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Abstract

In the past decades, compressed sensing emerges as a promising technique for signal acquisition in low-cost sensor networks. For prolonging the monitoring duration of biosignals, compressed sensing is also exploited for simultaneous sampling and compression of electrocardiogram signals in the wireless body sensor network. This article presents a comprehensive analysis of compressed sensing for electrocardiogram acquisition. The performances of involved important factors, such as wavelet basis, overcomplete dictionaries, and the reconstruction algorithms, are comparatively illustrated, with the purpose to give data reference for practical applications. Drawn from a bulk of comparative experiments, the potential of compressed sensing in electrocardiogram acquisition is evaluated in different compression levels, while preferred sparsifying basis and reconstruction algorithm are also suggested. Relative perspectives and discussions are also given.

Keywords

Compressed sensing electrocardiogram wavelet basis dictionary learning

Introduction

Benefiting from the significant developments of wearable device and information technology, recent years have witnessed a dramatic progress of wireless body sensor network (WBSN).^1,2 As illustrated in Figure 1, WBSN adopts various wearable or implantable sensors to acquire real-time biomedical information, which is then transmitted to a fusion center using wireless communication technology. Subsequently, a powerful and wide-band network may be employed for transmitting the massive fusion data to a remote server where deep learning or other computer-aided technologies^3,4 have been developed for diverse medical or health-care applications. Currently, almost all of the countries worldwide suffer from dramatic social and economic pressures derived from citizen’s medical services, and WBSN is expected to be an effective solution for low-cost health-care and medical treatments.

Figure 1.

The wireless body sensor network.

Energy efficiency is the most important metric of the WBSN,⁵ as it plays a critical role for the lifespan of biomedical sensors and further affects continuous monitoring of physical condition. Through comprehensive analysis, wireless transmission is found to be the most energy-consuming procedure in a WBSN node;² therefore, signal acquisition and data processing also play critical roles for the energy consumption. That is because if amounts of samples are collected or the data compression method is not satisfactory, it will consequently bring overloads to the wireless communication module, which is the most energy-consuming procedure as mentioned above. To be concluded, low-cost signal acquisition and data compression methods are highly demanding in WBSN applications.

In recent years, compressed sensing (CS)^6–8 emerges as a promising solution for low-cost signal acquisition and compression. By exploiting sparsity feature of involved signals, CS simultaneously implements signal acquisition and compression using a simple linear projection of plain signals. In this scenario, the high-frequency Nyquist sampling is not required and the elaborate data compression module can be saved at the same time. On the contrary, relative complex optimization algorithms are usually required for signal reconstruction in the decoding end. However, this asymmetry of complexity, fortunately, matches practical applications where signal acquisition devices are generally resource constrained but the reconstruction operations are usually implemented on powerful servers.⁹ The WBSN is indeed a typical case. The biosensors have limited energy, computation, memory, and storage; meanwhile, they are required to perform long-term signal acquisition and wireless communication. Conversely, the subsequent reconstruction and analysis of these signals are usually implemented in a remote data center, which can be actually regarded as ultimate powerful.

The application of CS in WBSN is therefore a matter of course. Using CS for biosignal acquisition started with the electroencephalography (EEG),^10–12 where primary attention is paid to the sparsity modeling of EEG. Specifically, Aviyente¹⁰ found that EEG is sparse in Gabor frame basis and the orthogonal matching pursuit (OMP) algorithm is demonstrated to be effective for reconstructing multi-channel EEG signals. Then, EEG recovery in Slepian basis is also validated.¹¹ The first time considering CS for biosignal acquisition from the WBSN perspective is given by Mamaghanian et al.¹³ Taking electrocardiogram (ECG) acquisition as an example, Mamaghanian et al.¹³ quantified the potentials of CS for low-cost signal acquisition in a resource-limited WBSN node. The experiments are implemented in real hardware platforms, and it is found that the CS-based ECG sampling algorithm can prolong 37.1% of the node’s lifespan in comparison with the wavelet-based counterparts. This groundbreaking achievement brings the booming research on CS applications in WBSN, which can be classified into two aspects. The former tried to evacuate the potential of CS from a network point of view, such as Mamaghanian’s work and the achievement of Li et al.¹⁴ who investigate the energy-saving potential of CS for the Internet of things (IoT) in terms of sensing, transmission, and reconstruction. The latter emphasized on the promotion of reconstruction quality for various biosignals when they are sampled via CS technique, such as the works that investigate the sparsifying basis for EEG.^10,11 Related works regarding the applications of CS in WBSN will be reviewed in the following section.

