SIViP DOI 10.1007/s11760-013-0476-8

ORIGINAL PAPER

Low sampling rate algorithm for wireless ECG systems based on compressed sensing theory Mohammadreza Balouchestani · Kaamran Raahemifar · Sridhar Krishnan

Received: 6 January 2013 / Revised: 28 March 2013 / Accepted: 29 March 2013 © Springer-Verlag London 2013

Abstract Wireless body area networks (WBANs) consist of small intelligent biomedical wireless sensors attached on or implanted in the body to collect vital biomedical data from the human body providing continuous health monitoring systems. The WBANs promise to be a key element in wireless electrocardiogram (ECG) monitoring systems for next generation. ECG signals are widely used in healthcare systems as a noninvasive technique for diagnosis of heart conditions. However, the use of conventional ECG system is restricted by patient’s mobility, transmission capacity, and physical size. Therefore, there is a great demand to improve wireless ECG systems. With this in mind, compressed sensing (CS) procedure as a new sampling approach and the collaboration of the sensing matrix selection algorithm based on dynamic thresholding approach are used to provide a robust low-complexity detection algorithm in gateways and access points with high probability and enough accuracy. Advanced wireless ECG systems based on our approach will be able to deliver healthcare not only to patients in hospitals and medical centers, but also at their homes and workplaces thus offering cost saving, and improving the quality of life. Our simulation results show an increment of 1 % for sensitivity as well as 0.15 % for the prediction level and good detection accuracy. The simulation results also confirm that the binary Toeplitz matrix provides the best signal-to-noise ratio and compression performance with the highest energy efficiency for random sensing matrix in CS procedure. M. Balouchestani (B) · K. Raahemifar · S. Krishnan Electric and Computer Engineering Department, Ryerson University, Toronto, ON, Canada e-mail: [email protected] K. Raahemifar e-mail: [email protected] S. Krishnan e-mail: [email protected]

Keywords Wireless ECG systems · Detection accuracy · Compressed sensing · Prediction level · Random sensing matrix

1 Introduction Wireless ECG systems are expected to be a breakthrough in information communication technology (ICT) and in healthcare areas such as hospital and home care, mobile health, electronic health. Wireless ECG systems play an important role in remote cardiac patient monitoring, intelligent emergency care management systems, and ubiquitous wireless healthcare applications. The biomedical wireless sensors collect and transmit the vital signals of cardiac patients wirelessly. The current ECG systems are restricted by size, patient’s mobility, power, and transmission capacity. Therefore, the current ECG systems need to be further developed in order to accommodate user’s mobility and allow wireless monitoring of several patients at the same time. The wireless ECG signals generally illustrate the redundancy between adjacent heartbeats due to its semi-periodic structure. It is evident that this redundancy provides a high fraction of common support between consecutive heartbeats that are a good candidate for compression. The compressed sensing (CS) is a revolutionary idea for the acquisition and recovery of sparse signals that enables sampling rate significantly below the classical Nyquist-rate. The CS theory says a small number of random linear measurements of bio-sparse signals contain enough information to collect, process, transmit, and recover the original signal [1].The signal representing sparsity in any orthogonal basis can be well reconstructed using 1 norm minimization, while satisfying the restricted isometry property (RIP) condition for random measurement matrix  which offers by CS theory and orthogonal  in any domain

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[2]. This paper presents a contribution of CS approach, and the collaboration of the sensing matrix selection (SMS) algorithm based on dynamic thresholding approach (DTA) to establish a high-reliability detection algorithm for wireless ECG systems. Our simulation results illustrate an increment of 1 % for sensitivity as well as 0.15 % for the prediction level and a good level of quality for detection accuracy. The simulation results also confirm that the binary Toeplitz matrix (BTM) provides the best SNR and compression performance with the highest energy efficiency for random sensing matrix in CS procedure. The structure of this paper is organized as follows. Section 2 provides an overview of CS theory in general and specifically for wireless ECG systems. In Sect. 3, we propose two new algorithms for detecting wireless ECG signals with high probability and enough accuracy. Simulation results are presented in Sect. 4, and in Sect. 5, we explain the main contribution of this paper. The conclusion is drawn in Sect. 6.

