Compressive sensing based the multi-channel ECG reconstruction in wireless body sensor networks

doi:10.1016/j.bspc.2020.102047

Biomedical Signal Processing and Control

Volume 61, August 2020, 102047

https://doi.org/10.1016/j.bspc.2020.102047 Get rights and content

Highlights

•
A CS-based method with low-rank constraint is proposed for effective data acquisition and signal reconstruction in the energy-constrained WBSN.
•
An optimization formula consisting of two constraints is defined; the sparsity constraint and the low-rank constraint.
•
A robust and efficient ADMM-based method is developed to efficiently reconstruct the multichannel ECG signals.
•
Numerical experiments verify that the proposed algorithm achieves superior performance as compared to the latest CS-based recovery methods.

Abstract

Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-channel Electrocardiogram (MECG) signals. In this paper, we have used the Kronecker sparsifying bases to exploit the spatio-temporal correlations of the MECG signals for improving the compression of the signals transmitted by the sensors. Furthermore, a compressed sensing-based method with low-rank constraint is proposed for effective data acquisition and signal reconstruction in the energy-constrained wireless body sensor networks. More specifically, in the proposed algorithm, an optimization formula consisting of two constraints is defined. The sparsity constraint is presented through the minimization of the $l_{1}$ norm and the low-rank constraint is specified through the minimization of the nuclear norm. Afterward, a robust and efficient alternating direction method of multipliers (ADMM) based method is developed for the reconstruction of the MECG signals that solves the resulting optimization problem more effectively. Numerical experiments verify that the proposed algorithm achieves greater reconstruction accuracy with the smaller number of required transmissions, lower computational complexity, and smaller reconstruction errors, as compared to the latest CS-based recovery methods.

Introduction

The ambulatory monitoring of the bioelectric signals has received considerable attention by different scholars in recent years. Such monitoring procedures offer several advantages, such as constant patient observation, increased patient mobility, and decreased healthcare costs [1]. However, there are difficulties with these devices, such as wearable device size, energy consumption, and energy costs. The energy consumption of these devices has long been considered the most important challenge. Moreover, in ambulatory environments, there is a strong need for the proper management of a large volume of bioelectric signals, generated by the health monitoring devices/sensors [1]. Hence, the lossy compression methods have captured considerable attention. These devices are mainly used to reduce the transmitted information, while ensuring maximum signal quality. In this regard, compressive sensing (CS) is one of the most popular methods of compression, which is built-in and well suited to the energy-efficient wearable and mobile devices/sensors; this method is used to reduce the data to be stored and the data required by the micro-controllers and the analog-digital converters. Therefore [2], suggested that it is possible to utilize compressive sensing to reduce energy consumption. It helped to decrease the hardware complexity of the wireless body sensor network enabled ECG monitors as well.

The authors of [3] have explored several practical designs of ECG signal tele-monitoring CS based on the wireless body sensor networks. In this regard, various encoder structures and different measurement matrix combinations were incorporated into these designs. In [4], a block sparsity structure was used to reveal the temporal correlations among the ECG signals; the ECG signals were also reconstructed using the block sparse Bayesian learning (BSBL) method. The proposed algorithm in [5] exploits the temporal correlation of the ECG signals using the wavelet representation structures to improve the performance of the proposed algorithm at the signal compression and reconstruction rates.

There are some other CS-based methods that extract the spatial correlation of the ECG signals too. For example, in [6], the authors jointly reformulated the ECG signal reconstruction equation by replacing the traditional l₁ norm with l₁/l₂ norm to obtain the satisfactory compression rate and a small reconstruction error. In [[7], [8], [9]], by assigning more weights to the clinically important features of the ECG signals, the other parts were given lower priorities, and therefore the signal compression rate and the energy consumption of the sensors were improved.

In our study, we found that, in addition to the inter-channel temporal dependencies of the information within a signal, the information in other channels contains spatial dependencies too. As Fig. 1 shows, since the information in the channels is recorded through the sensors installed on different parts of the patient body, the MECG signals show temporal correlations (inter-channel) and spatial correlations (intra-channel) by nature. Therefore, to improve the performance of the CS-based MECG signals compression algorithms, the spatio-temporal correlations must be taken into account. Recently, [10] used spatio-temporal sparse Bayesian learning-based reconstruction method to simultaneously extract the spatio-temporal correlations of the MECG signals, in which the signals are inserted into a data window and then jointly reconstructed.

Inspired by the promising results of the aforementioned methods, in this paper, we propose a sliding data window framework, in which the sensors acquire the ECG spatio-temporal signals sequentially, and a fusion center progressively reconstructs the current ECG signals from a sequence of periodically delivered compressive sensing measurements.

