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Diagnoses of heart diseases can be done effectively on long term recordings of ECG signals that preserve the signals’ morphologies. In these cases, the volume of the ECG data produced by the monitoring systems grows significantly. To make the mobile healthcare possible, the need for efficient ECG signal compression algorithms to store and/or transmit the signal efficiently has been rising exponentially. Currently, ECG signal is acquired at Nyquist rate or higher, thus introducing redundancies between adjacent heartbeats due to its quasi-periodic structure. Existing compression methods remove these redundancies by achieving compression and facilitate transmission of the patient’s imperative information. Based on the fact that these signals can be approximated by a linear combination of a few coefficients taken from different basis, an alternative new compression scheme based on Compressive Sensing (CS) has been proposed. CS provides a new approach concerned with signal compression and recovery by exploiting the fact that ECG signal can be reconstructed by acquiring a relatively small number of samples in the “sparse” domains through well-developed optimization procedures. In this paper, a single-lead ECG compression method has been proposed based on improving the signal sparisty through the extraction of the signal significant features. The proposed method starts with a preprocessing stage that detects the peaks and periods of the Q, R and S waves of each beat. Then, the QRS-complex for each signal beat is estimated. The estimated QRS-complexes are subtracted from the original ECG signal and the resulting error signal is compressed using the CS technique. Throughout this process, DWT sparsifying dictionaries have been adopted. The performance of the proposed algorithm, in terms of the reconstructed signal quality and compression ratio, is evaluated by adopting DWT spatial domain basis applied to ECG records extracted from the MIT-BIH Arrhythmia Database. The results indicate that average compression ratio of 11:1 with PRD
_{1} = 1.2% are obtained. Moreover, the quality of the retrieved signal is guaranteed and the compression ratio achieved is an improvement over those obtained by previously reported algorithms. Simulation results suggest that CS should be considered as an acceptable methodology for ECG compression.

Heart disease is the leading cause of mortality in the world. The ageing population makes heart diseases and other cardiovascular diseases (CVD) an increasing heavy burden on the healthcare systems of developing countries. The electrocardiogram is widely used for the diagnoses of these diseases because it is a noninvasive way to establish clinical diagnosis of heart diseases. It reveals a lot of important clinical information about the heart, and it is considered as the gold standard for the diagnosis of cardiac arrhythmias. Long-term records have become commonly used to detect information from the heart signals; thus the volume of the ECG data produced by monitoring systems can be quite large over a long period of time. In these cases, the quantity of data grows significantly and compression is required for reducing the storage space and transmission times. Thus, ECG data compression is often needed for efficient storage and transmission for telemedicine applications. Recently, to make the mobile healthcare possible, the need for an efficient ECG signal compression algorithms has been raising exponentially [

In technical literature, many compression algorithms have shown some success in ECG compression; however, algorithms that produce better compression ratios and less loss of data in the reconstructed data are needed. These algorithms can be classified into two major groups: the lossless and the lossy algorithms. The traditional approach of compressing and reconstructing signals or images from measured data follows the well-known Shan- non sampling theorem, which states that the sampling rate must be twice the highest frequency. Similarly, the fundamental theorem of linear algebra suggests that the number of collected samples (measurements) of a discrete finite-dimensional signal should be at least as large as its length (its dimension) in order to ensure reconstruction. In recent years, CS theory [

Compressed sensing is a pioneering paradigm that enables to reconstruct sparse or compressible signals from a small number of linear projections. CS research currently advances in three major fronts: 1) the design of CS measurement matrices, 2) the development of new and efficient reconstruction techniques, and finally 3) the application of CS theory to novel problems and hardware implementations. The first two topics have already achieved a certain level of maturity, and many advanced methods have been developed. Currently, very high efficiency CS measurement systems have been developed with different characteristics (deterministic/non-de- terministic, adaptive/non-adaptive) that can be adopted in a variety of signal acquisition applications. On the other hand, reconstruction methods span a wide range of techniques that include Matching Pursuit/Greedy, Basis Pursuit/Linear Programming, Bayesian, Iterative Thresholding, among others [

The application of CS in ECG compression is still at its early stages, it has already led to important results [_{1}-minimization algorithm with a weighting scheme based on the standard deviation of the wavelet coefficients at different scales was derived. In addition, the weighting scheme also takes into consideration the fact that the approximation subband coefficients accumulate most of the signal energy.