Essentially, this work belongs to the latter category. In specific, we focus on applying CS for the acquisition and reconstruction of ECG signals, motivated by the fact that ECG monitoring is critically important for cardiovascular diseases that are the most fatal life murderers worldwide. This article is different from a related work of Mishra et al.,¹⁵ who conclude that the reverse biorthogonal wavelet family is more satisfactory for ECG recovery. The conclusion is drawn from a set of experiments, where 10 ECG samples and three compression ratios (CRs) are adopted. However, only a single reconstruction algorithm ( $l_{1}$ norm) is adopted and the CR is limited to 1:2, 1:4, and 1:6. Thus, the reported results may not be able to precisely and extensively illustrate the best sparsifying basis in different sub-regions. Besides, Mishra only considered the wavelet family basis, yet state-of-the-art overcomplete dictionaries which have been proved more powerful for signal reconstruction of ECG measurements were overlooked. Considering this, the application of CS for ECG acquisition is comprehensively and comparatively analyzed in this article.

In this article, diverse reconstruction algorithms, wavelet sparsifying basis, some overcomplete dictionaries are compared in terms of various CRs, reconstruction quality, and the execution time.

Our contributions are summarized as follows.

The signal reconstruction performances of various wavelet family bases are comprehensively analyzed and separately illustrated, and the preferred wavelet basis is consequently obtained.

The superiorities of overcomplete dictionaries are experimentally verified, and these advantages further reveal the research focus in the future.

Comparisons of widely adopted reconstruction algorithms are conducted, and preferable ones in different CRs are concluded.

Perspectives are discussed, and the potentials of CS for biosignal acquisition are theoretically illustrated.

This article takes the following structure. The next section introduces the basic theory of CS and reviews its applications in WBSN. CS of ECG is comprehensively and comparatively analyzed in the “Comparative analysis” section, while relative discussions are given in the “Discussion and perspective” section. Finally, conclusions will be drawn in the last section.

CS with applications in WBSN

CS

CS emerges as a revolutionary framework for signal acquisition by exploiting the concept of sparsity.^6–8 Instead of the traditional sampling-then-compression data collection mechanism, CS illustrates that the required measurements can be dramatically reduced given that the signal is sparse or compressible in certain basis. In this scenario, CS directly acquires the data in a compressed fashion at a lower rate. The sampling process is illustrated in Figure 2 and described as follows.

Figure 2.

Sampling process of the CS.

Denote the signal to be sampled as a column vector $x = (x_{1}, x_{2}, \dots, x_{N})^{T}$ and assume that it is $k$ -sparse under the basis $Ψ$ , that is

x = Ψ s

(1)

where $‖ s ‖_{0} = # {i : s_{i} \neq 0} = k << N$ . The measurement vector is $y = (y_{1}, y_{2}, \dots, y_{M})^{T}$ ; in other words, the CS sampling product is the inner multiplication of $x$ with a certain test function. That is

y = Φ x = Φ Ψ s

(2)

in which the measurement matrix $Φ$ is composed of $M = O (k \cdot \log (N / k)) < N$ pre-determined projection vectors. It is obvious that $M < N$ indicates the dimension reduction and therefore CS charges for lower sampling rate in comparison with the Nyquist sampling theorem. To be concluded, traditional solution, high-frequency sampling by Nyquist theory and then data compression with sparse transform, has been replaced by a simple low-rate linear projection in the CS acquisition process. Thus, the system complexity is relaxed, and energy efficiency can be promoted.

Signal recovery is implemented by linear sinc interpolation in Nyquist sampling theorem and this does not fit the CS framework which is characterized by an underdetermined linear system. Leveraging the sparsity assumption, innate nonlinear method resolves to the following optimization problem

\min ‖ s ‖_{0} subject to y = Φ Ψ s = Θ s

(3)

and then the original signal $x$ is recovered by $x = Ψ s$ . It is not hard to observe that solving equation (3) requires exhaustively search all $k$ sub-columns from $N$ ones, and it is concluded to be a non-deterministic polynomial-time (NP)-hard problem for the signals of normal size.¹⁶ Alternative reconstruction method refers to the convex relax form of equation (3), that is

\min ‖ s ‖_{1} subject to y = Θ s

(4)

To guarantee unique and stable solution of this optimization problem, it is necessary that the sensing matrix $Θ$ satisfies restricted isometry property (RIP) of order $2 k$ , that is, there exist a constant $δ_{2 k} \in [0, 1]$ such that

(1 - δ_{2 k}) ‖ x ‖^{2} \leq ‖ Θ x ‖^{2} \leq (1 + δ_{2 k}) ‖ x ‖^{2}

holds for all $2 k$ -sparse signals $x$ .¹⁶ The recovery accuracy is dominated by the following theorem.

