Clifford Wavelet Entropy for Fetal ECG Extraction
Abstract
:1. Introduction and Motivation
2. FECG Extraction Brief Review
3. Two Wavelet/Multiwavelet Processors
3.1. The Haar–Faber–Schauder System
3.2. Clifford Wavelets and Multiwavelets
3.3. Brief Comparison between the Two Classes of Wavelets/Multiwavelets
4. Methodology
4.1. Wavelet/Multiwavelet Processing
4.2. Wavelet/Multiwavelet Entropy
4.3. The FECG Extraction
Algorithm 1 FECG extraction |
Input AbdECG Output FECG Begin [Detail1,App1] = Wavelet/multiwavelet decomposition(AbdECG); MECG = Wavelet/multiwavelet reconstruction(App1); [Detail2,App2] = Wavelet/multiwavelet decomposition(MECG); App3 = App1-App2; FECG = Wavelet/multiwavelet reconstruction(App3); Return FECG End |
4.4. Performance Measurements
5. Results
5.1. Data Collection and Bases
5.2. The Processing of DAISY Signals
5.3. The Processing of Cinc Challenge Database
6. Discussion
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
ECG | Electrocardiogram |
MECG | Mother electrocardiogram |
FECG | Fetal electrocardiogram |
WHO | World Health Organization |
AbdECG | Abdominal electrocardiogram |
EKG | Electrocardiography |
The probability at the level j | |
Se | Sensitivity |
PPV | Positive predictive value |
DAISY | Data base for the Identification of Systems |
CinC Challenge 2013 | Computing in Cardiology Challenge 2013 |
R-peaks | Real peaks |
STFT | Short time Fourier transform |
QRS | ventricular depolarization curve |
RR | Interval between two R-peaks |
FHR | Fetal heart rate |
QT | The sum of depolarization (QRS) and repolarization (T) |
SNR | Signal-to-noise ratio |
R-Wave | Ventricular depolarization |
HFSCH | Haar-Faber-Schauder |
TD | Truly diagnosed |
FP | False positive |
FN | False negative |
Approximation of the fetal electrocardiogram at the level J | |
Approximation of the mother electrocardiogram at the level J | |
Approximation of a signal S at the level j | |
Detail component of the fetal electrocardiogram at the level J | |
Detail component of the mother electrocardiogram at the level J | |
Detail component of a signal S at the level J | |
detail coefficient at the level j and the position k | |
Approximation coefficient at the level j and the position k | |
The energy of a signal S at the level j | |
The total energy of a signal S | |
The entropy of the signal | |
The entropy of the signal at the level J |
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Ch. No. | Total pks | Pks det in [105] | HFSch Multiwavelet pks det for FECG | pks det | pks det | pks det |
---|---|---|---|---|---|---|
2 | 22 | 22 | 22 | 22 | 22 | 22 |
3 | 21 | 21 | 21 | 21 | 21 | 21 |
4 | 21 | 22 | 21 | 21 | 21 | 21 |
Channel Number | Acc [105] | HFSch Multiwavelet Acc for FECG | Acc Using | Acc Using | Acc Using |
---|---|---|---|---|---|
2 | 100 | 100 | 100 | 100 | 100 |
3 | 100 | 100 | 100 | 100 | 100 |
4 | 86.95 | 100 | 100 | 100 | 100 |
Channel Number | Sens [105] | HFSch Multiwavelet Sens for FECG | Se Using | Se Using | Se Using |
---|---|---|---|---|---|
2 | 100 | 100 | 100 | 100 | 100 |
3 | 100 | 100 | 100 | 100 | 100 |
4 | 95.23 | 100 | 100 | 100 | 100 |
Sig. No. | Total pks | HFSch Multiwavelet pks det | pks det | pks det | pks det |
---|---|---|---|---|---|
a12 | 5 | 5 | 5 | 5 | 5 |
a29 | 5 | 5 | 5 | 5 | 5 |
a47 | 5 | 5 | 5 | 5 | 5 |
a59 | 5 | 5 | 5 | 5 | 5 |
Sig. No. | HFSch Multiwavelet Acc for FECG | Acc Using | Acc Using | Acc Using |
---|---|---|---|---|
a12 | 100 | 100 | 100 | 100 |
a29 | 100 | 100 | 100 | 100 |
a47 | 100 | 100 | 100 | 100 |
a59 | 100 | 100 | 100 | 100 |
Sig. No. | HFSch Multiwavelet Sens for FECG | Se Using | Se Using | Se Using |
---|---|---|---|---|
a12 | 100 | 100 | 100 | 100 |
a29 | 100 | 100 | 100 | 100 |
a47 | 100 | 100 | 100 | 100 |
a59 | 100 | 100 | 100 | 100 |
Database | Accuracy (%) | Se (%) | PPV (%) | |
---|---|---|---|---|
DAISY | 100 | 100 | 100 | 100 |
CinC | 100 | 100 | 100 | 100 |
Method | TA/[106] | EKS/[106] | SQA + FTM [101] | New Method |
---|---|---|---|---|
TP | - | - | 9573 | 10,088 |
FP | - | - | 639 | 24 |
FN | - | - | 596 | 81 |
Accuracy(%) | 88.57 | 98.96 | ||
Se (%) | 94.13 | 99.76 | ||
PPV (%) | 93.74 | 99.2 | ||
93.9 | 99.47 |
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Jallouli, M.; Arfaoui, S.; Ben Mabrouk, A.; Cattani, C. Clifford Wavelet Entropy for Fetal ECG Extraction. Entropy 2021, 23, 844. https://doi.org/10.3390/e23070844
Jallouli M, Arfaoui S, Ben Mabrouk A, Cattani C. Clifford Wavelet Entropy for Fetal ECG Extraction. Entropy. 2021; 23(7):844. https://doi.org/10.3390/e23070844
Chicago/Turabian StyleJallouli, Malika, Sabrine Arfaoui, Anouar Ben Mabrouk, and Carlo Cattani. 2021. "Clifford Wavelet Entropy for Fetal ECG Extraction" Entropy 23, no. 7: 844. https://doi.org/10.3390/e23070844