In this paper, a single-lead compression method has been proposed. It is based on improving the signal sparisty through the extraction of the significant ECG signal features. The proposed method starts with a preprocessing stage that detects the peaks and periods of the Q, R and S waves of each beat. Then, the QRS-complex for each signal beat is estimated. The estimated QRS -complexes are subtracted from the original ECG signal and the resulting error signal is compressed using CS technique. Throughout this process DWT sparsifying dictionaries have been adopted. The performance of the proposed algorithm in terms of the amount of compression and the reconstructed signal quality is evaluated using records extracted from the MIT-BIH Arrhythmia Database. Simulation results validate the superior performance of the proposed algorithm compared to other published algorithms. The rest of the paper is organized as follows. Section 2 introduces the compressed sensing Framework. Section 3 details the compressed sensing of ECG signal. Controlling the ECG signal sparisty using DWT basis is explained in Section 4. The solutions of CS problem including greedy algorithms, l_{1}-minimization, and TV minimization are presented in Section 5. Section 6 introduces the methodology used for improving the ECG signal sparisty using QRS-complex estimation. Section 7 details the metrics adopted for measuring the performance of the proposed CS ECG signal compression algorithm. Sections 8 and 9 present the simulation results and the main conclusions respectively.

In a traditional ECG acquisition system, all samples of the original signal are acquired. Thus the number of signal samples can be in the order of millions. The acquisition process is followed by compression, which takes advantage of the redundancy (or the structure) in the signal to represent it in a domain where most of the signal coefficients can be discarded with little or no loss in quality. Hence, traditional acquisition systems first acquire a huge amount of data, a significant portion of which is immediately discarded. This creates important inefficiency in many practical applications. Compressive sensing addresses this inefficiency by effectively combining the acquisition and compression processes. Traditional decoding is replaced by recovery algorithms that exploit the underlying structure of the data [

CS has become a very active research area in recent years due to its interesting theoretical nature and its practical utility in a wide range of applications; especially in wireless telemonitoring of ECG signals. Compared to traditional data compression technologies, it consumes much less energy thereby extending sensor lifetime, making it attractive to wireless body-area networks. In the following we provide a brief overview of the basic principles of CS, since they will form the basis of the proposed ECG compression algorithms. The basic CS framework is an underdetermined inverse problem, which can be expressed as

where, in the context of data compression,

In fact, the measurement process is not adaptive, meaning that

a) Instead of point evaluations of the signal, the system takes M inner products of the signal with the basis vector

b) The number of measurements

If

a highly sparse representation [

After the acquisition process, an estimate of the signal is obtained by a reconstruction algorithm. A common and practical approach used to determine the sparse solution is to solve this problem as a convex optimization problem. The original work on CS employed regularization based on

where

The

The measurement matrix

That is, the matrix

A related condition, referred to as incoherence, requires that the rows of

with a lower bound given by ^{ }

We say that a dictionary is incoherent if

Direct construction of a measurement matrix

each of the

RIP and incoherence can be achieved with high probability simply by selecting

The matrix

The matrix

CS theory also proposes that rather than acquire the entire signal and then compress, it should be possible to capture only the useful information to begin with. The challenge then is how to recover the signal from what

would traditionally seem to be an incomplete set of measurements. The ECG signal

The question is now how we can actually recover

It has been proven that computing the sparsest solution directly generally requires prohibitive computations of exponential complexity [

Generally speaking, a greedy algorithm refers to any algorithm following the metaheuristic of choosing the best immediate or local optimum at each stage and expecting to find the global optimum at the end. It can find the global optimum for some optimization problems, but not for all [

In [

The solution to the above problem can be found with relative ease. There are methods that will find the solution to the BP problem but does it lead to a sparse solution? The answer in general is no but under the right conditions it can be guaranteed that BP will find a sparse solution or even the sparsest solution. This is because