Theorem 1. Suppose that $Θ$ satisfies the RIP of order $2 k$ with $δ_{2 k} < \sqrt{2} - 1$ , the solution $s^{*}$ to equation (4) obeys

‖ s^{*} - s ‖_{2} \leq C \frac{σ_{k} {(s)}_{1}}{\sqrt{k}}

where $C$ is a constant and $σ_{k} (\cdot)_{1}$ denotes the best $k$ -term approximation using $l_{1}$ norm.¹⁷

Typical examples satisfying RIP with overwhelming probability are random matrices, entries of which are independent realizations of Gaussian random variables, Bernoulli random variables,¹⁸ or the structurally random matrices.¹⁹ Besides, advances reveal that such matrices are also incoherent with the commonly used sparsifying basis, which means the products of these matrices multiplying with traditional sparsifying basis also own RIP with overwhelming probability. Therefore, we can conclude that such matrices are valid measurement matrices for CS. In other words, the sampling process of CS can be realized by randomly projecting the incoming signal into these noisy-like functions, as described in equation (2).

The signal reconstruction of CS refers to the optimization problem as demonstrated in equation (4). In literature, relative research strives for better signal reconstruction and lower computation complexity at the same time. The popular reconstruction algorithms can be identified into three categories,²⁰ the so-called convex optimization, greedy pursuit, and iterative thresholding. The basis pursuit (BP) is a typical convex optimization approach, which is based on optimizing the $l_{1}$ norm, whereas greedy algorithms seek the most important particles in the sparsity basis; representative algorithm is OMP and compressive sampling matching pursuit (CoSaMP). Iterative thresholding such as iterated hard shrinkage (IHT) is generally able to solve this problem with satisfactory efficiency. Compared with the low-cost linear sampling process, signal reconstruction of CS is relatively more complicated and energy-consuming. However, as signal recovery is always performed in a data center, which can be indeed regarded as owing huge power, the complexity is generally not a critical issue for CS applications. On the contrary, the reconstruction algorithms may impact the quality of the retrieved signals; thus, various reconstruction algorithms are also valuable for comparative analysis.

Application of CS in WBSN

The research of CS for WBSN applications can be primary categorized into the following twofolds.

On one hand, there are some works studying the applicability and suitable architecture of CS when it is used for signal acquisition in WBSN. For a “good” reconstruction quality, Mamaghanian et al.¹³ first experimentally found that CS can achieve 37.1% extension of node’s lifetime in comparison with the wavelet-based compression counterparts. The energy-consumption problem of both digital and analog CS was studied by Brunelli and Caione,²¹ who have conducted fair comparison using a real resource-constrained hardware platform for investigating the effect of CS parameter on the signal recovery performance and sensor’s lifespan. Mangia et al.²² discussed the tradeoffs between data compression and signal reconstruction in the rakeness-based CS architecture together with a zeroing technique. By developing a novel cluster-sparse signal reconstruction means,¹⁴ potential of CS for signal acquisition in IoT has been extensively exploited in terms of sensing, transmission, and reconstruction to relax the energy consumption and prolong the network capacity. State-of-the-art blind CS and low-rank techniques are combined by Majumdar and Ward,²³ and then a Split Bregman approach is derived to solve the reconstruction problem of EEG signals in WBSN. Furthermore, secure transmission of the acquired signals in WBSN is considered by Peng et al.,²⁴ in addition to the consumption-efficient signal sampling procedure. Specifically, chaos theory was introduced into the CS network to generate a secret measurement matrix, so that a joint signal acquisition, compression, and encryption system is developed. Such a design indicates the dramatic potential of chaos-based CS,^9,25–27 for secure CS in WBSN and other IoT applications. For dramatic progress of signal recovery while reducing communication requirements at the same time, sliding window processing technique was also evacuated.²⁸ Wang et al.²⁰ found that the quantization module is an overlooked but important factor for energy consumption of the whole CS sampling process, and further proposed two illuminative configurable quantized CS architectures for body sensor networks. Besides, Li et al.²⁹ paid more attention to group sparse signals recovery algorithm by capitalizing on biosignals’ sparsity feature, based on which a weighted group sparse reconstruction method has been developed for signal recovery at the fusion center. Systematic design and implementation of CS in ECG and electromyography (EMG) sensors are evaluated by Dixon et al.³⁰