RIP with high probability, where is suitable condition for recovering the original signal in the receiver side [1]. Thus, CS scenario has two important steps. First step in CS offers a stable measurement matrix [] M×N to ensure that the main information in any compressible signal is not distorted by the dimensionality reduction from D ∈ R N down to C ∈ R M . In the second step, the CS theory offers a reconstruction algorithm under certain condition and enough accuracy to recover original signal D from the compressed signal [4]. Therefore, we can exactly reconstruct the original signal D with high probability via 1 norm by solving the following convex opti mization problem ( D 1 = n |Dn |): min  D 1 subject to C =  D . D ∈ RN

(4)

Certain conditions need to be met to guarantee the accuracy of this recovery. Firstly, the number of random linear measurements, the number of coefficients, and the number of nonzero coefficients must satisfy the following equation [5]:

2 Overview of compressed sensing

M ≤ K /C(log N ),

Any compressible signal D in R N can be expressed like [3]:

where M, N , and K are the number of random linear measurements, the number of samples, and the number of nonzero coefficients, respectively. Secondly, for any vector a of the original signal [D], matrix [] must satisfy the following condition for some ε  0:

D=

N 

Ci i .

(1)

i=1

Therefore, the compressed signal C is found as: [C] M×1 = [] M×N [D] N ×1 .

(2)

Thus, the compressed signal is found as: [C] M×1 = [] M×N [] N ×N [C] N ×1 = [] M×N [C] N ×1 .

(3)

Fortunately, [] and [] have two interesting and useful properties. First, they are incoherent with the basis [].It means they do not depend in any way with the basis []. The spectral coherence is a statistic that can be applied to examine the relation between two matrixes. Second, they have the Fig. 1 Wireless ECG systems based on CS theory

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1 − ε ≤ a 2 /  a 2 ≤ 1 + ε,

(5)

(6)

where satisfies RIP property for the random dictionary matrix. In order to recover K-sparsity of the original signal, now we have M × K system of linear equations, with M equations and K unknowns [6]. It is possible to find out the K-sparsity of the original signal, because of M ≥ K . Figure 1 shows a wireless ECG system based on CS theory. As it can be seen, the ECG signals are compressed by biomedical wireless sensors. The collected compressed ECG biomedical data are then transmitted wirelessly to access points

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(APs) at hospital, ambulance, or helicopter [7] via gateways. The APs recover compressed biomedical data for diagnostic and therapeutic purposes.

3 Proposed algorithm The wireless ECG systems provide vital information of the heart to physicians and medical staff at anytime and anywhere by removing constraints of time and location of patients while increasing both the mobility and the quality of healthcare systems [8]. Our new procedure consists of two algorithms: (1) detection algorithm and (2) SMS algorithm. In the proposed algorithm, compressed sensing (CS) procedure and the collaboration sensing matrix selection (SMS) approach and robust low-complexity detection procedure are combined together to provide a robust algorithm for low sampling-rate wireless ECG systems. In this section first, the proposed procedure to find out the best fit for random sensing matrix in CS scenario is illustrated. Second, the proposed approach to detect wireless ECG signal with high probability and enough accuracy in GWs and APs is provided. Figures 2 and 3 show the combination of two algorithms in the transmitter and receiver sides of wireless ECG systems.

3.1 Detection algorithm The proposed algorithm consists of two stages: (1) Feature extraction stage after the compression, including digital filtering and linear transformation to generate ECG features such as QRS complex and (2) Decision make stage is performed on compressed ECG signal to locate R peak. The digital filtering is performed to limit the filtering operation to just once. The decision stage is based on adaptive threshold mechanism (ATM) to detect the ECG signal. The threshold value depends on RP-intervals and R peaks and is updated periodically based on ECG features [9]. The hamming window (HM) for the feature extraction stage and the peak-finding schemes (PFS) for the decision stage are applied to simulate the high-reliability detection algorithm [10]. The output signal of the filtering process with HM is a bipolar signal, and thus, a rectification process is employed to prevent the detection problems where ECG signals change polarity due to bipolar R part and negative QRS-part [11]. By employing the Shannon energy transformation (SET) in the feature extraction stage, the energy values E s smaller than the threshold are set to zero and other energy values are retained. Table 1 illustrates the proposed algorithm. In the PFS step, the peak clipping is employed to minimize deviation between the detective peaks of the ECG signal. The