In the broad area of compressive sensing,

The time-domain representation of the ECG signal has low signal sparisty. Thus, ECG signal is not the true signal itself but its representation under a certain basis is sparse or compressible. Various researchers have reported ECG signals to be sparse in other bases [

The wavelet transform describes a multi-resolution decomposition process in terms of expansion of a signal onto a set of wavelet basis functions. Wavelet transforms have become an attractive and efficient tool in many applications especially in coding and compression of signals because of multi-resolution and high-energy compaction properties. Wavelets allow both time and frequency analysis of signals simultaneously because of the fact that energy of wavelet is concentrated in time and still possesses the wave like characteristics. As a result wavelet representation provides a versatile mathematical tool to analyze ECG signals.

Discrete Wavelet Transformation (DWT) has its own excellent space frequency localization property. The key issues in DWT and inverse DWT are signal decomposition and reconstruction, respectively. The basic idea behind decomposition and reconstruction is low-pass and high-pass filtering with the use of down sampling and up sampling respectively. The result of wavelet decomposition is hierarchically organized decompositions. One can choose the level of decomposition

so that the output of the inverse DWT is identical to the input of the forward DWT. In this environment, ECG signal representation using a wide variety of wavelets, drawn from various families including symlets and Daubechies’ bases has been adopted. In this context, the transform coefficients are arranged in decreasing order of magnitude, and count the number of coefficients accounting for 99% of the signal energy (as parser representation requires less number). “Symlet” and “Daubechies” families generally offer more compact representation com- pared to Meyer wavelet as well as biorthogonal and reverse biorthogonal families. In particular, the sparsest re-

presentation is provided by the “sym4” (closely followed by the “db4”) wavelet basis for abroad class of ECG signals [

The correlation between the consecutive ECG beats can be exploited to improve the ECG signal sparisty. For this purpose, in this paper, the QRS-complex has been estimated based on the peaks and locations of Q, R and S waves. Then the estimated QRS-complex is subtracted from the original ECG signal and the resulting differential signal is manipulated using CS technique. The proposed compression scheme is presented in

1) The signal is decomposed into windows; each of length 1024 samples. This short window length is considered in order to generate an approximate real time transmission. At the same time, many heartbeats in the window are incorporated to recover the signal with fewer samples.

2) The signal is preprocessed to determine the amplitudes and locations of the Q, R and S peaks. These parameters are used to estimate the QRS-complexes.

3) From the estimated QRS-complexes and the locations of the R-peaks locations, the error signal with more sparisity compared to the original ECG signal is determined as the difference between the original ECG signal and the estimated QRS-complexes.

4) Fewer measurements are determined from the resulting error signal and the sensing matrix.

5) The amplitudes and locations of the Q, R and S peaks and the measurement matrix are quantized.

6) The resulting quantized values are packetized for possible storage and/or transmission.

In this section, the signal sparisty is controlled through the extraction of the significant ECG signal features. These features are extracted by estimating the QRS-complex for each signal beat. Then, the estimated QRS -complex is subtracted from the original ECG signal. After that, the resulting error signal is transformed into DWT domain and the resulting transformed coefficients are compressed using CS technique. A typical scalar ECG heartbeat is shown in

electro surgery equipment. The power spectrum of the ECG signal can provide useful information about the QRS -complex estimation.

The aim of the QRS -complex estimation is to produce typical QRS -complex waveform using parameters extracted from the original ECG signal [

where,

where,

To illustrate the QRS-complex estimation process, consider 1200 samples ECG signal extracted from record 103 of MIT-BIH arrhythmia database [

Values and durations | Period number | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Q-values | −0.0469 | −0.0537 | −0.0483 | −0.0464 |