On the contrary, some researchers focus on the reconstruction of a specialized biosignal in CS acquisition applications. As aforementioned, Mamaghanian et al.¹³ comprehensively quantified the performance of CS for ECG acquisition. The energy reduction was improved to 52.04% finally.²⁹ Researchers at University of Bologna conducted compressive ECG sampling in a real hardware platform, which is a 180 nm complementary metal–oxide–semiconductor (CMOS) circuit that allows acquisition of biosignals up to 100 kHz.³¹ The proposed system can fully exploit the rakeness architecture³² and maximize the output from the measurements. Researchers also paid their attention to the CS acquisition of noninvasive fetal ECG, which is an important branch in health-care applications and can be used for the discovery of fetal development and disease.^33,34 The negative factors of fetal ECG, including strong noise and nonsparsity which are not suitable for standard CS framework, have been well solved by sparse Bayesian learning; the raw fetal ECG recordings are reconstructed with satisfactory quality while reserving interdependence relations of multi-channel signals simultaneously. Different from aforementioned pre-defined sparsifying basis, dictionary learning (DL) emerged as a promising technique for constructing better sparsifying basis. An overcomplete dictionary was constructed by Wang et al. using k-means singular value decomposition (K-SVD)³⁵ and is proved valid for ECG reconstruction from the CS measurements.³⁶ Besides, Engan et al.³⁷ adopted a series of iterative least square–based DL algorithms while multi-scale DL is exploited by Polania and Barner³⁸ to evacuate the correlation within each wavelet sub-band. Multiple overcomplete dictionaries are used by Craven et al.,³⁹ and furthermore, two-stage reconstruction was creatively developed at the same time. The ECG signal was first recovered using the standard K-SVD dictionary, and then QRS detection was performed to decide whether there is a QRS complex and location of the QRS in this reconstructed signal piece. Then, a most appropriate one of the overcomplete dictionaries was selected and the reconstruction was implemented again to promote the signal quality. Experimental results revealed the superiority of the proposed approach.³⁹ Besides the application in ECG acquisition which is the primary concern of this article, CS is also applicable for compressed and low-cost acquisition of EEG,^40,41 EMG,^30,42 and PPG (photoplethysmogram)⁴³ in WBSN. For example, Baheti and Garudadri⁴³ developed a CS-based hardware system for noninvasive monitoring of pulse oximeter. It is shown that only 1/20 data of Nyquist sampling is sufficient for CS acquisition of PPG; thus, the lighting time of LED can be reduced and sensor’s lifespan is dramatically prolonged.

With the increasing requirements of real-time and large-volume tele-monitoring in modern health-care systems, CS is expected to be one of the most promising solutions and will definitely have much more applications in health-care field.

Comparative analysis

Illustration of comparison

Amounts of experiments have been conducted, with the purpose to give precise and exhaustive comparisons of the ECG acquisition using CS. The source codes are open accessible for reproduction and extension. (The codes can be obtained via https://github.com/lurenjia212/Copmare_ECG_CS. As there is randomness in the projection and reconstruction processes, the numerical results may be slightly different, yet the conclusions are stable relatively.) Relative issues of the experiments are given in advance.

Samples of ECG. The ECG samples in our experiments are obtained from MIT-BIH Arrhythmia Database (the MIT-BIH Arrhythmia Database is open accessible via http://www.physionet.org/physiobank/database/mitdb/).⁴⁴ The modified limb lead II (MLII) is used and all of introduced records are sampled at 360 Hz. A total of 100 ECG recordings are employed for the experiments; they are produced from 10 original recordings, each of which contributes 10 independent recordings with length of 1024. There are other 30 original ECG recordings introduced for training of standard K-SVD,^35,36 and relative overcomplete dictionaries of a state-of-the-art algorithm.³⁹

Performance indicators. The comparisons are mainly conducted in terms of the CR and reconstruction quality. There are many different indicators for evaluating these two metrics, whereas the following definitions are used in this article. Following popular definitions, the adopted CR is

CR = 1 - \frac{M}{N}

It is obvious that CR is a floating number less than 1, while larger CR means that less CS measurements are acquired and thus more plaintext information has been compressed. Percentage root-mean-squared difference (PRD) is employed to numerically measure the distortion between the reconstruction signal $\hat{X}$ with original signal $X$ , that is

PRD = \frac{‖ \hat{X} - X ‖}{‖ X ‖} \cdot 100

(5)

Besides, the reconstruction algorithms’ efficiency is evaluated by execution time.

Sparse basis. Two overcomplete dictionaries, six kinds including 52 specified wavelet basis, are employed for comparison. The first overcomplete dictionary is constructed by standard K-SVD approach,^35,36 whereas another one refers to the adaptive dictionary by Craven et al.³⁹ (abbreviated as JBHI in the following analysis). Six kinds of wavelet basis, including haar, daubechies, symlet, coiflet, biorthogonal, and reversebior, are employed. Taking the control parameters of these wavelet categories into consideration, a total of 52 specified wavelet basis are adopted: they are haar, dbn (n = 2–10), symn (n = 2–8), coifn (n = 1–5), biornr.nd (nr = 1, nd = 1, 3, 5; nr = 2, nd = 2, 4, 6, 8; nr = 3, nd = 1, 3, 5, 7, 9; nr = 4, nd = 4; nr = 5, nd = 5; nr = 6, nd = 8), and rbionr.nd (nr = 1, nd = 1, 3, 5; nr = 2, nd = 2, 4, 6, 8; nr = 3, nd = 1, 3, 5, 7, 9; nr = 4, nd = 4, nr = 5, nd = 5; nr = 6, nd = 8).

