Exploiting multi-scale signal information in joint compressed sensing recovery of multi-channel ECG signals
Graphical abstract
Introduction
Compressed sensing (CS) is a signal processing technique that enables signal reconstruction from a small set of linear projections, called measurements, provided the signal is sparse in some domain [1]. CS exploits the signal structure and enables data acquisition at sub-Nyquist rate, outputting directly the compressed form of the signal. Consequently, the signal encoding becomes quite simple and energy-efficient in the CS framework. This feature of CS motivated its use in many resource-constrained applications [2], [3]. Wireless body area network (WBAN)-enabled electrocardiogram (ECG) telemonitoring is one such prominent application, where CS has been successfully used to lower the on-chip computations, energy consumption, and complexity of the system [4]. A typical block diagram of a CS-based telemonitoring system is shown in Fig. 1. The figure illustrates a digital paradigm of CS, called ‘digital CS’ [4], where a simple matrix-vector multiplication after analog to digital conversion (ADC) gives the compressed form of the physiological signal x. The reduced dimension vector y also called the compressed measurement vector, is sent to the remote terminals (Hospitals/Health care centers) through the wireless links, where the original signal is reconstructed using CS-based recovery techniques and can be used further for clinical purposes.
CS-based techniques exploit the inherent sparse nature of the ECG signals either in the time domain [5], [6], or in the wavelet domain [4], [7], [8], [9], [10]. The conventional wavelet-based ECG compression methods [11] have higher data compression capabilities than CS, but when it comes to the real-time processing with minimum energy and computational cost, CS-based techniques outperform the wavelet-based methods [4]. Previous works in this area include the pioneering work by Mamaghanian et al. [4] who established and quantified the potential of CS for the first time for low complexity and energy-efficient data reduction in WBAN-enabled ECG monitors. Various design considerations were later studied by Dixon et al. [5] for CS-based data acquisition and reconstruction systems. In a similar framework, Zhang et al. proposed a system for fetal-ECG [6] and electroencephalograph (EEG) [12] remote monitoring using a block sparse Bayesian learning approach. Recent advances in the CS field are to incorporate signal structure information in the traditional CS reconstruction algorithms [7], [8], [9] with a goal to achieve superior reconstruction results. In the aforementioned works, the telemonitoring systems studied are limited to single channel ECG signals. However, cardiologists mostly prefer multi-channel or multi-lead ECG (MECG) signals for detailed diagnosis. This is because of the appearance of pathological features in more than one leads [13]. In literature, so far limited research [10], [14] is available for MECG signals. This motivated the study of MECG signals in a CS framework for remote healthcare applications in the present work. The ECG signals acquired through different channels are not independent and they share mutual cardiac information common to all channels (Fig. 2). The source of this common information is the electrical heart vector whose projections in different directions lead to ECG signals in different channels. In such a scenario, conventional channel-by-channel processing of MECG is not optimal in terms of computational cost as well as system performance. Hence, new unified approaches are required for the correlated MECG signals.
Existing CS-based works [4], [5], [10] exploit only the sparsity of the ECG signals and thus ignore the important structural signal information that is known a priori. Recently, few works have been reported which use the prior signal knowledge to improve the decoding quality of CS [8], [9]. Though, the above techniques exploit the anticipated signal information about the single channel ECG but they fail to utilize the spatial information shared across the channels. This is because of their design to process each ECG channel individually. In this work, we exploit the inter-channel correlation of MECG signals by processing all channels simultaneously in a joint CS framework. A multiple measurement vector (MMV) CS model [15] is used for this purpose instead of traditional single measurement vector (SMV) CS model. The MMV, or row-sparse modeling of the MECG signals, helps in exploiting the natural group sparsity of different channels, which is present because of their inherent correlated structure. The MMV model relies on the fact that all the channels have a common support set, i.e., the ensemble is jointly sparse or row sparse. Approximately joint sparse behavior in wavelet domain (Fig. 3) enables the row sparse modeling of MECG signals.