R-values | 0.3027 | 0.3013 | 0.2808 | 0.2983 |

S-values | −0.0376 | −0.0415 | −0.0449 | 0.0493 |

QR-duration | 12 | 12 | 13 | 12 |

RS-duration | 10 | 8 | 8 | 5 |

A practical compression algorithm should not focus totally on compression itself. Many applications have requirements for the quality of the de-compressed signal. A robust compression algorithm should have the ability to maintain the quality of the de-compressed signal while achieving reasonable compression ratio. This is because only good quality signal reconstruction makes sense in reality. The evaluation of performance for testing ECG compression algorithms includes three components: compression efficiency, reconstruction error and com- putational complexity. All data compression algorithms minimizes data storage by reducing the redundancy wherever possible, thereby increasing the Compression Ratio (CR). Thus, the compression efficiency is measured by the CR. The compression ratio and the reconstruction error are usually dependent on each other. The computational complexity component is part of the practical implementation consideration. The following evaluation metrics were employed to determine the performance measures of the proposed method [

where

Quality of lossy compression schemes is usually determined by comparing the de-compressed data and the original data. If there are no differences at all, then the compression is lossless. Conventional measurements are based on mathematical distortions, such as percentage root mean square difference (PRD) and signal-to-noise ratio (SNR), etc. These measurements are not specific for ECG signals; they reflect the distortion of signal by statistics criteria. They are of general purpose, so the criteria may not be very accurate to describe the characteristics of a specific signal type.

For example, the ECG signal is for medical use, so what concerns medical specification most is the diagnostic feature, which is not covered in the general mathematical descriptions. Thus, in [

Measurement | Definition | Feature |
---|---|---|

PRD | Percentage root mean square difference | |

RMSE | Root mean square error | |

SNR | Signal to noise ratio | Often used for data transmission |

STD | Standard deviation | |

QS | Quality score | |

CC | Cross correlation | Evaluate the similarity between the original signal and its reconstruction |

MAXERR | Maximum error | |

PARE | Peak amplitude related error | |

WDD | Weighted diagnostic distortion | Utilization of diagnostics features |

where,

The CR and PRD have the close relationship in the lossy compression algorithms. In general, the CR goes higher with the higher lossy level, while the error rate goes up. The final goal of the proposed compression algorithm is to keep the PRD value smaller than that of the conventional methods while maintaining the similar CR. Thus, quality score defined as the ratio between CR and PRD (QS = CR/PRD) is sometimes used to quantify the overall performance of the compression algorithm, considering both the CR and the error rate. A high score represents a good compression performance. Another distortion metric is the root mean square error (RMSE). In data compression, we are interested in finding an optimal approximation for minimizing this metric as defined by the following formula:

Since the similarity between the reconstructed and original signal is crucial from the clinical point of view, the cross correlation (CC) is used to evaluate the similarity between the original signal and its reconstruction.

where

der to understand the local distortions between the original and the reconstructed signals, two metrics, the maximum error (MAXERR) and the peak amplitude related error (PARE), should be computed. The maximum error metric is defined as

and it shows how large the error is between every sample of the original and reconstructed signals. This metric should ideally be small if both signals are similar. The PARE is defined as

By plotting PARE, one will be able to understand the locations and magnitudes of the errors between the original and reconstructed signals.

Compressive sensing directly acquires a compressed signal representation without going through the intermediate stage of acquiring N samples, where N is the signal length. Since CS-based techniques are still in early

Range of | Quality |
---|---|

Very good | |

Good | |

Not good | |

Bad |

stages of research and development, specially the development of Analog to Information Conversion (AIC) hardware, signals that are used for experimentation are acquired in the traditional way. The CS measurements of these data are computed from the original ECG signal. Tests were conducted using 10-min long single-lead ECG signal extracted from records 100, 107, 115 and 117 in the MIT-BIH Arrhythmia database. Record 115 is included in the data set to evaluate the performance of the algorithm in the case of irregular heartbeats. The data are sampled with 360 Hz and each sample is represented with 11-bit resolution. The records are split into non- overlapping 1024 samples windows that are processed successively. Then the characteristic points of the ECG waveforms are detected using the procedure introduced in Section 6.2. It relies on the extraction of Q, R and S peaks and locations and the estimation of the QRS-complex. We begin by first detecting the R peaks, since they yield modulus maxima with highest amplitudes. This enables the segmentation of the original ECG record into individual beats. Then, multi scale wavelet decomposition is performed on the difference between the given ECG window, and the estimated QRS-complexes.

