Complex study on compression of ECG signals using novel single-cycle fractal-based algorithm and SPIHT

1 Vol.:(0123456789) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports complex study on compression of ecG signals using novel single‑cycle fractal‑based algorithm and SpiHt Andrea nemcova1*, Martin Vitek1 & Marie novakova2 compression of ecG signal is essential especially in the area of signal transmission in telemedicine. there exist many compression algorithms which are described in various details, tested on various datasets and their performance is expressed by different ways. There is a lack of standardization in this area. this study points out these drawbacks and presents new compression algorithm which is properly described, tested and objectively compared with other authors. this study serves as an example how the standardization should look like. Single-cycle fractal-based (SCyF) compression algorithm is introduced and tested on 4 different databases—CSE database, MIT-BIH arrhythmia database, High-frequency signal and Brno University of Technology ECG quality database (BUT QDB). Scyf algorithm is always compared with well‑known algorithm based on wavelet transform and set partitioning in hierarchical trees in terms of efficiency (2 methods) and quality/distortion of the signal after compression (12 methods). Detail analysis of the results is provided. The results of SCyF compression algorithm reach up to avL = 0.4460 bps and PRDN = 2.8236%. The general development of information and communication technologies manifests in medicine as well and contributes to improvement of health care worldwide. It is very important nowadays when we are facing fast ageing of population1, increasing number of chronic diseases2 and thus higher press on healthcare providers. The most common cause of death worldwide are cardiovascular diseases (CVD)3. According to World Health Organization (WHO)3, CVD killed 17.9 million people in 2016 which represents 31% of worldwide deaths. Thus, the early detection and treatment of people with risk factors is important. For this purpose, telemedicine, especially its third largest area—patient remote monitoring4—is used. Within remote patient monitoring area, there belong electrocardiogram (ECG) recording. ECG is considered a noninvasive gold standard for identification of many health problems such as cardiac arrhythmias, bundle branch blocks, coronary artery disease, ventricular hypertrophy, heart failure, and many others5. For efficient transmission of data between patient and doctor or between two doctors or hospitals and medical centers, compression is necessary. The aim of compression is to reach maximum efficiency of data reduction without loss of diagnostic information. Transmission in telemedicine can be real-time (synchronous)—the patient is monitored by the doctor 24h a day (small delay may be accepted—e.g. for compression); or store-and-forward (asynchronous)—the data are stored and transmitted when the internet connection is accessible4,6. Thanks to the compression, the transmission is faster7, it has lower energy consumption (especially in case of wireless transmission)8,9, thus the device has prolonged battery life10, and transmitted data needs less storage capacity7,11. Lower energy consumption leads to miniaturization of mobile devices. The channel bandwidth is limited; thus the compression is necessary for high volume data6,12. Compression can be utilized for archiving of data or even big data13. To gain significant data reduction and minimize power consumption in ECG monitoring, lossy compression is preferred8 to lossless variant. Lossy compression is always connected with information loss. However, good compression algorithm should not lose or distort diagnostic information. As a matter of principle, compression is always compromise between size of the data and their quality14. Therefore, the assessment of ECG signal quality open 1Department of Biomedical Engineering, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 12, 616 00 Brno, Czech Republic. 2Department of Physiology, Faculty of Medicine, Masaryk University, Kamenice 753/5, 625 00 Brno, Czech Republic. *email: [email protected] 2 Vol:.(1234567890) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports/ after compression and the determination of compression efficiency should be an essential part of compression itself15. There exist many methods for ECG signal compression. These methods work with various successfulness and they are based on various principles. Many of them use intra-beat, inter-beat and/or inter-channel correlation of ECG signals12. Lossy methods are divided into one-dimensional (1D) and two-dimensional (2D) groups12. 