Compressed sensing for ECG signal compression using DWT based sensing matrices

ABSTRACT In this article, we have investigated the 1-D discrete wavelet transform (DWT)-based measurement matrices for electrocardiogram (ECG) compression. Moreover, the current work examines the suitability of the diverse DWT matrices, namely Symlets, Battle, Coiflets, Vaidyanathan, and Beylkin wavelet families, for ECG compression. Furthermore, this article shows the comparative performance study of the proposed DWT matrices with conventional deterministic and random measurement matrices. Overall, the Battle1 wavelet-based measurement matrices demonstrate the enhanced performance against the db3, coif5, and sym6 based measurement matrices in terms of Percentage Root-Mean Squared Difference (PRD), Root Mean Square Error (RMSE), and Signal-to-Noise Ratio (SNR). Finally, it was seen that the proposed Battle1 matrix demonstrates the improved performance against the conventional measurement matrices such as the Karhunen–Loeve transform (KLT), Discrete Cosine Transform (DCT) matrix, and random Hadamard measurement matrix. Thus, the result shows the adequacy of DWT measurement matrices for the compression of ECG. GRAPHICAL ABSTRACT


Introduction
Compressed sensing (CS) is a novel signal compression scheme, wherein signal is compressed at the hour of acquisition.As a result, this practice shrinks the memory requisite of the system.The researchers Donoho [1], Baraniuk [2], and Candes et al. [3] pioneered the CS theory, which initiated the exploration in diverse field, e.g.Wireless Sensor Networks [4], Image Processing [5], and electrocardiogram (ECG) compression [6,7].
ECG is an investigative tool that is excercised to assess and record the electrical movement of the heart with an extremely delicate detail.The detail interpretation provides a diagnosis of a broad range of heart disorders.Therefore, the extensive records have turn into general to distinguish evidence from the heart signals.Since the memory dimension of data grows significantly, the data compression turns out to be necessary for dipping the storage space and transmission period.
Compared to conventional ECG compression algorithms, CS moves the computational load from encoder to the decoder and consequently proposes a simple hardware realization for the encoder [8,9]; it utilized the random Gaussian and Bernoulli matrix for compression of ECG signal.Furthermore, Parkale Yuvraj and Nalbalwar Sanjay [10] described comprehensive literature review on CS-based ECG compression.Recently, Parkale Yuvraj and Nalbalwar Sanjay [10,11] proposed various Daubechies wavelet matrices for compression of ECG.The result demonstrates that the db3 sensing matrices display the preeminent performance against the other Daubechies matrices.Hamza et al. [12] proposed the hardware platform based on CS and Internet on Things (IoT) for patients biometric.The author achieved up to 30% compression ratio (CR) and 98.88% of patient identification rate.Poian Giulia et al. [13] proposed the CS-based compression of ECG (specifically abdominal fetal) recording and obtained the real-time knowledge of fetal heart rate.Moreover, Poian Giulia et al. [14] estimated the heart rate using CS, which results in reduced power.Fei-Yun et al. [15] proposed CS-based framework for IoT and Wireless Sensor Network (WSN).
Moreover, this article presents complete work on proposed discrete wavelet transform (DWT)-based matrices for ECG compression.The different measurement matrices such as Symlets, Coiflets, Battle, Vaidyanathan, and Beylkin wavelet families were implemented.Furthermore, this study validates the comparative performance study of the diverse DWT matrices, namely Symlets, Coiflets, Battle, Vaidyanathan, and Beylkin wavelet families.Finally, this article demonstrates the comparative performance study of proposed DWT matrices with conventional deterministic and random matrices.The quality of the restored ECG signal is verified with measures like CR, percentage root mean squared difference (PRD), root mean square error (RMSE), signal-to-noise ratio (SNR), and signal reconstruction time.Finally, this article reveals the effective application of DWT matrices for compression of ECG signal.
The article is outlined as follows: Section 2 explains the procedure to design proposed measurement matrices; Section 3 demonstrates the results with discussions; and finally, Section 4 presents the conclusion.

Proposed DWT-based measurement matrices
In this work, we have proposed diverse DWT-based measurement matrices [11].The following steps show the procedure to construct these matrices:

Results and discussions
The simulation experiment is carried out on ECG signal from MIT-BIH Arrhythmia Database [16].The specification of the ECG signal utilized are: 100.dat, 1024 no. of samples are selected.The discrete cosine transform (DCT) is used as basis matrix.An ECG signal was recovered via L1-minimization [17].The results are analyzed using different performance measures such as RMSE, CR, SNR, and PRD (in %) and reconstruction time of the signal.PRD indicates the distinction between the original signal and the recovered signal and is given by Equation (1) as follows: wheere f ðnÞ is the original signal, f ðnÞ is the recovered signal, and N is the total length of the signal.
CR is obtained using Equation (2) as follows: where N is the length of speech signal and M is the number of measurements taken from sensing matrix.The range of CR varies between 0 and 100.However, for the simplicity, we have shown the CR in the range between 0 and 1 (×100) on X-axis, which is nothing but 0%-100% CR.RMSE is given by Equation (3) as follows: where f ðnÞ is the original signal, f ðnÞ is the recovered signal, and N is the total length of the signal.SNR is given by Equation (4) as follows: where f ðnÞ is the original signal, f ðnÞ is the recovered signal, and N is the total length of the signal.Besides, signal reconstruction time is computed to provide the amount of time required to recover the original signal using reconstruction algorithm.The amount of time required to construct the sensing matrix is also an important parameter and should be minimum.