Reconstruction algorithms and hardware platform. As aforementioned, there are three categories of reconstruction algorithms, that is, convex optimization, greedy pursuit, and iterative thresholding. In specific, five kinds of the widely used signal reconstruction algorithms are employed. They are OMP, BP, CoSaMP, iteratively reweighted least squares (Irls), and subspace pursuit (SP). It will be shown that these algorithms vary significantly in terms of the quality and efficiency of the signal reconstruction process. The experiments are implemented on a personal computer with Intel Core i7-7700HQ 2.80 GHz, 8 GB Memory, and 256 GB hard disk. The coding platform is Matlab 2014a. The measurement matrix is a fixed Bernoulli random one, while the experimental CRs range from 10% to 90%.

Results versus wavelet basis

The experiments are first conducted by performing signal reconstruction in various wavelet bases, and BP is fixed as the reconstruction algorithm for fair comparison. The results are presented in Table 1 and Figure 3. Obviously, PRD decreases with the increasing of CR, that is, the more the measurements, the better the reconstruction. As indicated from the results, rbio5.5 is a good wavelet basis on almost each CR region. Besides, bior2.8 and rbio4.4 also own satisfactory PRD when CR is less than 20%, whereas rbio4.4, rbio6.8 and bior1.3 are better alternatives when CR is within the range (30%–80%). In the case that CR is larger than 80%, one can use bior1.3, bior1.5, and rbio4.4 as replacements. It is frustrated to say that bior3.1, bior3.3, rbio3.1, rbio3.3, rbio3.5, rbio3.7, and rbio3.9 are always not good choices; the PRDs reconstructed with these wavelet basis are severely higher than their counterparts. To be concluded, they indeed cannot be used as sparsifying basis for ECG reconstruction in CS applications.

Table 1.

PRD of the reconstructed signals in various wavelet bases.