1D methods split in three groups—direct compression methods, transform-domain methods and parameter extraction methods16. Some compression methods combine several basic principles and therefore cannot be included in one single group. Short survey on some recent compression methods follows. Compression based on wavelet transform (WT) is popular and efficient12. There belong e.g. method based on WT and Set Partitioning in Hierarchical Trees (SPIHT) algorithm originally published by Lu13 and modified by Hrubes17. Agulhari18 combined WT with threshold based selection of significant coefficients, their quantization and modified run-length encoding (RLE). Bilgin19 modified WT-based JPEG2000 algorithm to enable ECG data compression. Pandey20 recently introduced compression algorithm based on JPEG2000 and 2D discrete cosine transform. Jha21 started the compression procedure with filtering, continued with backward signal difference, WT, thresholding and quantization, and ended with RLE. Padhy22 used WT in combination with Singular Value Decomposition (SVD) and energy-based thresholding for multilead ECG compression. Bera23 used hybrid compression of ECG starting with SVM-based binary classifier of ECG beats to normal and abnormal. He continued with wavelet-based compression of abnormal beats and combined waveletand Principal Component Analysis (PCA)-based compression of normal beats. Fractal-based algorithms (e.g. Khalaj24, Lin11, Ibaida25) are considered highly efficient11. Fractal-based methods are used also for image26 and video27 compression. Nowadays, methods based on Compressed Sensing (CS) are very popular and perspective. Balestrieri28 introduced a variant of CS method suitable for efficient real-time ECG acquisition in the Internet of Medical Things area. Adamo29 combined CS with dictionary based method using k-LiMapS algorithm to obtain sparse vector and Huffman coder to encode sparse coefficients. Singh30 combined PCA, CS, quantization and Huffman encoding for multilead ECG compression. Nasimi31 introduced selective compression method which is based on assessing the similarity between consecutive segments (beats). If the segments are similar, compression is provided using CS and if the segments are not similar it points to some pathology and thus the segment is preserved and transmitted without compression. Other authors combined Empirical Mode Decomposition with encoding of extracted parameters (Khaldi32), extraction of extrema points (Zhao33), or WT (Wang34, Jha35). Following methods are based on various principles. Elgendi9 used for compression simple scheme—combination of low-pass filter and downsampling by factor K. For ECG compression, Ma36 introduced combination of Adaptive Fourier Decomposition (AFD) and symbol substitution. Fira37 developed compression method where local minima and maxima are extracted. These points are called skeleton. Skeleton is further optimized by discarding and adding appropriate samples using thresholding. To enhance the efficiency of this compression algorithm, delta and Lempel–Ziv–Welch (LZW) coding is applied. Lee14 introduced compression method based on peak-to-peak segmentation, Discrete Cosine Transform (DCT), window filtering, and Huffman coding. Tan38 recently introduced Blaschke unwinding adaptive Fourier decomposition method. Boom of deep learning manifests in compression as well—Wang39 introduced promising deep learning based Spindle Convolutional Auto-Encoder (SCAE) method. More complex reviews on compression methods can be found in studies by Jalaleddine40 (1990), Manikandan12 (2014), Kale16 (2016), Rajankar41 (2018), Tiwari42 (2019). Summary of quality assessment of ECG signals after compression are in reviews by Dandapat43 (2015) and Nemcova15 (2018). There is a lack of standards for evaluation of ECG signal quality after compression44. Compression algorithms should be tested on the whole standard ECG databases including all signals and all leads22,30. However, the usual practice is that authors test their algorithms on selected and/or shortened signals/leads11,13,17–19,24,29,33,34,36,37 from standard or even non-standard databases. In some studies, the tested database25,32 or detail information such as number of tested signals25 or number and type of leads9,14,21,34 of the signals on which the algorithms were tested are missing. Some studies tested their algorithm on one signal only32. In the growing Internet of Things (IoT) era, there is growing need to focus on ECGs sensed by up-to-date devices under free-living conditions. Such data were sensed by us and used in this study; the data are described in Data section as a Brno University of Technology ECG quality database (BUT QDB). In many studies, the authors use Percentage Root Mean Square Difference (PRD) to evaluate quality of the ECG signal after compression and reconstruction. However, many of them do not subtract the offset and/or DC component and thus the results are artificially better and objective comparison with other authors is irrelevant. This topic was discussed in our previous study15 where the details and recommendations for quality assessment of ECG signal after compression and reconstruction can be found. The first aim of this study is to point out drawbacks, gaps, and mistakes present in the area of compression to make compression results objective, reliable and to enable objective comparison between authors. The second aim of the study is to introduce new Single-Cycle Fractal-Based (SCyF) compression method and to compare it with WT + SPIHT based method. Description of the SCyF algorithm as well as the testing scheme and results prevent general compression drawbacks described in this study and serves as an example how the standardization should look like. Methods Data. In this study, four various databases of ECG signals are used. They differ in recording device, number of signals and leads, sampling frequency, duration, bit resolution and signal content (noise, pathologies, artifacts). A. Common Standards