RMSE 
0.1100 
0.08540 

SNRimp 
9.4500 
15.4300 

117.dat 
MSE 
0.0283 
0.00890 
RMSE 
0.1680 
0.09430 

SNRimp 
9.3400 
13.0100 

119.dat 
MSE 
0.0459 
0.00880 
RMSE 
0.2140 
0.09380 

SNRimp 
8.1300 
13.9500 

122.dat 
MSE 
0.0411 
0.00630 
RMSE 
0.2020 
0.07930 

SNRimp 
8.0700 
16.7400 
Table 3. Comparison of the denoising results of the WGN (5dB) in the record 101.dat
Criteria 
ADWT [12] 
ADTFDWT [7] 
Proposed Method 
MSE 
0.0050 
0.0042 
0.0023 
RMSE 
0.0720 
0.0640 
0.0479 
SNRimp 
9.0980 
10.2300 
19.6100 
Table 4. SNR_{imp} comparison of denoising results of the WGN (5dB) in some record taken from MITBIH database
Record N° 
ADWT [12] 
MABWT [12] 
ADTFDWT [7] 
Proposed Method 
100.dat 
9.90 
7.80 
9.70 
19.22 
101.dat 
9.09 
6.90 
10.23 
19.61 
103.dat 
7.13 
7.70 
9.10 
19.68 
113.dat 
7.82 
7.90 
9.33 
21.05 
115.dat 
7.19 
7.80 
9.45 
15.43 
117.dat 
8.62 
7.90 
9.34 
13.01 
119.dat 
7.27 
7.60 
8.13 
13.95 
122.dat 
7.86 
6.90 
8.07 
16.74 
Table 5. Comparison between filtered results using the AFD, EEMD, EMD and the proposed method with noisy signals at 10dB SNR level in terms of MSE criterion
MITBIH Record N° 
EMD [12] 
EEMD [12] 
AFD [8] 
Proposed Method 
101.dat 
126.9 
97.4 
36.0 
24.55 
102.dat 
83.3 
60.0 
32.6 
19.32 
103.dat 
189.4 
147.0 
76.0 
44.93 
104.dat 
151.6 
109.5 
55.7 
28.22 
105.dat 
180.6 
128.1 
73.6 
48.52 
106.dat 
245.6 
192.5 
98.9 
57.82 
107.dat 
771.6 
574.9 
572.6 
88.98 
108.dat 
103.2 
76.9 
24.0 
14.45 
109.dat 
237.2 
179.7 
112.1 
98.20 
201.dat 
67.1 
38.6 
38.3 
26.82 
202.dat 
131.0 
76.3 
28.4 
25.32 
203.dat 
279.7 
206.5 
321.3 
45.70 
205.dat 
72.5 
55.0 
29.5 
19.22 
207.dat 
129.7 
99.9 
93.9 
53.32 
208.dat 
361.2 
232.0 
199.2 
67.32 
209.da 
140.3 
103.3 
60.8 
45.22 
Table 6. Comparison between the filtered results of MPEKF, EKS, EKF and the proposed method in the presence of artificial and real noises in terms of MSEPWRD index


MSEPWRD $(\operatorname{mean} \mp S D)(m v)$ 

Noise type 
Method 
0 dB 
1dB 
3 dB 
5 dB 
Gaussian White Noise 
MPEKF 
1.2840±0.2250 
1.3290±0.2240 
1.4340±0.2310 
1.5520±0.2420 
EKS 
1.3580±0.1800 
1.4580±0.1960 
1.6780±0.2370 
1.9239±0.2880 

EKF 
1.6770±0.1830 
1.8240±0.2000 
2.1580±0.2420 
2.5520±0.2970 

Proposed Method 
0.3860±0.0470 
0.4584±0.0780 
0.5176±0.0597 
0.5547±0.3210 

Real Muscle Artifact 
MPEKF 
1.4680±0.1990 
1.5520±0.2000 
1.7470±0.2230 
1.9870±0.2550 
EKS 
2.9330±0.4550 
3.2470±0.5140 
3.9920±0.6560 
4.9180±0.8360 