The main contributions of this paper are summarized as follows:

•
Since the extraction of both spatial and temporal dependencies substantially influences the accuracy of the recovered ECG signals, the proposed algorithm utilizes Kronecker sparsifying bases to efficiently improve the recovery performance at a low number of measurements. Low measurement requirement reduces the on-chip computations and can eventually lead to reduction in the volume of the data to be transmitted over power hungry wireless links. Therefore, the proposed method is able to achieve a good quality of signal reconstruction with reduced computational load at the encoder, which may lead to significant power savings in CS-based MECG tele-monitoring applications.
•
The proposed reconstruction algorithm utilizes a defined optimization formula that offers the sparsity constraint (by minimizing the l₁ norm) and the low-rank constraint (by minimizing the nuclear norm). In order to solve the formulated cost optimization problem, an alternating direction multiplier method (ADMM) based algorithm is efficiently developed. Since the ADMM algorithm is guaranteed to have fast global convergence from any initialization in just a few iterations [from letter references], the proposed algorithm can quickly converge. Therefore, the presented algorithm can meet the real-time requirements of the wearable ECG tele-monitoring.
•
In this paper, a novel and extensive comparative analysis is presented, in which the proposed CS-based algorithm offers superior performance in terms of signal reconstruction quality to all the latest major CS-based methods in the literature. Crucially, the proposed algorithm provides higher levels of precision and less complexity by acquiring less information from the sensors.

The rest of this paper is organized as follows: in Section 2, the latest related works are reviewed in brief. In Section 3, the system model is presented in detail. Then, the spatio-temporal correlation of the MECG signals is simultaneously extracted in Section 4. In Section 5, a fast and efficient analytical solution to the minimization problem is developed. Summary of the proposed algorithm and the experimental results are presented in Sections 6 and 7. Section 8 concludes the paper.

Section snippets

Related works

In wireless body sensor networks, sensors have limited computation capability and power resources without assistance of any established infrastructures; many studies in the literature validate the potential of CS for energy-efficient ECG compression [[11], [12], [13], [14], [15]]. In this sense, the proposed algorithm in [9] assigns not only more weights to important parts of the ECG signals but also low priorities to other parts. Subsequently, by integrating an iterative weighted CS-based

System model

As Fig. 2 shows, a single-fusion center single-hop wireless body area network (WBAN) in which $N$ sensors are capable of reading, sensing and transmitting the ECG signals in a sliding data window with a constant length ( $L$ ). Let $F (τ) \in R^{N \times L}$ represent the data window size $L \geq 1$ at time instant $τ$ . This window, which includes $L$ sequential data readings of $N$ sensors at time instants ${τ - L + 1, \dots ., τ}$ , is expressed as $F (τ) = [\begin{matrix} f_{1} (τ - L + 1) & \begin{matrix} \dots & f_{1} (τ - 1) \end{matrix} & f_{1} (τ) \\ \begin{matrix} ⋮ & \begin{matrix} ⋱ & ⋮ \end{matrix} \end{matrix} & ⋮ & ⋮ \\ f_{N} (τ - L + 1) & \begin{matrix} \dots & f_{N} (τ - 1) \end{matrix} & f_{N} (τ) \end{matrix}]$ where $f_{n} (τ)$ denotes the data reading by

Simultaneous extraction of the spatio-temporal correlations

In this section, we develop a mathematical way to find out, (a) a suitable dictionary ( $Ω$ ) to extract the spatio-temporal correlation of the sensor signals in a data window with the length of L, and (b) how to utilize the resultant dictionary in the optimization problem in (7). Referring to the sensors data model specified in (1), the data window $F (τ)$ at time instants ${τ - L + 1, \dots ., τ}$ with a window size of $L \geq 1$ consists of spatio-temporal correlations. Hence, (1) can be expressed as follows. $F (τ) = [\begin{matrix} \underline{f} (τ - L + \end{matrix}]$

Development of a fast and efficient analytical solution for the optimization problem

Although the constraints applied to (12) are useful in several ways, the convex optimization problem with non-smooth regularization of different norms causes excessive computational complexity. Therefore, because ADMM is suitable for large-scale and convex optimization problems [34], in this paper, we provide an ADMM style implementation to efficiently solve the optimization problem in (12). For this purpose, the optimization problem is converted into the following equivalent constrained-form

Summary of the proposed algorithm

The proposed compressed sensing data acquisition method with joint signal ensemble recovery based on sparsity norm $l_{1}$ and nuclear norm optimizations is summarized in Algorithm 1. At each time slot $τ \geq 1$ , the fusion center periodically gathers the compressed sensing measurements in a data window by acquiring the reading from a set of the sensor nodes. Then, the sparsity constraint (i.e., by minimizing the $l_{1}$ norm) and low-rank constraint (i.e., by minimizing the nuclear norm) are incorporated in a