for Quantitative Electrocardiography (CSE) database45,46 is a standard database which contains 125 signals, each including 15 leads (12 standard and 3 Frank leads). The duration of each signal is 10s, sampling frequency is 500Hz, and bit resolution is 16 bits per sample (bps). Signals no. 67 and 70 3 Vol.:(0123456789) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports/ contain pacemaker peaks. Signals no. 86–97 have a duration of 8s, thus the rest 2 padded seconds were cut. Three Frank leads of signals no. 60, 68, 76, 84, 92, 100, 108, and 124 which are not ECG signals (include constant signal) were excluded. It is not effective to compress constant signals by compression algorithm which is designed for ECG signals. It will be much more efficient and faster to use RLE of constant segments before the compression of ECG itself. B. Massachusetts Institute of Technology–Beth Israel Hospital (MIT-BIH) arrhythmia database (MITADB)47,48 is the most cited standard database46. It consists of 48 half-hour ECG signals, each including 2 leads. The sampling frequency is 360Hz, bit resolution 11 bps. C. High-frequency signal was recorded by the International Clinical Research Center of St. Anne’s University Hospital Brno in cooperation with the Institute of Scientific Instruments of the Czech Academy of Sciences49,50. In this study, one signal containing 19 leads is used. The sampling frequency is 5000Hz, bit resolution is 24 bps, and duration is ca. 21min. The signal is further called UPT signal. This signal is not publicly available. D. Our own experimental database of ECG signals (BUT QDB)47,51 was recorded using Bittium Faros 180. In this study, three single-lead signals from this database are used. The duration of each signal is minimally 24h, the sampling frequency is 1000Hz, bit resolution is 16 bps. The signals were sensed from 3 different people under free-living conditions. The signals were manually annotated by 3 ECG experts in terms of the quality of the signal. The first class contains segments suitable for full-wave analysis; the second class includes segments suitable for reliable QRS detection and heart rate variability (HRV) analysis; the third-class segments are not recommended for any reliable analysis. The data are publicly available on Physionet. compression algorithm based on Wt and SpiHt. As a well-known, advanced, efficient, and popular compression algorithm, WT based method in combination with SPIHT is used. This method is considered as a gold standard for the purpose of this study. SPIHT is the progressive iterative compression algorithm. The output bit flow can be controlled by the user in terms of Average Value Length (avL) or Normalized Percentage Root Mean Square Difference (PRDN). SPIHT uses the Temporal Orientation Tree, where one wavelet coefficient in lower frequency bands corresponds to two wavelet coefficients (offspring) in higher frequency bands or has no offspring. Individual coefficients or the whole trees are coded according to their significance (threshold is used). The detail principle is difficult to explain; thus, it is only briefly sketched in here, details and example can be found in13. At first, WT (discrete time WT using wavelet filter bank bior4.4 and decomposition level 6)17 is performed in frame of ECG (length 1024 samples)17 and Temporal Orientation Tree is created. Then the first threshold is calculated and List of Insignificant Sets (LIS), List of Insignificant Points (LIP), and List of Significat Points (LSP) are initialized. After that sorting pass in LIP, sorting pass in LIS, and refinement pass are performed. Then the threshold is reduced, and the process repeats until the criterium (desired effectivity or quality) is met. In this study, algorithm described and implemented by Hrubes17 and on 1D signals originally introduced by Lu13 is used. Moreover, this algorithm is based on different principle than newly introduced SCyF method, which supports objectivity of this study. Scyf compression method. As the basis for the SCyF compression algorithm, the fractal-based one by Ibaida25 was chosen. The reason is great compression efficiency (Compression Factor (CF) = 42) and low compression error (PRD < 1%). During implementation of this method in Matlab, a few mistakes were found. The equations for calculation of scale coefficient and Fractal Root Mean Square (FRMS) are inaccurate in the original article25. Correct equations are in the article by Al-Shammary52. Ibaida25 used not-normalized equation for calculation of the PRD and did not mention the DC component and the offset subtraction. It means that the PRD error is artificially lower than the normalized PRD (PRDN) as proved by Nemcova15. Ibaida25 also did not mention which signal(s) from MITADB they used to reach the results mentioned above. SCyF compression method is based on Ibaida’s25 method with correct equations by Al-Shammary52. SCyF algorithm utilizes self-similarity of ECG signal. The principle is shown in Fig.1. At first, as a preprocessing step, the DC component (including offset) is subtracted from the original signal. Domain. The algorithm utilizes the quasiperiodicity of the ECG signal. Single cycle of the currently compressed ECG is picked as a domain. Single cycle is selected manually as the most representative cycle of the beginning of currently compressed ECG signal. It