EKF 
3.0570±0.4730 
3.3930±05340 
4.1880±0.6810 
5.1790±0.8660 

Proposed Method 
0.3932±0.0599 
0.4530±0.0499 
0.5877±0.0546 
0.6932±0.0385 
Figure 13. Comparative results in the terms of SNR_{output}
Figure 14. Comparative results in the terms of RMSE
In order to further assess the efficiency of the proposed technique, Figures 13 and 14 show the comparisons based on SNR_{output} and RMSE, for the proposed method and the new approaches labeled (FSSTHNLM and NLM) [6] applied on a synthetic ECG signal simulated using Opensource electrophysiological Toolbox (OSET) [52], distorted by many noises of various SNR_{input} levels. By a visual inspection of Figures 13 and 14 we can see that the proposed approach outperforms the other three techniques by achieving higher SNR_{output}and lower RMSE.
Following this analysis, the proposed method will be further tested against a modelbased method described by Hesar and Mohebbi [15], which presents an ECG signal denoising method labelled MPEKF. This method uses an automatic particle weighting strategy and an extended Kalman filter. The proposed method is compared to our method in terms of an ECG diagnostic distortion measure called the MultiScale Entropy based Weighted Distortion Measure [15, 53]. We use a similar method as that utilized by Hesar and Mohebbi [15] to calculate this measure. A weighted percentage root square difference (WPRD) is used as a metric, which is generated by comparing the original subband wavelet coefficient with the filtered signals. It uses weights that are the same as the corresponding subband’s multiscale entropies. Using this measure allows to achieve an accurate representation of the distortion of the filtered signal at all subbands [15, 53]. It was necessary to decompose both signals using wavelet filters up to L levels in order to calculate this metric. Both the sampling frequency and the nature of the signal dictate the number of levels. An accurate ECG trace will include a sharp QRS complex segment and the slow P and T waves, therefore, effective decomposition of an ECG should display an effective representation of the detail coefficients of the QRS complexes and the approximation coefficients of the P and T waves. As such, Daubechies 9/7 biorthogonal wavelet filter [54] was used for decomposition purposes. This led us to choose L=4 for sampling frequency of 128Hz [55].
The multiscale entropybased weighted PRD measure is defined as:
$M S E W P R D=w_{A_{L}} \times$$\left(\sqrt{\frac{\sum_{k=1}^{N_{A_L}}\left[A_{L}(k)\tilde{A}_{L}\right]^{2}}{\sum_{k=1}^{N_{A_L}}\left[A_{L}(k)\right]^{2}}} \times 100\right)$$+\sum_{j=1}^{L} w_{D_{j}} \times\left(\sqrt{\frac{\sum_{k=1}^{N_{D} j}\left[D_{j}(k)\tilde{D}_{j}(k)\right]^{2}}{\sum_{k=1}^{N_{D} j}\left[D_{j}(k)\right]^{2}}} \times 100\right)$ (15)
where: $w_{A_{L}}$ denotes the weight of the L^{th} approximation band; $W_{D j}$ denotes the weight of the j^{th} level details sub band; A_{L} and $\tilde{A}_{L}$ denote the L^{th} approximation band coefficients of the original and the denoised signals, respectively; and $D_{j}$ and $\widetilde{D}_{i}$ denote the j^{th} details band coefficients of the original and the denoised signals, respectively. The weights are: $w_{A_{L}}$ and $w_{D j}$.
The results of the comparison between our method and that of MPEKF, EKF and EKS, as detailed in Hesar and Mohebbi study [15], using a MSEWPRD with various input SNR levels, are shown in Table 6. These results were generated by determining the MSEWPRDs of 200 filtered ECG segments that were selected from the MITBIH database. However, the chosen segments used in our algorithm can be not the same as those segments used by Hesar and Mohebbi [15].
4.3 Discussion