To evaluate the performance of the proposed method concerning the amount of data compression, the sparisity of the ECG signal in both the time-domain and the wavelet-domain are measured. As it has been mentioned before, the sparisity of an array x is defined as the number of non-zero entries in x. For this purpose two ECG signals, each of length 6 seconds, extracted from records 100 and 106 of the MIT-BIH database are considered. ^{th} level. Thresholding is performed such that 98% of the total coefficients’ energy is kept and small coefficients are thrown away.

To explore the effect of controlling the signal sparisity using other wavelet families, sparse representation is checked using bi-orthogonal (bior4.4) DWT filters and compared with that using Daubechies (db6) filters. In both cases the transformation is performed with four detailed levels and one approximation level. Another important process is also considered to improve the signal sparasity; that is by thresholding the wavelet coefficients in different decomposition levels according to the energy content in each subband. In this case, the wavelet coefficients have been thresholded to preserve 98%, 96%, 94% and 90% of the coefficients energy in the 1^{st}, 2^{nd}, 3^{rd}, and 4^{th} details subbands respectively. Moreover, the coefficients in the approximation subband are kept without threshold. After that, the resulting wavelet coefficients are mapped into significant and insignificant coefficients by ones and zeros respectively.

the original ECG signal and the estimated QRS-complex together with the mapping of the significant and insignificant coefficients for the two wavelet filters. The ECG signal considered here is of length 1200 samples extracted from record 103.

Next, the performance of the proposed compression method has been compared with traditional wavelet based ECG compression techniques.

Record number | Reference | CR | PRD_{1} % |
---|---|---|---|

Record 100 | The proposed method (signal differences) | 12.37 | 1.07 |

The proposed method (original ECG signal) | 9.06 | 1.62 | |

Polania et al., [ | 8.49 | 6.09 | |

Lu et al., [ | 8.42 | 6.19 | |

Record 107 | The proposed method (signal differences) | 9.79 | 3.12 |

The proposed method (original ECG signal) | 8.89 | 4.39 | |

Polania et al., [ | 8.19 | 6.05 | |

Lu et al., [ | 8.13 | 6.12 | |

Record 115 | The proposed method (signal differences) | 9.46 | 2.89 |

The proposed method (original ECG signal) | 8.71 | 3.80 | |

Polania et al., [ | 8.65 | 5.92 | |

Lu et al., [ | 8.73 | 5.84 | |

Record 117 | The proposed method (signal differences) | 9.39 | 1.24 |

The proposed method (original ECG signal) | 8.61 | 1.89 | |

Polania et al., [ | 7.23 | 2.57 | |

Lu et al., [ | 7.23 | 2.57 |

in compressing 1024 samples of the signal differences. This figure indicates that the proposed method achieved low reconstruction error. This corresponds to high quality recovered ECG signal and even outperforms the two other techniques [

This paper investigates CS approach as a revolutionary acquisition and processing theory that enables reconstruction of ECG signals from a set of non-adaptive measurements sampled at a much lower rate than required by the Nyquist-Shannon theorem. This results in both shorter acquisition times and reduced amounts of ECG data. At the core of the CS theory is the notion of signals sparseness. The information contained in ECG signals is represented more concisely in DWT transform domain and its performances in compressing ECG signals are evaluated. By acquiring a relatively small number of samples in the “sparse” domain, the ECG signal can be reconstructed with high accuracy through well-developed optimization procedures. Simulation results validate the superior performance of the proposed algorithm compared to other published algorithms. The performance of the proposed algorithm, in terms of the reconstructed signal quality and compression ratio, is evaluated by adopting DWT spatial domain basis applied to ECG records extracted from the MIT-BIH Arrhythmia Database. The results indicate that average compression ratio of 11:1 with

Mohammed M. Abo-Zahhad,Aziza I. Hussein,Abdelfatah M. Mohamed, (2015) Compression of ECG Signal Based on Compressive Sensing and the Extraction of Significant Features. International Journal of Communications, Network and System Sciences,08,97-117. doi: 10.4236/ijcns.2015.85013