Fig. 2 Wireless ECG systems/transmitter

Fig. 3 Wireless ECG systems/receiver

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SIViP Table 1 Detection algorithm for wireless ECG systems

Table 2 The best fit for sensing matrix

Algorithm 1 Detection ECG signals

Algorithm 2 The best fit for random sensing matrix 

1. Received ECG signal at GW 2. Feature extraction stage

Enter: Raw ECG data Digital filtering

1: Apply Dynamic Thresholding Approach to Raw ECG data

Energy transformation

2: Select Initial Square Matrix

Tools

3: Apply Row Selection Scheme (select the first M rows as the initial sensing matrix ) 4: Compare with binary Toeplitz Matrix

1. Hamming tool

3. Decision stage

5: If  is binary Toeplitz Matrix Stop, the Algorithm is completed

2. Shannon energy transformation code tools in C++ Peak-finding schemes

6: M = M + 1 7: Go to Step 4

Peak clipping Tools 1. Peak finding 2. Peak clipping code in C++ 4. Detect ECG features for medical purposes

peak clipping adaptive threshold is illustrated as [12]: PT = 0.1 × max(E T H )

(7)

Then, the peak clipping is performed with the following equation [13]:  ifE T H ≤ PT ET H PC = (8) PT otherwise In the SET step, the Shannon energy (SE) of the normalized  E CG is determined as [14]:  2  log ECG[n]  SE = −ECG[n] (9) Finally, a true peak locator (TPL) of PSC approach is employed to accurately extract the main features of the ECG signal [15]. 3.2 Proposed SMS algorithm The random measurement matrix [] is a key component of CS theory [16]. Two key features are needed for a successful implementation of CS approach: sparsity of the biomedical signal and incoherence between the random sensing matrix and the sparsity basis [17]. That is why; the random sensing matrix must exhibit a high degree of incoherence with the sparsity basis [] [18]. In this part, the new SMS procedure is presented to select the best fit for the random sensing matrix []. Herein, Bernoulli Toeplitz, Gaussian circulant, and binary Toeplitz matrices are examined to find out the best fit for random sensing matrix [19,20]. Table 2 illustrates our new algorithm to select the best fit for random sensing matrix . In the step 1 of the proposed algorithm, the DTA procedure is applied to the raw ECG data [21,22]. The principal

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objective of the DTA is to vary the sparsity level of a raw ECG signal to convenient level [23]. In the simulation part, the convenient level is defined 98 %. In the step 2, the initial square matrix is used for each of the sensing matrices in the experiments [24,25]. In the step 3, a row selection scheme (RSS) is applied to reduce the number of rows from N to M [26,27]. Two RSSs approaches are compared as follows: (1) select first M rows from the initial N × N matrix and (2) randomly select M rows from the initial N × N matrix. The first RSS approach demonstrates better performance than the second RSS approach [28,29]. So, only the first RSS approach is utilized in the proposed algorithm.

4 Simulation results The proposed algorithm is applied for records 105, 108,200, 203, and 205 of 48 half-hours 2-channel ECG recordings of MIT-BIH Arrhythmia Database (MITADB) which sampled at 360 Hz with 11-bit resolution. The sensitivity percentages (SP) and positive prediction percentages (PPP) are employed to determine the validation of the proposed algorithm. The sensitivity can be expressed as: SP % = PT /(PT + N F ) × 100

(10)

where PT and N F are the number of true-positive part and the number of false-negative parts, respectively. The positive prediction is obtained of the following equation: PPP % = PT /(PT + PF ) × 100

(11)