Comparative study of Coiflets wavelet-measurement matrices
This part presents the relative performance study of the diverse Coiflets wavelet family-based measurement matrices (Please refer to Table 1 to Table 5 for details).
It is observed from Figure 1(a) that the coif5 wavelet matrix achieves lower values of PRD (%) against other Coiflets wavelet matrices.In addition, the coif4 wavelet matrix could be the subsequent best choice since it also shows lower values of PRD.
It is observed from Figure 1(b) that coif5 wavelet matrix attains the minimum RMSE against other Coiflets matrices.Furthermore, the coif4 wavelet matrix also shows lower RMSE.Figure 1(c) demonstrates that coif5 measurement matrix shows a higher SNR than other matrices.Furthermore, the coif4 wavelet matrix also attains higher values of SNR.
From Figure 1(d), it is noted that the coif1 wavelet matrix shows faster signal recovery compared to other Coiflets matrices.In addition, coif4 and coif5 wavelet matrices show a close performance through small reconstruction time.As a result, in general, the coif5 matrix displays an excellent performance, in view of the fact that it exhibits lower values of PRD and RMSE and attains high SNR with faster reconstruction time compared to other Coiflets matrices.Besides, the coif4 could be the succeeding best choice of matrix.

Comparative study of the Symlets wavelet-measurement matrices
This part validates the comparative performance study of the diverse Symlets wavelet family-based matrices (Please refer to Table 6 to Table 12 for details).
It is notable from Figure 2(a) that the sym6 wavelet matrix shows lower values of PRD (%) against other Symlet matrices.Furthermore, the sym10 matrix could be the next best choice because of its lower values of PRD.
It is observed from Figure 2(b) that sym6 matrix attains the minimum RMSE against other Symlets matrices.In addition, the sym10 matrix also achieves lower RMSE.
Furthermore, Figure 2(c) shows that sym6 matrix shows a high SNR against other Symlets matrices.In addition, the sym10 matrix also attains higher values of SNR.Thus, it is evident from Figure 2(a-d) that, on the whole, the sym6 matrix exhibits lower values of PRD and RMSE, attains high SNR with faster reconstruction time, and therefore showsbetter performance against other Symlet matrices.Furthermore, the sym10 could be the subsequent alternative of measurement matrix pursued by the sym9.13 to Table 17 for details).

Comparative study of the Battle, Vaidyanathan, and Beylkin measurement matrices
It is noted from Figure 3(b) that the Battle1 matrix attains the minimum RMSE against other Battle matrices.In addition, the Battle5 matrix also shows lower RMSE.Figure 3(c) shows that the Battle1 matrix exhibits high SNR against other Battle matrices.In addition, the Battle5 matrix also indicates higher values of SNR.From Figure 3(d), it is noted that the Battle5 matrix shows faster signal reconstruction against other Battle matrices.Also, it is followed by Battle1 matrices, showing quicker recovery of ECG signal.
Thus, it is notable that, in general, the Battle1 matrix shows lower values of PRD and RMSE and attains high SNR with faster reconstruction time, which consequently indicates better performance against Beylkin, Vaidyanathan, Battle3, and Battle5.
Moreover, the Battle5 could be the next choice because of its overall good performance.

Comparative study of the best of DWT-measurement matrices: Battle1, db3, coif5, and sym6, respectively
This part demonstrates the comparative performance study of the best of the proposed DWT matrices, i.e.Battle1, db3, coif5, and sym6 wavelet families.
Figure 4(a) indicates that the Battle1 matrix clearly surpasses the db3, coif5, and sym6 matrices in view of PRD.From Figure 4(b), it is noted that the Battle1 matrix shows minimum values of RMSE. Figure 4(c) shows that the Battle1 matrix exhibits higher SNR against the db3, coif5, and sym6 matrices.However, from Figure 4(d), it is observed that db3 matrix achieves smaller reconstruction time against other matrices.Besides, coif5 shows faster recovery of ECG signal pursued by sym6 and Battle1.
Thus, it can be evident from Figure 4(a-d) that, in general, the Battle1 matrix shows the enhanced performance against the db3, coif5, and sym6 matrices in views of PRD, RMSE, and SNR.Moreover, the db3 could be the subsequent finest choice of measurement matrix due to its smaller reconstruction time, PRD, RMSE, and SNR.