starts with the beginning of P wave and ends just before the beginning of the following P wave. Domain is divided into overlapping blocks called domain blocks (DB) of size called block size (BS). Overlapping is controlled by predefined jump step (JS), which is the distance between two adjacent DB. BS should be smaller (usually) or equal to the length of the domain. compression. ECG signal is divided into non-overlapping blocks called range blocks (RB) which are of equal length BS. Then for each RB the most similar DB is searched. As a similarity metric, FRMS52 is used. To enhance the similarity between RB and DB, DB shape can be optimized using fractal coefficients and affine transform. In this study, two fractal coefficients are used: shift (offset) and scale25,52; and either affine transform (swapping each two adjacent samples) can be used or the block is not transformed (none transform). In our study, only one affine transform and none transform are used instead of four used by Ibaida25. The reasons are: a) the selected affine transform or none transform are the most common according to the testing we provided; b) it enhances the efficiency of compression because one type of affine transform and information about no transform can be expressed by one bit; c) it shortens the time of compression. If the most similar transformed DB still does not meet predefined FRMS limit, RBs are divided into two halves (each of length of ½ BS) and each one is 4 Vol:.(1234567890) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports/ compressed separately. This idea was published by Khalaj24. It means that for each smaller RB the most similar DB of the same length (½ BS) is searched. Transformations are done in the same manner as on larger block. If the criterion is still not met, RB can be further divided. Maximum number of divisions is preset by the user and it also depends on the initial setting of BS. Ideally, BS is set to 2n, where n is integer and BS is smaller or equal to the length of the domain. The higher the number of divisions, the higher quality of the signal after compression and reconstruction but also higher computational demand necessary for compression and lower effectivity. If the FRMS is not below the limit after the last division, the algorithm saves the best transform settings (with the lowest FRMS) for the shortest ranges (for the last possible division). Divided and already transformed RBs are drawn in Fig.2 in green and dark blue color (two colors are used for better differentiation between adjacent blocks). The process of adjusting RB to be as much similar as possible to DB using fractal coefficients and affine transform is shown in Fig.2 in blue and yellow borders. The domain is highlighted in red. Reconstruction. The reconstruction is provided in reverse manner using all outputs in single iteration unlike the original method25 which uses 4 iterations. Thus, the reconstruction is faster and less computational demand. On the DB with stored index, the transform coefficients are applied and the reconstruction RB is created. RBs are then joined into one signal. Inputs of the SCyF algorithm are: ECG signal, BS, JS, FRMS limit, maximum number of block divisions and the beginning and the end of the single cycle of ECG. Outputs of the compression part of the algorithm are: domain, index of DB, shift coefficient, scale coefficient, type of transform (affine/none) and number of divisions (all in binary form). Optional modifications. The domain can be computed as a downsampled version of the original signal. It means that two adjacent samples are averaged. Thus, the domain occupies less storage space, and the signal is smoother. Smoother signal means less noise but usually also distortion of high-frequency details (such as lowering of R peak). The signal can be smoothed after compression and reconstruction to improve the connections between reconstructed RBs. For smoothing, the best method seems to be local regression using weighted linear least squares and a 2nd degree polynomial model. In some signals, smoothing improves the quality of the signal after compression and reconstruction and in some signals the quality is worsen. Figure1. Block diagram of SCyF compression method. Blue color is for compression and red one for reconstruction part of the method. Blocks that are new against Ibaida’s25 work, are saturated and optional ones have thick solid border. Dashed line borders blocks that create compressed file. 5 Vol.:(0123456789) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports/ Especially shorter signals can be extended on both sides (e.g. 10 samples on each side) to reach higher fidelity. It is balanced by higher computational demand, duration of compression and the amount of stored data. SCyF algorithm is further compared with the original algorithm by Ibaida25. Because the original version is not publicly available, we implemented the algorithm on our own. The algorithm was implemented as much similarly as described in the article. However, we avoided mistakes in FRMS and scale coefficient. BS and JS were set according to the authors to 35 and 10, respectively. Ibaida25 recommended 4 iterations for reconstruction process. Our results are shown for 4 iterations (which seems to be not enough) and 10 iterations (which is more than the authors recommended but the signal has