Experimental results and discussion

In this section, the multi-channel electrocardiogram (MECG) signals in the MIT-BIH [36] and PTB [37] databases are used to assess the proposed algorithms. The MIT-BIT database contains 2-channel signals with the sampling frequency $f_{s} = 360 H z$ and resolution of 11 bits. The PTB database includes 15-channel signals collected from 290 patients at the sampling frequency $f_{s} = 1 k H z$ and resolution rate of 16 bits. In the simulation results, all of the multi-channel signals in these two databases were

Conclusion and future works

This paper considers a compressed sensing acquisition and the joint reconstruction of spatio-temporal correlated multi-channel Electrocardiogram (MECG) signals in the wireless body sensor networks. A successive framework based on moving data window is developed to efficiently recover a portion of sensors signals within the window from periodically delivered compressed sensing measurements via exploiting the spatio-temporal dependencies among MECG signals by utilizing Kronecker sparsifying

CRediT authorship contribution statement

Javad Afshar Jahanshahi: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation. Habibollah Danyali: Visualization, Software, Validation, Writing - review & editing. Mohammad Sadegh Helfroush: Visualization, Software, Validation, Writing - review & editing.

Acknowledgment

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. Moreover, the authors thank the authors of all the involved papers [9,10,16,17,20,21,24,25,43,44] for providing their results and part of their source codes for improving our comparison results.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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In [15], authors proposed a new block space model with raised cosine kernel that provided CR of 10 and variable PRD between 2.5 and 5.5. Using CS in [16], the authors proposed Kronecker sparsifying bases that resulted in CR and PRD of 8 and 5, respectively. A hybrid encoding was proposed by P. Bera et al. [17] to normal and abnormal beats that resulted in CR of 21.25 and variable PRD between 2.45 and 9.54.
The multilead electrocardiogram (MECG) signal provides much more detailed information related to the cardiac activity of the human heart than single channel signal. Long-term recording of MECG data needs a huge amount of storage space, thus data compression becomes truly necessary.
In this work, a beat-wise MECG data compression is proposed that is based on adaptive Fourier decomposition (AFD). To reduce dimensionality, an ECG beat was treated as a multiagent, upon which principal component (PC) analysis was used in non-linear space. A new Möbius transform was introduced along with AFD, to convert the dominant PCs in complex domain using Nevanlinna factorization. An offline trained multilayer perceptron neural network was also employed to provide optimal decomposition levels in AFD to limit the PRD within 3%.
The entire work was tested on 546 ptbdb MECG records available in Physionet which yielded an average compression ratio and a percent root mean squared difference (PRD) of 48.21 and 3.88, respectively. Regardless of annotation type, PRD variance within each lead was found to be nearly uniform.
Within a single beat, the agent-based compression established a hybrid compression technique, almost completely preserving critical clinical aspects.
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In order to monitor the patient’s health, the medical signals are regularly sampled at equal intervals and sent to the coordinator [30]. In fact, each biosensor periodically senses the body and samples the corresponding signal such as ECG, EEG, EMG, SpO2, and etc, encodes the sample as a binary string, and sends its packet to the coordinator [32]. Table 3 and Fig. 5 show an example for medical signal of each biosensor used in/on the body.
We study the problems of energy consumption and interference for Wireless Body Area Networks (WBANs). Our model relies on a real medical monitoring, where the patient’s vital signals such as EEG, ECG, and EMG are regularly sampled at equal intervals to send to a medical center. For this purpose, an efficient scheme called Energy- and Interference-aware Routing and Scheduling (EIRS) is presented, which is based on three phases. EIRS first uses an energy-aware scheme to develop a data aggregation routing tree for each WBAN. In phase 2, it finds a set of appropriate channels for developed tree in terms of interference. Phase 3 employs a greedy algorithm to assign interfering transmissions to distinct time slots, while scheduling non-interfering transmissions at the same time slot. To realize energy efficient and reliable communication, EIRS jointly employs Euclidean distance, residual energy, channel diversity, multi-radio technology, and spatial reuse. As another advantage, the proposed scheme reduces inter-WBAN interference as well as intra-WBAN interference. Numerical results confirm the superiority of EIRS in terms of network lifetime, consumption of radio resources, interference, and delay.
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Fortunately, as an attractive technology, compressed sensing (CS) theory provides efficient compression and accurate reconstruction of the signal by random down-sampling, which improves the real-time performance of crack signal analysis in SHM of rails [2,3]. In recent years, CS theory has been used mainly for tasks such as processing audio signals [4], image [5–10], video [11–13], etc. There are various methods for CS, such as Basis Pursuit (BP) algorithms [14], Matching Pursuit (MP) algorithms [15], gradient projection algorithm [16], Alternating Direction Method of Multipliers (ADMM) [17], etc.
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The second is DCT based DOST [31] where average values over the dataset are reported. The third algorithm is based on Kronecker sparsifying bases for compressed sensing [32]. Table 3 presents a summary of their results compared to ARMP-PKS.
Electrocardiogram (ECG) signal compression is a vital signal processing area, especially with the growing usage of wireless body sensor networks (WBSN). ECG signals need to be compressed for efficient storage or transmission. Traditional compression methods acquire the ECG signal and perform compression in the sensors, where most of the computations are performed. Therefore, sensors have significant complexity and power consumption. On the other hand, compressed sensing transfers the complexity from the encoder to the decoder, thus allowing for cheap, low-power sensors, with longer lifetime. In this paper, we propose the adaptive reduced-set matching pursuit with partially known support (ARMP-PKS) compressed sensing reconstruction algorithm. ARMP-PKS performs sparse signal reconstruction at very high accuracy and speed. Furthermore, it takes advantage of prior support information, which further improves the performance. Our proposed algorithm achieves 35 dB reconstruction SNR at 50% compression and about 22.5 dB at 25%, significantly faster than related algorithms.
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The rationale of CS delivery of lossy compression for the data is to provide a minimal loss in its fidelity and a maximum compression ratio [6]. The compression and reconstruction applications of CS in the electroencephalogram (EEG) and ECG have been successful in sampling and encoding algorithms [7,8], e.g., a sampling method in [9] requires 43% less energy consumption than traditional Nyquist sampling rate. Iterative hard thresholding and compressive sampling matching pursuit methods are applied for ECG reconstruction in [10], by exploiting the support among the wavelet coefficients of ECG.
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The simulation experiments of one- and two- dimensional signals, using a new matrix show a superior in evaluating recovered signals with parameters and the visual effect of the restored images.