A recently reported MMV-based work [14] has used a ℓ1/ℓ 2-based mixed-norm minimization (MNM) algorithm for CS-based MECG data compression/reconstruction. MNM-based algorithms are known to be efficient for joint sparse recovery [16], however, they suffer from the disadvantage of amplitude dependence similar to traditional ℓ1-norm minimization [17], [18]. The nonzero rows corresponding to the higher coefficients in joint sparse representation are penalized more heavily than the rows corresponding to the lower coefficients during the optimization procedure [17]. Because of this, the reconstruction accuracy decreases, especially when the number of measurements is low (at higher compression ratios). This might be the reason that MNM algorithm used in [14] is not able to preserve clinically important larger wavelet coefficients during the joint CS recovery, resulting in higher reconstruction error. To address this issue in SMV problems, iterative reweighted-based methods were proposed, where weights were designed inversely proportional to the coefficient's amplitude [17]. These algorithms received significant attention due to their improved performance over their non-weighted counterparts. Later, iterative reweighted ℓ1-based algorithms were extended using mixed-norms for solving MMV problems [19]. Recently, an iterative reweighted ℓ1/ℓ 2 algorithm is proposed for recovering block sparse signals [20]. In the weighting-based sparse recovery algorithms, there is flexibility to adopt different weighting rules depending on the understanding of the problem and that in return, improves the estimation of latent data [18], [21].
In the present work, an improved family of weighted MNM (WMNM) algorithms is proposed for the joint CS reconstruction of MECG signals. In this family, various weighted versions of standard MNM algorithm are analyzed. In particular, two specific classes of MNM algorithms are proposed which are referred to as subband weighted MNM (SWMNM) and prior weighted MNM (PWMNM). The former is an iterative reweighted version of standard MNM, where a weighted MNM problem is solved and weights are updated in each iteration based on the solution of the previous iteration. Here, the weighting rule is defined on the basis of diagnostic information contents of the wavelet subbands captured in the form of subband energy, subband entropy and subband amplitudes. The second algorithm, i.e., PWMNM is a non-iterative algorithm, which solves a weighted MNM using the weights designed in a priori. The a priori weight selection is based on the prior structural knowledge of MECG wavelet representation. This type of weighting is used in a earlier work [9] for SMV recovery of single channel ECG signals using weighted ℓ1-minimization. However, it is shown in this work that the performance of traditional SMV recovery can be improved significantly when all the channels are recovered simultaneously in an MMV paradigm. Experimental results on publicly available MECG databases show that the proposed weighting strategies can significantly improve the diagnostic quality of the reconstructed MECG signals with a lower number of measurements compared to the non-weighting-based methods [14] and the traditional weighting-based methods [19], [20].
The rest of the paper is organized as follows: the proposed method is discussed in Section 2. Experimental results and related discussions, including recovery performance and comparative analysis are given in Section 3. The concluding remarks are presented in Section 4.
Section snippets
Proposed method
In standard practice, MECG signals are recorded in a twelve channel format [13]. Out of these twelve channels, there are eight independent channels: Lead I, Lead II, V1, V2, V3, V4, V5, V6; and the remaining four are derived channels: Lead III, aVR, aVL, aVF. We have processed the eight independent channels in this work as the derived channels can be synthesized using Lead I and Lead II. Hereafter, MECG will refer to eight channels instead of twelve channels. The MECG signals are jointly
Results and discussions
The performance evaluation of the proposed method is carried out using publicly available Physikalisch-Technische Bundesanstalt (PTB) [26], [27] and Massachusetts Institute of Technology-Boston's Beth Israel Hospital (MIT-BIH) database [26], [27], and commercially available Common Standards for Electrocardiography (CSE) [28] database [28]. The PTB database contains 15 channels of various pathological MECG datasets from 290 patients sampled at 1 kHz with 16-bit resolution, while the MIT-BIH
Conclusion
In this work, WMNM-based joint sparse recovery algorithms were proposed for joint CS-based MECG compression/reconstruction in telemonitoring applications. The proposed recovery algorithms exploit multi-scale signal information through a subband weighting strategy. This weighting strategy incorporates additional information about diagnostically relevant wavelet coefficients in the optimization problem formulation and emphasizes them in the final reconstruction. The proposed methods were found
Acknowledgment
The authors would like to thank the anonymous reviewers for their thoughtful and detailed comments, which helped us to enhance the quality of the manuscript in every possible way. The authors would also like to thank Mr. Rajesh Tripathy for his help in implementing the classifier, which is used for evaluating the classification results in the proposed work.
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