Reversible Watermarking for Electrocardiogram Protection
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data Description
2.2. General Reversible Watermarking Scheme
2.3. Reversible Contrast Mapping Difference Expansion
2.4. Integer Transform-Based Difference Expansion
2.5. Prediction Error Expansion
2.6. Lossless Compression-Based Watermarking
2.7. Prediction Algorithms
2.7.1. Neighbor-Based Prediction
2.7.2. Inter-Lead Prediction
2.7.3. Physical Signal Prediction
2.7.4. Compression Algorithms
2.8. Data and Metrics
2.8.1. Performance Metrics
2.8.2. Database
3. Results
3.1. Prediction Algorithm Comparison
3.2. Compression Algorithm Comparison
3.3. Performance Comparison
3.4. Final Outcomes
4. Conclusions
- If minimizing container distortion is critical, one should use PEE algorithms (with prediction based on adjacent samples or linear-dependence formulas) or LCBP (featuring Huffman coding and a low number of modified bit planes). This situation may arise, for instance, when a physician performs a preliminary ECG analysis before extracting the watermark and restoring the signal’s original appearance.
- If a high and predictable embedding capacity is more important, applying the RCM-DE method with a larger number of bits per pair of container samples or the ITB-DE algorithm is advisable. A significant embedding capacity might be required, for example, if error-correcting coding is implemented to ensure accurate container recovery even after any distortions or interference during file transmission or storage.
- If a compromise is needed, then LCBP with Huffman coding and a higher number of modified bit planes should be used. However, if simplicity of implementation and low computational complexity are prioritized, as well as the option to embed in all channels simultaneously, one can opt for ITB-DE or RCM-DE with a smaller number of bits per pair of container samples
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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# | Notation | Description |
---|---|---|
1 | Regression by file | Training a separate regression model for each ECG file, where one lead is used for prediction and the remaining leads are used for model training |
2 | Regression by collection of files | Training a common regression model for a collection of ECG files, where one lead is used for prediction and the remaining leads are used for model training |
3 | Physical prediction | Physical prediction using formulas from Section 2.7.3 |
4 | Neighbor averaging (1,0) or (0,1) | or |
5 | Neighbor averaging (2,0) or (0,2) | or |
6 | Neighbor averaging (1,1) | |
7 | Neighbor averaging (2,2) |
Notation | Embedding Method | Prediction Method | Compression Method | Parameters Used |
---|---|---|---|---|
lcb-huff-bp8 lcb-huff-bp7 lcb-huff-bp6 | LCB | - | Huffman | The number after the letters “bp” indicates the number of the lower of the two successive bit planes that were compressed and overwritten. Obviously, in practice, the bit planes have to be chosen based on the required balance between BPS and PSNR. |
itb | ITB | - | - | Method has no adjustable parameters |
rcm-bl1 rcm-bl2 rcm-bl3 rcm-bl4 | RCM | - | - | The number after the letters “bl” means the number of digital signal bits built into one pair of host signal samples. In this case, BPS is equal to half of this number |
lcbp-huff-neighchan-ps2 | LCBP | neighchan * | The suffix “ps2” means that two bit planes are used to record the compressed prediction errors. To minimize distortion, it is reasonable to use the least significant bit planes. | |
lcbp-huff-depchan-ps2 | depchan * | Huffman | ||
lcbp-huff-depchan-ps4 | depchan * | |||
pee-neighchan | PEE | neighchan * | These combinations differ in prediction methods. The neighbor prediction algorithm is used only here because it is not applicable to the prediction error compression method (LCBP). | |
pee-neigh | neigh * | - | ||
pee-depchan | depchan * | |||
lcbp-huff-neighchan-ps4 | LCBP | neighchan * | Huffman | The “ps4” suffix means that four bit planes are used to record the compressed prediction errors, which significantly increases the embedding volume compared to the two-plane option. |
lcbp-huff-depchan-ps4 | depchan * |
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Andreev, P.; Denisova, A.; Fedoseev, V. Reversible Watermarking for Electrocardiogram Protection. Sensors 2025, 25, 2185. https://doi.org/10.3390/s25072185
Andreev P, Denisova A, Fedoseev V. Reversible Watermarking for Electrocardiogram Protection. Sensors. 2025; 25(7):2185. https://doi.org/10.3390/s25072185
Chicago/Turabian StyleAndreev, Pavel, Anna Denisova, and Victor Fedoseev. 2025. "Reversible Watermarking for Electrocardiogram Protection" Sensors 25, no. 7: 2185. https://doi.org/10.3390/s25072185
APA StyleAndreev, P., Denisova, A., & Fedoseev, V. (2025). Reversible Watermarking for Electrocardiogram Protection. Sensors, 25(7), 2185. https://doi.org/10.3390/s25072185