Using a set of type2fuzzy IfThen rules, we constructed a type2 fuzzy adaptive filter that was able to adaptively change in order to reduce the criterion functions to their minimum values. The obtained results show that the proposed filter is highly effective in denoising the ECG signal; however, the efficiency of the method’s performance is determined by the number of fuzzy adaptive filter rules and the parameters of the optimization algorithm. The effectiveness of the investigated technique was compared to simulation results from both model and nonmodelbased methods using SNR, MSE and RMSE criteria, with the SNR being the power ratio between signal and noise. As such, a larger SNR indicates reduced background noise and, therefore, an increase signal denoising performance. Conversely, the MSE is a tracking accuracy measurement of the filtered signal compared to the original signal, therefore, the performance of the signal information retention is better when the MSE is smaller and the RMSE is used to calculate the variance between the real signal and its estimate. A smaller RMSE leads to a smaller difference. Figures 414 show that the proposed method is very effective when we are dealing with real noises, white Gaussian noise and their combination with different SNR_{input} levels. As such, it can be deduced that this method is both accurate and robust. Furthermore, by filtering the EMG artefact and comparing the outcomes with those of other benchmark methods, it can be seen that the proposed filter is statistically more effective than FSSTHNL, ADTFDWT and other methods described by Bing et al. [611]. Comparison results between the proposed method’s denoising performance using white Gaussian noise of 5dB SNR level with the ADTFDWT and other methods [712] are shown in Tables 24. These results show that the proposed method has improved results in terms of MSE, RMSE and SNR_{imp} when compared to ADTFDWT, ADWT and MABWT methods. Furthermore, the proposed approach provides an important solution for the problem of highdensity noise as shown with the results of the 5dB white Gaussian noise. Table 5 displays a deeper comparison of the filtered results under MSE performance using the proposed approach and the AFD, EEMD and EMD methods detail [913]. These results also show that the proposed approach is again, more effective. Moreover, the results displayed in Table 6 shows the comparison between the proposed method and MPEKF and EKF/EKS [15] using the MSEWPRD on two types of noise with four different input SNRs (0dB, 1dB, 3dB and 5dB). Notice that the MPEKF and EKF/EKS have higher MSEWPRDs for each noise type at all SNR_{input}levels compared to the proposed method indicating that our method is more effective than the MPEKF and EKF/EKS in preserving the diagnostic information and morphology of the ECG signals.
In this paper, a novel adaptive type2 fuzzy filter for ECG signal denoising was presented. The main blocks used in the filter were a type2fuzzy system and a TLBO optimization. TLBO algorithm was designed to updating a type2 fuzzy system parameters. The proposed filter was utilized to denoise ECG signals and was found to be highly effective at removing electrode motion noise, EMG noise and white Gaussian noise. In addition, a number of comparisons were made between the performances of the proposed approach with a number of other methods that have been presented in previously published studies. The results of these comparisons show that our filtering technique has better outcomes with a higher SNR_{output} and an improved SNR_{imp}, MSE, RMSE and MSEPWRD than the other model based and nonmodelbased methods detailed in the researches [6, 7, 9, 13, 15]. additionally, the proposed filter was able to preserve the morphology of the ECG signal and maintain the diagnostic performance.
The type2 fuzzy adaptive filter proposed in this paper may open up new horizons for efficient denoising of ECG signals. Therefore, as future work, we suggest further development of the proposed filter to (1) Minimize the processing time and (2) Increase the robustness:
(1) For the first point, it is known that the main problem with the type2 fuzzy systems is the type reduction process which is computationally complicated, especially when there are many MFs and the rule base is large, therefore as a perspective of this work we propose to reduce the computational burden, using a faster typereduction method. Several algorithms are being developed for this purpose, including the modified enhanced KarnikMendel (MEKM) method, enhanced KarnikMendel (EKM) method, the enhanced iterative algorithm with stop condition (EIASC) method and many other methods reported by Tai et al. [46].
(2) For the second point, we propose to use other optimization algorithms such as BBO, IWO, CMA. ES, SCE. UA, SFLA, PSO and even combine them in one algorithm in order to consider the advantage of every one and create a more robust optimization.
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