better quality). Evaluation of compression efficiency and quality of the reconstructed signal. Compression efficiency was calculated as CF and avL. CF is in some studies called Compression Ratio (CR), but we follow recommendations and definitions from our previous study15. Average Value Length15 (avL) is calculated as a ratio between bit size of the output stream (compressed ECG) and length of the original signal in samples. The unit is bits per sample (bps). avL informs about the number of bits that are needed on average to compress one sample of the signal. For assessment of ECG signal quality after compression, altogether 12 methods we previously recommended15,53 were used. These methods are namely: percentage similarity using standard deviation of normal-to-normal intervals (PSim SDNN), quality score (QS), signal to noise ratio (SNR), mean square error (MSE), PRDN1, maximum amplitude error (MAX), standard error (STDERR), wavelet-energy based diagnostic distortion using stationary wavelet transform (WEDD SWT), spectra difference (Spectrum), similarity— positions with tolerance of 10 (SiP10), similarity—positions and amplitude with tolerance of 10 (SiPA10), and dynamic time warping—percentage match of fiducial points (DTW pmfp2). Details about these methods can be found in15,53. the testing scheme. According to the aims of the study, the step by step testing scheme was created. The order was set according to the database which was used for testing. In the first two points, all four databases were used. In points 3–5, 6–7, 8–10, 11–12, the CSE database, MITADB, UPT signal and BUT QDB were used, respectively. The “Results and Discussion” chapter is divided accordingly. Figure2. Transforming domain block to be as much similar as possible to the range block. Upper picture shows original ECG signal (black), domain (red), and compressed and reconstructed range blocks (dark blue and green; two adjacent RBs have different color). Two lower images show transformation process of domain block to be as much similar to the range block as possible. Transformation consists of affine/none transform (in this case none transform), application of scale coefficient (changes the size and ratio of the block) and application of shift coefficient (changes the offset of the block). 6 Vol:.(1234567890) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports/ 1. Comparison of two compression algorithms based on different principles: WT + SPIHT and SCyF compression algorithms (all 4 databases). 2. Testing two variants of SCyF algorithm—with and without smoothing (all 4 databases). 3. Comparison of compression of 15 leads (CSE database). 4. Testing the compression algorithms on short (10s) signals (CSE database). 5. Comparison of the results on the whole database and the database without two signals with pacemaker peaks (CSE database). 6. Comparison of the results with other authors (MITADB). 7. Comparison of the original fractal-based algorithm (with minimum changes) with the SCyF one (MITADB). 8. Testing the algorithms on high-frequency high-resolution signals (UPT signal). 9. Comparison of compression of 19 leads of high-frequency signal (UPT signal). 10. Testing how sampling frequency influences effectivity and quality of compression (UPT signal). 11. Testing the algorithms on free-living data (BUT QDB). 12. Comparison of effectivity and quality of compression in terms of the quality of the original signal (BUT QDB). At first, the signals are compressed using SCyF algorithm. The settings of the SCyF algorithm are shown in Table1. “Divisions” in the Table1 stands for maximum number of block divisions. The SPIHT algorithm was controlled in terms of avL which was set individually for each signal according to the output avL of SCyF method. To test how the sampling frequency influences effectivity and quality of compression, it was necessary to downsample the high-frequency UPT signal. Downsampling was performed 5 times to create signals with sampling frequencies of 2500Hz, 1000Hz, 500Hz, 250Hz, and 125Hz. Results and discussion Comparison of two compression algorithms based on different principles (all 4 data‑ bases). The numerical results in terms of compression efficiency and quality of the signal after compression and reconstruction are shown in Table2. The rows of the Table2 show compression algorithms (SPIHT means WT + SPIHT, SCyF and SCyF S are single-cycle fractal-based methods without and with smoothing, respectively, P means dataset with signals no. 67 and 70 in case of the CSE database). The rows are grouped according to the database on which the compression algorithms were tested. The columns show sampling frequency (fs), original bit resolution of the signal (bit res), avL and CF as measures of effectivity of the compression and 12 methods named in “Methods” section as measures of the quality or distortion. The green and yellow colors highlight whether the results are better for WT + SPIHT or SCyF method, respectively. It is evident that the SPIHT algorithm in most cases beats the SCyF algorithm for majority of quality indexes. However, there are some cases when the SCyF algorithm is better; these are: WEDD SWT metric, sometimes PSim SDNN and DTW pmfp2 and highly downsampled signal (fs = 125Hz). The avL and CF are slightly better for SCyF algorithm because the SPIHT algorithm was set according to