Wavelet basis	10%	20%	30%	40%	50%	60%	70%	80%	90%
haar	2.3211	4.0925	6.2765	9.4294	14.0322	21.3021	33.4367	54.1247	88.2235
db2	1.7549	3.0392	4.7367	7.2725	11.2787	18.5382	30.7969	51.7472	85.0654
db3	1.5899	2.7707	4.3257	6.9072	10.8491	17.3796	29.2758	51.5331	85.9931
db4	1.5098	2.6527	4.2960	6.8158	10.8888	17.8198	30.6590	51.9620	87.0034
db5	1.5058	2.6813	4.2708	6.8001	11.1207	18.4599	31.6098	52.7041	86.8047
db6	1.4807	2.6378	4.2858	7.0380	11.2137	18.6847	31.8903	53.7012	86.6005
db7	1.4737	2.6758	4.3458	7.0999	11.4512	19.0426	32.0250	54.4362	87.2675
db8	1.4703	2.6560	4.3795	6.9988	11.3765	19.1398	32.8056	54.5431	87.8595
db9	1.5026	2.7203	4.5121	7.4488	12.4559	20.6913	33.8881	55.3468	87.8241
db10	1.4813	2.7224	4.4493	7.3803	12.2143	20.8124	34.7156	56.9515	87.8298
sym2	1.7549	3.0392	4.7367	7.2725	11.2787	18.5382	30.7969	51.7472	85.0654
sym3	1.5899	2.7707	4.3257	6.9072	10.8491	17.3796	29.2758	51.5331	85.9931
sym4	1.5236	2.6568	4.1504	6.6328	10.3490	17.0350	29.7468	51.5696	86.1611
sym5	1.4552	2.5463	4.0154	6.3448	10.2048	17.2520	29.6064	51.3775	84.8554
sym6	1.4615	2.5768	4.0605	6.4742	10.2912	16.6845	29.1475	51.5472	86.2636
sym7	1.4222	2.5419	4.1334	6.4989	10.8192	17.7137	30.1764	51.2691	85.7480
sym8	1.4392	2.5572	4.0495	6.4622	10.3465	17.0209	29.3854	51.8574	86.3331
coif1	1.7703	3.0300	4.7102	7.1380	11.2018	18.0570	30.3761	51.4292	85.3857
coif2	1.4948	2.6150	4.1332	6.4819	10.2935	16.5776	28.9609	51.1692	85.6736
coif3	1.4313	2.5462	4.0427	6.4822	10.2227	16.7361	29.5586	51.2777	86.0801
coif4	1.4236	2.5411	4.0747	6.5510	10.5173	17.2035	29.9375	51.6959	86.1275
coif5	1.4234	2.6017	4.0962	6.6164	10.7081	17.9533	30.5871	52.3658	86.1534
bior1.1	2.3211	4.0925	6.2765	9.4294	14.0322	21.3021	33.4367	54.1247	88.2235
bior1.3	1.4571	2.5443	4.0473	6.3582	10.0309	16.2233	27.4911	47.9502	84.6293
bior1.5	1.4006	2.5102	4.0734	6.6734	11.0437	17.4747	28.8824	48.5434	84.6548
bior2.2	1.9910	3.4517	5.7735	9.5047	15.8877	26.3680	41.8112	62.3219	91.2709
bior2.4	1.5279	2.6406	4.4211	7.3605	12.3486	21.0667	34.7405	55.5491	87.5353
bior2.6	1.3977	2.4850	4.2356	7.1266	11.9201	19.9199	33.5662	54.4616	86.9416
bior2.8	1.3635	2.4551	4.2229	7.1915	11.9178	19.8936	33.2761	54.3222	86.8670
bior3.1	3.7198	7.2577	13.6934	24.7112	39.7052	61.4477	94.2679	128.5368	131.4076
bior3.3	1.8741	3.3755	5.9216	11.3763	21.1025	35.1898	56.7019	83.5707	105.4617
bior3.5	1.5522	2.8301	5.0306	10.2872	18.9899	31.6185	50.0010	73.3868	97.7755
bior3.7	1.4397	2.6798	4.8505	9.7514	17.7558	30.1019	47.3372	70.4372	95.8074
bior3.9	1.3980	2.6343	4.8346	9.4788	17.3852	29.3738	46.1335	69.4700	95.2249
bior4.4	1.8445	3.2800	5.3634	8.8321	14.0135	22.3886	35.1475	56.3760	88.0639
bior5.5	2.2607	4.1482	6.7195	11.0770	17.4695	27.1862	42.0425	65.5566	94.4734
bior6.8	1.5356	2.7508	4.5008	7.2266	11.4691	18.4317	30.8613	52.5530	85.9586
rbio1.1	2.3211	4.0925	6.2765	9.4294	14.0322	21.3021	33.4367	54.1247	88.2235
rbio1.3	2.6642	4.7998	7.5881	11.8592	17.5130	25.4684	38.3984	58.5937	90.2421
rbio1.5	2.7864	5.0406	8.1507	12.8508	18.9671	27.4430	40.5676	60.5989	91.2770
rbio2.2	1.9323	3.5723	6.0632	10.1514	15.9516	24.1588	37.4212	59.7463	91.1133
rbio2.4	1.9540	3.5744	5.8505	9.7388	15.2304	23.4451	38.3265	61.2881	92.2241
rbio2.6	2.0228	3.7400	6.1587	10.0693	15.7110	24.1875	38.9667	62.3262	92.9941
rbio2.8	2.0808	3.9032	6.3835	10.3915	16.3940	24.9881	39.6118	63.1962	93.5851
rbio3.1	16.6282	22.4646	24.0258	25.6251	28.4075	35.1832	48.9059	75.5554	100.5898
rbio3.3	4.0771	11.9386	21.7599	29.7953	35.8406	42.3580	53.6348	75.6547	101.8383
rbio3.5	3.2092	7.9554	16.8515	26.1288	34.5967	42.8495	54.5494	76.1665	102.4546
rbio3.7	3.0248	7.5351	14.7681	24.0990	33.4152	42.6619	54.9246	76.8131	103.0842
rbio3.9	2.9689	7.4755	14.0375	23.2308	32.6194	42.6270	55.4278	77.2903	103.5802
rbio4.4	1.3472	2.2959	3.5835	5.4764	8.6845	14.6599	26.6033	49.1542	83.8708
rbio5.5	1.1441	1.9159	3.0023	4.7104	7.6399	13.3145	25.0320	46.6320	82.2511
rbio6.8	1.4267	2.5104	3.9317	6.1385	9.9285	16.6337	29.1565	52.2028	86.1687

PRD: percentage root-mean-squared difference.

Figure 3.

PRD versus different wavelet basis.