Based on detection algorithm, Fig. 4 illustrates the SP of the selected ECG records and obtained by empirical mode decomposition (EMD)-based method and the proposed algorithm. As depicted in Fig. 4, sensitivities of received ECG signal are increased by the proposed algorithm. This ability allows achieving better performance of wireless ECG systems based on CS theory. Figure 5 demonstrates the PPP for selected ECG records and compares it for EMD-based

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Fig. 6 The mutual coherence μ(, ) Fig. 4 Comparing the SP of EMD-based method and the proposed algorithm

Fig. 7 The number of nonzero entries Fig. 5 The comparative work on PPP in the EMD-based and proposed algorithm

method and the proposed algorithm. As it can be seen in Fig. 5, the proposed algorithm shows an increase in the prediction level at gateways or APs for wireless ECG systems. The simulation result illustrates satisfying quality of prediction level for wireless ECG systems with CS theory. This ability allows providing the detection algorithm with high probability. The binary√Toeplitz sensing matrix with nonzero entries equal to ±1/ 2 is considered for  in order to decrease execution time during the simulation process [27]. The random binary matrix  has M nonzero entries equal to 1, with M  N [28]. The mutual coherence μ(, ) as an important parameter between random matrixes  and sparsity basis  is decreased by increasing the number of nonzero entries in matrix  [29]. Based on SMS algorithm, Fig. 6 illustrates the mutual coherence versus the number of nonzero entries for three matrices of . Based on the results of Fig. 6 and suitability of the random binary matrix, the random binary matrix is applied to all the records of the MIT-BIH ECG database to optimize the number of nonzero entries in order to simulate signal-to-noise ratio (SNR). Figure 7 shows the resulting average output SNR

in terms of the number of nonzero elements in the random binary matrix  for different values of compressed ratio (CR) that is defined as: CR = N /M

(12)

As depicted in the Fig. 7, the satisfying quality for SNR can be achieved by minimizing CR, which results in an increase in the number of nonzero elements. As it can be seen, the output SNR increased after the number of nonzero entries M = 15, which is the reference value for the rest of simulation results.

5 Main contribution The emerging application of CS theory in medical areas has been potentially powerful to provide wireless ECG systems due to the lack of conventional ECG systems. The use of conventional ECG system is restricted by patient’s mobility, transmission capacity, and physical size. That is why; there is a critical need to develop wireless ECG systems to achieve extended patient’s mobility. The main contribution of this paper lies in the use of CS approach and the collaboration of the SMS algorithm based on DTA to establish a new a highly reliable algorithm for detection of wireless ECG signals as gateways or APs. The work by Mamaghanian et al. [3]

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considers CS theory for wire ECG systems, and the work by Simunic et al. [12] emphasizes wireless ECG systems without CS theory. While the present study is provided, a new detection algorithm for wireless ECG signal based on CS theory. It capitalizes on a new detection algorithm for wireless ECG systems at gateways and access points with high probability and enough accuracy at hospitals or medical centers for diagnostic and therapeutic purposes.

6 Conclusion This paper has presented new algorithm with a contribution of CS approach, and SMS procedure based on DTA to establish a robust ultra-low-power for normal and abnormal ECG signals. The proposed algorithm has consisted of filtering, SET, and peak clipping steps. The simulation results show that the proposed algorithm achieves significantly better detection rate in comparison with EMD-based method. We have also developed a new algorithm based on combining CS theory and wireless ECG framework. Our simulation results validate the suitability of the new algorithm for a real-time energy-efficient ECG compression on resource constrained in wireless body are networks (WBANs). As expected, our simulation results illustrate an increment of 1 % for sensitivity as well as 0.15 % for the prediction level and a good level of quality for detection accuracy. The simulation results also confirm that the BTM provides the best SNR and compression performance with the highest energy efficiency for random sensing matrix in the CS scenario. The wireless ECG systems based on the proposed algorithm give patients greater mobility and increased comfort by freeing them from the need to be connected to hospital equipments.

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7 Future work 16.

We have simulated the benefit of CS to wireless ECG systems for particular ECG records. Our future work involves developing the CS theory to other records of ECG signal, including abnormal records for wireless ECG systems.

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