it. Testing of two variants of SCyF algorithm—with and without smoothing (all 4 databases). The difference between SCyF algorithm without and with smoothing is not easily describable (as can be seen in Table2). Sometimes smoothing improves the quality of the signal and in some cases, algorithm without smoothing reaches better results. Therefore, this block remains as an optional modification of the algorithm and it is not a core part of it. Comparison of compression of 15 leads (CSE database). Figure3 shows the results of testing WT + SPIHT and SCyF algorithms on 15 leads of signals from the CSE database including signals no. 67 and 70 with pacemaker peaks. From Fig.3, it is evident that various leads of CSE database are compressed with different effectivity and quality. In Fig.3, there are only 3 selected methods of quality assessment and one method for efficiency assessment (avL); results of all 12 quality assessment methods are included in Supplementary Fig.S1 online. Both algorithms have similar trend of the results of effectivity and quality, although the principles of both algorithms are different. It means that compression performance is probably dependent on the content of the signal much more than on the compression algorithm itself (relatively, because the absolute difference between both algorithms can be seen). To make a general statement, testing more compression algorithms based on various principles is necessary. It may be one of the challenging parts of compression general knowledge. Table 1. Settings of the SCyF algorithm for each database. Database BS JS FRMS limit Divisions CSE 256 1 12 2 MITADB 128 1 5 3 UPT signal 256 1 12 2 BUT QDB 256 1 12 2 7 Vol.:(0123456789) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports/ Testing of the compression algorithms on short (10 s) signals (CSE database). In case of SCyF algorithm, the domain (single cycle of ECG) is stored as a part of compressed data and thus, it occupies relatively more memory capacity for short signals. It is also shown in Table2 that it is quite big difference between quality of signals from CSE database compressed using SPIHT and SCyF algorithms; the difference is probably caused by the short length of signals. For other databases, the difference is not that big. comparison of the results on the whole database and the database without two signals with pacemaker peaks (CSE database). In Table2, there are results for the whole CSE database (SCyF P and SPIHT P) and for comparison the results for the CSE database without signals 67 and 70 which include pacemaker peaks. In case of WT + SPIHT algorithm, the results are very similar for both datasets. On the other hand, in case of SCyF algorithm, the results are better when the signals 67 and 70 are excluded. The SCyF algorithm is not tuned for pacemaker signals with high frequencies, because in this variant it uses downsampling of the Table 2. Results of testing WT + SPIHT and ScyF compression algorithms on four different databases. P stands for the whole CSE database including pacemaker signals no. 67 and 70; S stands for smoothing. For MITADB, there are also results for original fractal-based algorithm implemented according to Ibaida23. These results are named Fract 10 and Fract 4, where the number stands for iterations needed for reconstruction. fs bit res avL CF PRDN1 MSE SNR1 STDERR MAX WEDD SWT PSim SDNN QS Spectrum SiP10 SiPA10 DTW pmfp2 CSE SPIHT P 500 16 1.0488 15.2562 4.7094 100.7594 28.3278 9.5374 48.2217 2.0797 97.5140 4.9308 2362419.0601 79.8973 29.4847 31.6940 SPIHT 500 16 1.0421 15.3539 4.7342 96.5846 28.2858 9.4010 47.0056 2.0736 98.0108 4.9420 2323408.5419 80.0623 29.7253 31.7482 SCyF P 500 16 1.0379 15.4164 8.1892 2123.6845 23.2802 21.6813 294.0787 2.9501 93.3572 2.7005 5258342.6076 74.8889 25.1353 26.9794 SCyF 500 16 1.0313 15.5138 7.5759 513.2921 23.5432 17.3078 223.3170 2.8186 94.7236 2.7403 4208485.3014 75.1204 25.3356 26.8837 SCyF S P 500 16 1.0379 15.4164 8.9291 4069.0730 22.8338 24.7600 344.4997 3.0319 93.0708 2.5929 5485071.7917 74.7542 25.0521 24.4068 SCyF S 500 16 1.0313 15.5138 7.9520 539.6155 23.1480 18.0763 229.0043 2.8410 94.4501 2.6325 4209783.9523 74.9685 25.2502 24.5082 MITADB SPIHT 360 11 1.0669 10.3106 6.3618 10.4023 25.3866 3.1903 38.9690 3.6660 98.2545 4.8620 1120205785.2599 71.1236 44.1272 30.2637 SCyF 360 11 1.0564 10.4131 7.1453 14.3400 24.0498 3.7264 69.6907 4.0194 97.4486 4.1559 1489034684.7454 65.5188 40.1796 32.2328 SCyF S 360 11 1.0564 10.4131 8.2330 20.1852 22.8223 4.3598 88.8274 4.1631 97.4802 3.6740 1478663266.7037 64.2345 38.0227 26.6084 Fract 10 360 11 1.3801 7.9704 17.6934 169.6435 16.4466 10.3373 570.8439 4.7123 96.2083 0.8554 4236258651.2527 61.9129 34.2773 17.9204 Fract 4 360 11 1.3801 7.9704 127.2374 17341.8980 1.7358 78.9780 8205.0611 40.2822 49.9718 0.1744 32565669237.8462 29.7975 11.4004 7.2404 BUTQDB SPIHT 1000 16 0.6959 22.9934 3.7047 449.9587 28.6577 20.4499 1791.8478 1.4881 99.9212 7.4847 11283354268739.3000 91.7806 50.6814 19.9373 SCyF 1000 16 0.6902 23.1806 5.9563 1379.6115 24.7491 34.0263 13813.2789 1.3394 99.8190 4.1442 20868883674399.1000 91.7446 46.2574 13.9173 SCyF S 1000 16 0.6902 23.1806 5.5894 1217.1330 25.2882 31.9523 14588.0656 1.3393 99.8048 4.3985 17229168487443.3000 91.7646 47.2625 14.1848 UPT SPIHT 5000 24 0.4504 53.2870 2.5988 77.2330 32.0444 8.5369 451.3934 0.6920 99.3738 23.0201 