Results using overcomplete dictionaries

In recent years, DL has drawn much attention for signal reconstruction in the CS applications. The standard K-SVD approach and state-of-the-art adaptive dictionary technique³⁹ (i.e. the JBHI) are employed for comparison. (The PRD is defied in a different way in the original paper;³⁹ thus, there may be certain performance difference in appearance.) The involved dictionaries are with size 192 × 500; in other words, there are 500 atoms each of which has a length of 192. The results are listed in Table 2 and also illustrated in Figure 4, where the performance records of some wavelet basis that are relatively better in corresponding families are also introduced. Apparently, signal reconstruction using overcomplete dictionaries owns prominent superiorities in comparison with the wavelet counterparts. This advantage is more obvious when CR is lower, that is, fewer measurements are accessible. For example, when CR is 90% (data volume is only 10% of its origin), the PRD is over 80 if reconstructed with wavelet basis, yet it is only about 20 if using overcomplete dictionaries. The results completely match the current mainstream viewpoint, which places more emphasis on DL and its applications for signal acquisition in the CS scenario.

Table 2.

PRD of the reconstructed signals in wavelet basis and overcomplete dictionaries.

Sparse basis	10%	20%	30%	40%	50%	60%	70%	80%	90%
haar	2.3211	4.0925	6.2765	9.4294	14.0322	21.3021	33.4367	54.1247	88.2235
db3	1.5899	2.7707	4.3257	6.9072	10.8491	17.3796	29.2758	51.5331	85.9931
sym5	1.4552	2.5463	4.0154	6.3448	10.2048	17.2520	29.6064	51.3775	84.8554
coif2	1.4948	2.6150	4.1332	6.4819	10.2935	16.5776	28.9609	51.1692	85.6736
bior1.3	1.4571	2.5443	4.0473	6.3582	10.0309	16.2233	27.4911	47.9502	84.6293
rbio5.5	1.1441	1.9159	3.0023	4.7104	7.6399	13.3145	25.0320	46.6320	82.2511
K-SVD	1.3218	1.9681	2.4189	3.0114	3.8559	5.3517	7.9521	11.5163	24.6749
JBHI	1.4305	2.0493	2.5493	3.1606	3.8552	4.8281	6.2394	9.1033	17.6136

PRD: percentage root-mean-squared difference; K-SVD: k-means singular value decomposition.

Figure 4.

PRD of the reconstruction signals in wavelet basis and overcomplete dictionaries.

Results versus reconstruction algorithms

Regarding the comparison of signal reconstruction algorithms, both the PRD and execution time are considered.

Table 3 and Figure 5 demonstrate the PRDs of various reconstruction algorithms; db2 is employed as the sparsifying basis for reconstruction. As illustrated, apparent performance gaps exist among the comparative reconstruction techniques. The Irls approach owns relatively better PRD performance when CR is less than 50%, while a comparable PRD can be achieved by OMP, CoSaMP, and SP when CR is within the range (60%–70%) and is relatively better than that obtained with BP and Irls. In the case that CR is larger than 80%, BP and Irls appear to be better than their counterparts.

Table 3.

PRD of the reconstructed signals using various algorithms.

Algorithms	10%	20%	30%	40%	50%	60%	70%	80%	90%
OMP	2.5628	3.7035	4.8498	6.0488	7.7905	10.1464	14.7181	55.2331	123.8462
BP	1.7549	3.0392	4.7367	7.2725	11.2787	18.5382	30.7969	51.7472	85.0654
CoSaMP	3.3803	3.9903	4.7790	5.8465	7.2362	9.7375	15.6501	50.3499	110.4456
Irls	1.5228	2.4433	3.4632	4.7196	6.6486	10.0380	20.0927	48.5540	86.5639
SP	3.4749	4.0192	4.7158	5.6729	7.0174	9.1721	14.9335	46.1557	104.5956

PRD: percentage root-mean-squared difference; OMP: orthogonal matching pursuit; BP: basis pursuit; CoSaMP: compressive sampling matching pursuit; Irls: iteratively reweighted least squares; SP: subspace pursuit.

Figure 5.

PRD of the reconstruction signals using various algorithms.

However, there are more distinct differences regarding the implementation time of these signal reconstruction algorithms, as revealed in Table 4 and Figure 6. The longest execution time is always required by Irls, the operation time of which even increases more than 100 times when CR changes from 10% to 90%. On the contrary, the implementation duration of BP is relatively more satisfactory and only increases less than 10 times when CR varies from 10% to 90%. The execution duration of SP is comparable with BP when CR is larger than 80%; however, they increase dramatically when CR is less than 70%.

Table 4.

Reconstruction time of various algorithms.

Algorithms	10%	20%	30%	40%	50%	60%	70%	80%	90%
OMP	23.5122	15.0025	9.4692	5.4774	2.9063	1.2243	0.4187	0.1256	0.0209
BP	0.2071	0.1720	0.1383	0.1151	0.0956	0.0704	0.0540	0.0427	0.0315
CoSaMP	8.2103	5.5079	3.6170	2.2416	1.1144	0.4506	0.1939	0.0604	0.0142
Irls	25.1298	18.2659	12.5317	8.7262	5.7921	3.5378	1.7236	0.7506	0.2152
SP	4.4799	3.0238	1.6666	1.0212	0.5189	0.2671	0.1122	0.0402	0.0109

OMP: orthogonal matching pursuit; BP: basis pursuit; CoSaMP: compressive sampling matching pursuit; Irls: iteratively reweighted least squares; SP: subspace pursuit.