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Compressive sensing based the multi-channel ECG reconstruction in wireless body sensor networks

Highlights

Abstract

Introduction

Section snippets

Related works

System model

Simultaneous extraction of the spatio-temporal correlations

Development of a fast and efficient analytical solution for the optimization problem

Summary of the proposed algorithm

Experimental results and discussion

Conclusion and future works

CRediT authorship contribution statement

Acknowledgment

Declaration of Competing Interest

Comput. Electr. Eng.

Biomed. Signal Process. Control

Plaza Signal Proc. Contr.

Signal Process.

Compressed sensing for bioelectric signals: a review

IEEE J. Biomed. Health Inform.

Compressed sensing for real-time energy-efficient ECG compression on wireless body sensor nodes

IEEE Trans. Biomed. Eng.

Compressed sensing system considerations for ECG and EMG wireless biosensors

IEEE Trans. Biomed. Circuits Syst.

Compressed sensing for energy-efficient wireless telemonitoring of noninvasive fetal ECG via block sparse bayesian learning

IEEE Trans. Biomed. Eng.

Compressed sensing of ECG signal for wireless system with new fast iterative method

Comput. Methods Programs Biomed.

Power-efficient joint compressed sensing of multi-lead ECG signals

2014 IEEE International Conference on Acoustics, speech and Signal Processing (ICASSP)

On ECG reconstruction using weighted-compressive sensing

Healthc. Technol. Lett.

Block sparsity-based joint compressed sensing recovery of multi-channel ECG signals

Healthc. Technol. Lett.

Compressed sensing for real-time energy efficient ECG compression on wireless body sensor nodes

IEEE Trans. Biomed. Eng.

Compression of ECG signal based on compressive sensing and the extraction of significant features

Int. J. Commun. Netw. Syst. Sci.

Energy-efficient ECG compression on wireless biosensors via minimal coherence sensing and weighted l1 minimization reconstruction

IEEE J. Biomed. Health Inform.

Energy-aware bio-signal compressed sensing reconstruction on the WBSN-gateway

IEEE Trans. Emerg. Top. Comput.

Developing residential wireless sensor networks for ECG healthcare monitoring

IEEE Trans. Consum. Electron.

Exploiting prior knowledge in compressed sensing wireless ECG systems

IEEE J. Biomed. Health Inform.

Energy-efficient compressed sensing for ambulatory ECG monitoring

Comput. Bio. Med.

Impact of compressed sensing on clinically relevant metrics for ambulatory ECG monitoring

Electron. Lett.

Multi-scale dictionary learning for compressive sensing ECG

Proceedings of the IEEE Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE)

Efficient compression technique based on temporal modelling of ECG signal using principle component analysis

IET Sci. Meas. Technol.

A fast and robust non-sparse signal recovery algorithm for wearable ECG tele-monitoring using ADMM-based block sparse Bayesian learning

Sensors

Compressed sensing based method for ECG compression

Energy-efficient ECG compression on wireless biosensors via minimal coherence sensing and weighted $l_{1}$ minimization reconstruction