96158687670.3142 85.0308 79.2412 9.8066 SCyF 5000 24 0.4460 53.8075 2.8236 93.2677 31.3145 9.3343 699.5404 0.3487 99.5309 21.4683 118529830987.1510 82.6698 76.7006 8.9188 SCyF S 5000 24 0.4460 53.8075 2.7503 90.7084 31.5387 9.1441 778.2325 0.3487 99.4974 22.1113 110002611864.5470 83.4722 77.7566 9.2095 SPIHT 2500 24 0.5987 40.0862 3.1036 119.2674 30.4747 10.3169 291.2469 0.8869 99.3865 13.9966 41324146423.4832 81.5350 68.3870 14.3253 SCyF 2500 24 0.5942 40.3924 3.3270 139.3763 29.8303 11.1507 527.2850 0.4415 99.3735 13.0615 50723988166.3500 79.2959 64.1574 12.2383 SCyF S 2500 24 0.5942 40.3924 3.1557 126.5007 30.2918 10.5946 598.9050 0.4414 99.4071 13.7901 44994376858.1866 79.3436 65.1222 12.4471 SPIHT 1000 24 0.6968 34.4434 4.6177 292.6732 26.9926 15.7420 281.7973 1.3908 98.8438 7.9454 16679573847.0365 72.6602 44.0859 20.1145 SCyF 1000 24 0.6943 34.5679 5.3018 383.5786 25.6810 18.2689 477.8694 0.7723 98.7592 6.7762 20695196461.1235 67.5897 33.3061 16.5001 SCyF S 1000 24 0.6943 34.5679 5.1425 362.7726 25.9592 17.7194 638.4387 0.7729 98.7603 7.0042 18457498254.6048 67.7110 34.5002 15.8130 SPIHT 500 24 0.7387 32.4900 5.9744 501.6842 24.7253 20.5605 372.1225 2.0926 98.8132 5.7512 8096097942.0519 64.7696 24.2165 23.1012 SCyF 500 24 0.7337 32.7099 6.7569 641.0941 23.5649 23.5070 510.7945 1.3308 97.8098 5.0234 9373469489.2277 60.4468 17.4576 22.3098 SCyF S 500 24 0.7337 32.7099 7.1341 727.2670 23.0795 24.9425 607.0700 1.3399 97.7702 4.7459 9385623998.8872 60.4915 18.1222 19.1879 SPIHT 250 24 0.8103 29.6199 7.1481 714.7341 23.0646 24.8124 379.3518 3.2047 98.2643 4.2902 3480582488.0287 54.2397 7.8171 25.0421 SCyF 250 24 0.8004 29.9867 7.8367 872.3778 22.2707 27.4574 443.3152 2.0075 98.8663 3.9817 3929512403.7593 55.9642 9.0586 30.5852 SCyF S 250 24 0.8004 29.9867 9.9339 1504.9765 20.2571 35.5130 493.3531 2.1374 98.9450 3.1919 4810233155.3846 54.2050 8.3343 24.2959 SPIHT 125 24 0.8546 28.0831 10.1763 1481.2064 20.2103 35.4013 430.1090 6.5613 94.4320 3.0561 1705243470.1223 36.5118 1.0547 27.8588 SCyF 125 24 0.8435 28.4532 9.0255 1189.0763 21.1350 31.7842 488.5253 3.4901 97.3340 3.4145 1631374713.8616 51.8930 3.9826 46.5572 SCyF S 125 24 0.8435 28.4532 17.4115 5093.2861 16.0522 62.2599 651.2890 4.4976 92.4006 2.0890 2890830047.2584 36.8279 2.1481 29.4498 8 Vol:.(1234567890) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports/ domain. The results are concordant with this. This example also shows that selecting of only some signals from the database may lead to distortion of the results and may hide the shortcomings of the algorithm. Comparison of the results with other authors (MITADB). As the MITADB is the most used ECG database, results of our new SCyF algorithm tested on this database seem to be comparable with other published algorithms. Results of various compression algorithms based on various principles are included in Supplementary TableS1 online. The Supplementary TableS1 online is divided into 3 parts—3 groups of compression algorithms. In the first group, there are algorithms tested properly on the whole MITADB (48 signals, 2 leads) with subtracted DC component. The second group includes algorithms properly tested (DC subtraction and/or use of PRDN) on the part of the MITADB. In the third group, there are algorithms which (a) testing conditions (such as concrete signals, leads, subtraction of DC) are not properly described in the articles; (b) are tested on any other database excluding MITADB; c) are not correctly tested. The third group is clearly the major one. Figure3. Results of testing WT + SPIHT and SCyF algorithms on the 15 leads of signals from the CSE database (x axis) including signals 67 and 70. Blue color represents the results of WT + SPIHT algorithm, green and yellow colors represent results of SCyF method without and with smoothing, respectively. For clarity, only 4 representative graphs were selected; complete results are in Supplementary Fig.S1 online. 9 Vol.:(0123456789) Scientific RepoRtS | (2020) 10:15801 | https://doi.org/10.1038/s41598-020-72656-6 www.nature.com/scientificreports/ There is a lack of standardization in the area of testing and evaluating the performance of compression algorithms. To compare various algorithms developed by various authors, it is necessary to use standard databases as well as standard process of evaluation efficiency and quality of the compression. Alternatively, it is necessary to use the same data without any difference in baseline as the compared author used54. Nowadays, the evaluation of efficiency as well as evaluation of the quality of the signal after compression and reconstruction diverge. Also, the selection of the databases or even some signals from one database is non-objective. The most cited database is MITADB; it is also most commonly used for testing in the area of compression. However, many authors select only some signals, one lead or shorten the signals. Tiwari42 pointed out this problem and we have to agree. This way of testing is not suitable for any comparison. It is possible that authors select the signals according to the results they reached or fine-tuned their algorithms only on the selected signals. This means that not all of the pathologies and ECG human to human variability are considered. Rakshit55 wrote that in most studies, the upper channel (usually lead II) of MITADB is used. He also said that the