Figure 6.

Execution time of various reconstruction algorithms.

Taking overall consideration of Tables 3 and 4, Figures 5 and 6, we can come to the preferred reconstruction algorithm in different compression requirements. When CR is larger than 80%, the BP algorithm gets “acceptable” reconstruction quality and computation time. Such a conclusion is also available when CR is less than 20%. When CR ranges from 20% to 70%, tradeoff should be compromised between execution time and reconstruction quality. Typically, Irls has satisfactory PRD, yet much more time is also required; on the contrary, BP owns relatively a bit bad reconstruction quality but it is the most efficient one. The preferred algorithm depends on the specified requirements of practical applications.

Discussion and perspective

With the booming requirements of modern health-care applications, real-time and continuous biosignal monitoring will definitely play more important roles in our daily life. Large-volume and long-time biosignal acquisition and wireless communication are basic requirements, which accordingly yield growing demands of the node’s resources. The computation, memory, and storage constraints are expected to be solved with Moore’s law, whereas the energy science may not make comparable progress to meet the increasing requirement of WBSN. Thus, achieving better reconstruction with less sampling rate becomes the first choice. The CS is a promising solution, as it can simultaneously acquire and compress biosignals with a low-rate energy-efficient linear projection. The energy-consumption in both the sampling and compression processes can be thus reduced. Advanced signal-processing techniques including CS will definitely have increasing contribution in this field.

From the experimental results, applicability of CS for ECG acquisition has been comprehensively verified. The preferred sparsifying basis and signal reconstruction algorithms in distinct CRs are also achieved. In short summation, rbio5.5 is the most preferred wavelet basis, yet it is still much worse than the overcomplete dictionaries. Therefore, future works should pay more attention to DL method and then construct individual dictionaries for specified biosignals in WBSN. Regarding the reconstruction algorithms, there are much apparent performance differences. In different ratio regions, users can prefer appropriate algorithm or make compromise between signal recovery quality and execution complexity. Data records presented in this article are expected serving as the referenced support for practical applications.

Besides, state-of-the-art achievement reveals that CS also has certain cryptographic properties;^9,27 thus, it can further be exploited as a encryption scheme for the acquired data stream and indicates possible saving of the Advanced Encryption Standard (AES) encryption in WBSN protocols (generally in the Mac layer of IEEE 802.15.4/802.15.6/Bluetooth). In literatures, achievements in this kind have drawn increasing attention.^45,46 However, standard CS framework has been found vulnerable against plaintext attack from the cryptographic viewpoint. Therefore, revolutionary progress of confidential CS technique is required and will be definitely beneficial in WBSN and other IoT applications.

Conclusions

This article presents a comparative analysis of CS for ECG acquisition. An introduction of CS theory was given, and its usage in WBSN was reviewed in two aspects: the first kind exploits its applicability from a network point of view while the second strives for better reconstruction of a specified biosignal. Subsequently, amounts of experimental results are presented. The rbio5.5 is indicated to be the best wavelet basis for ECG reconstruction, yet overcomplete dictionaries have much more satisfactory performance. Assessments of reconstruction algorithms are conducted in terms of signal recovery quality and execution time as well. The BP owns relatively better efficiency, yet Irls is demonstrated doing better for signal reconstruction. It is also observed that other counterparts have their own advantageous in certain compression level generally; compromise between PRD and computation complexity is suggested. The presented experimental data are expected being referenced records for practical applications.

Footnotes

Handling Editor: Behrouz Jedari

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is funded by the National Natural Science Foundation of China (Nos. 61802055, 61702221, 61771121), Fundamental Research Funds for the Central Universities (Nos. N171903003), the Natural Science Foundation of LiaoNing Province (Key Program) (No. 20170520180), Postdoctoral Science Foundation of Northeastern University (No. 20180101), China Postdoctoral Science Foundation (No. 2018M630301).

ORCID iDs

Junxin Chen

Leo Yu Zhang

Lin Qi

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Compressed sensing for electrocardiogram acquisition in wireless body sensor network: A comparative analysis

Abstract

Keywords

Introduction

CS with applications in WBSN

CS

Application of CS in WBSN

Comparative analysis

Illustration of comparison

Results versus wavelet basis

Results using overcomplete dictionaries

Results versus reconstruction algorithms

Discussion and perspective

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iDs

References