Comparative study of the best of the proposed Battle1 matrix with conventional matrices
This part demonstrates the comparative study of the proposed Battle1 matrix and conventional matrices, i.e.DCT matrix, random Hadamard matrix, and the Karhunen-Loeve transform (KLT) transform sensing matrix for ECG compression (Please refer to Table 18 to Table 20 for details).
It is seen from Figure 5(a) that the Battle1-based sensing matrix shows smaller values of PRD (%) against the conventional matrices like DCT matrix, random Hadamard matrix, and KLT transform sensing matrix.
It is observed from Figure 5(b) that the Battle1 matrix attains the minimum RMSE against the conventional matrices.
Furthermore, it is noted from Figure 5(c) that the Battle1 matrix exhibits high SNR against the conventional matrices.Finally, from Figure 5(d), it is observed that the Battle1 matrix achieves faster reconstruction performance and clearly outperforms conventional sensing matrices.
As a result, it is apparent from Figure 5(a-d) that the Battle1 matrix indicates the enhanced performance against the conventional matrices like DCT matrix, random Hadamard matrix, and KLT transform sensing matrix.
(a) Create the Quadrature Mirror Filter (QMF) filters using various DWT family, e.g.Coiflets, Symlets, and wavelet families.(b) Next, build the identity matrix of dimension N×N.(c) After that, perform 1-D forward DWT on the identity matrix (N×N), which will construct N×N wavelet matrix.(d) Finally, choose the requisite number of samples (m) from N×N wavelet matrices.(e) As a result, sensing matrix of dimension m×N is constructed and applied for the compression of ECG.

Figure 2 (
Figure 2(d)  shows that the sym9 matrix shows faster signal reconstruction against other Symlet matrices.In addition, sym6 matrices also achieve a faster reconstruction of ECG signal.Thus, it is evident from Figure2(a-d) that, on the whole, the sym6 matrix exhibits lower values of PRD and RMSE, attains high SNR with faster reconstruction time, and therefore showsbetter performance against other Symlet matrices.Furthermore, the sym10 could be the subsequent alternative of measurement matrix pursued by the sym9.

Figure 3 (
Figure3(a) indicates that the Battle1 matrix shows lower values of PRD (%) against other Battle matrices.In addition, the Battle5 matrix could be the subsequent best choice because of its lower values of PRD (Please refer to Table13to Table17for details).It is noted from Figure3(b) that the Battle1 matrix attains the minimum RMSE against other Battle matrices.In addition, the Battle5 matrix also shows lower RMSE.Figure3(c)shows that the Battle1 matrix exhibits high SNR against other Battle matrices.In addition, the Battle5 matrix also indicates higher values of SNR.

Figure 1 .
Figure 1.(a) PRD of Coiflets matrices for various CR.(b) RMSE of Coiflets matrices for various CR.(c) SNR of Coiflets matrices for various CR.(d) Reconstruction time of Coiflets matrices for various CR.

Figure 2 .
Figure 2. (a) PRD of Symlets matrices for various CR.(b) RMSE of Symlets matrices for various CR.(c) SNR of Symlets matrices for various CR.(d) Reconstruction time of Symlets matrices for various CR.

Figure 4 .
Figure 4. (a) PRD of the best of DWT matrices for various CR.(b) RMSE of the best of DWT matrices for various CR.(c) SNR (dB) of the best of DWT matrices for various CR.(d) Recovery time of the best of DWT matrices for various CR.

Figure 5 .
Figure 5. (a) A comparison of PRD of the best-proposed Battle1 with conventional matrices.(b) RMSE of the best-proposed Battle1 with conventional matrices.(c) A comparison of SNR of the best-proposed Battle1 with conventional matrices.(d) Recovery time of the best-proposed Battle1 with conventional matrices.

Table 1 .
Performance analysis of Coiflet1 DWT sensing matrix for ECG compression.

Table 2 .
Performance analysis of Coiflet2 DWT sensing matrix for ECG compression.

Table 3 .
Performance analysis of Coiflet3 DWT sensing matrix for ECG compression.

Table 4 .
Performance analysis of Coiflet4 DWT sensing matrix for ECG compression.

Table 5 .
Performance analysis of Coiflet5 DWT sensing matrix for ECG compression.

Table 6 .
Performance analysis of Symlet4 DWT sensing matrix for ECG compression.

Table 7 .
Performance analysis of Symlet5 DWT sensing matrix for ECG compression.

Table 9 .
Performance analysis of Symlet7 DWT sensing matrix for ECG compression.

Table 8 .
Performance analysis of Symlet6 DWT sensing matrix for ECG compression.

Table 10 .
Performance analysis of Symlet8 DWT sensing matrix for ECG compression.

Table 12 .
Performance analysis of Symlet10 DWT sensing matrix for ECG compression.

Table 11 .
Performance analysis of Symlet9 DWT sensing matrix for ECG compression.

Table 13 .
Performance analysis of Vaidyanathan DWT sensing matrix for ECG compression.

Table 14 .
Performance analysis of Battle1 DWT sensing matrix for ECG compression.

Table 15 .
Performance analysis of Battle3 DWT sensing matrix for ECG compression.

Table 16 .
Performance analysis of Battle5 DWT sensing matrix for ECG compression.

Table 17 .
Performance analysis of Beylkin DWT sensing matrix for ECG compression.

Table 18 .
Performance analysis of KLT DWT sensing matrix for ECG compression.

Table 19 .
Performance analysis of DCT sensing matrix for ECG compression.

Table 20 .
Performance analysis of random Circulant sensing matrix for ECG compression.