upper channel is the more quality one. In some studies, the type of database or the details about testing signals are not available at all. The Supplementary TableS1 online shows that most compression algorithms are tested on a part of MITADB. The second problem is inconsistency in subtracting the DC component and offset which can cause different results of quality of the signal after compression and reconstruction. The third problem is inconsistency in methods used for ECG signal quality assessment. Many authors use PRD method which is not correct in case of offset and/or DC presence. This problem is discussed in detail in our previous study15. There may be the same problem with other quality assessment methods because some of them are less or more sensitive to DC and offset presence/subtraction (as discussed in15). Thus, the proper comparison of our algorithm with previously published algorithms except for WT + SPIHT tested by us is not possible. It can be done at a rough guess only. In the first group of methods in the Supplementary TableS1 online, there are only our newly published algorithm and algorithm based on WT and SPIHT tested by us. These two algorithms were compared within this study. Only these two algorithms were properly tested. Further, it seems that SCyF method is comparable with methods from the second group at a rough guess. In the third group, only methods highlighted in red are theoretically comparable with SCyF method. In practical way, it is quite difficult, because these methods (excluding DIF + WT + THRQ + RLE) reach high compression ratio balanced with high PRDN. Our method was not tested in this range, because we believe that the distortion will be highly visible even by eye and thus, the compression is pointless. The best results are reached using DIF + WT + THRQ + RLE method, where the CR is 44 and PRDN = 5.87% (the authors declare that all 48 signals were used, but their length and lead are not specified). It is wort mentioning that there exist MIT-BIH Compression Test database47,56 which includes various signals (clean, noisy, physiological, pathological) dedicated for compression, but the database is used only sporadically57. In case of lossless methods only once according to Tiwari42. The development of (not only) compression algorithms will be faster if standard databases are used properly and codes are publicly available for future development and comparison. Similar idea was recently published by Tiwari42 as well. One of the limitations of our study is the fact, that not all compression methods ever published are considered. Nevertheless, from the Supplementary TableS1 online it is evident the trend that none of the authors test their algorithms properly; it means testing the algorithm on the whole standard database (without any shortening or selecting of signals or leads), using proper quality assessment algorithms and/or subtracting the offset and/or DC and describing all the details about testing in the published articles. comparison of the original fractal‑based algorithm with the proposed Scyf algorithm (MITADB). Results for original fractal-based algorithm by Ibaida25 implemented by us with as little changes as possible are in Table2. This algorithm was tested on MITADB using two versions of reconstruction. In the first one (Fract 10), for reconstruction of the signal, 10 iterations were used. In case of the second one (Fract 4), only 4 iterations were used as recommended in the original article. The original algorithm fails when compressing signals no. 234 from the first lead and 102 and 220 from the second lead. In the resulting signal, impulses of 105 × higher magnitude than the signal appear. For example, for the second lead of signal 220, PRDN = 390.377% for 10-iteration reconstruction. Thus, these signals are not included in the mean results for Fract 10 and Fract 4 in Table2 because such a huge error will distort normal results. Using all the signals, the testing would be objective in terms of using the whole database but will distort the mean results of the majority of the signals. Anyway, the original method implemented by us provides much worse results (in terms of both efficiency and quality after compression) than new SCyF method and WT + SPIHT method. Current version of SCyF algorithm needs manual demarcation of representative single cycle of ECG, which is one of the limitations of the algorithm. This fact has no influence on the results of this method for the purpose of this article and the block of automatized demarcation of single ECG cycle can be added using any QRS detector or delineation algorithm. Testing of the algorithms on high-frequency high-resolution signals (UPT signal). The results of SCyF and SPIHT algorithms tested on high-frequency (5000Hz) high-resolution (24 bps) signals are shown in Table2. These signals enable the most efficient compression from tested signals for both compression algorithms; avL = 0.4460 bps and CF ≐ 54 for SCyF algorithm without smoothing. Also, the distortion is the lowest from the Table2. It means, there exists high redundancy in signals with high sampling frequency and resolution. On the other hand, in this study the influence of compression on high-frequency components of the ECG was not taken into account, which may be considered as the limitation of the study. To compare SCyF with SPIHT,