Deterministic Compressed Domain Analysis ofMulti-channel ECG Measurements
aa r X i v : . [ ee ss . SP ] F e b Deterministic Compressed Domain Analysis ofMulti-channel ECG Measurements
Dipayan Mitra
Dept. of Systems and Computer EngineeringCarleton University
Ottawa, [email protected]
Sreeraman Rajan
Dept. of Systems and Computer EngineeringCarleton University
Ottawa, [email protected]
Abstract —Continuous and long term acquisition of multi-channel ECG measurements are significant for diagnostic pur-poses. Compressive sensing has been proposed in the literaturefor obtaining continuous ECG measurements as it providesadvantages including a reduced number of measurements, re-duced power consumption and bandwidth for transmission.Reconstruction of the compressed ECG measurements is thendone to analyze the measurements for diagnostic purposes. How-ever, reconstruction of ECG measurements is computationallyexpensive. Therefore, in this paper, ECG analysis is carried outin the compressed domain without resorting to reconstruction.Multi-channel ECG measurements from MIT-BIH Arrhythmiadatabase is used to validate the compressed domain ECGanalysis. ECG signals are compressed at various compressionratios (CR) using morphology preserving deterministic sensingmatrix. Structural similarity measures are used to quantitativelydemonstrate the fidelity of the compressed measurements. R-peaks are detected in the compressed domain from compressedECG measurements. Detection performance metrics such assensitivity, positive predictivity and detection rate decrease asCR increases.
Index Terms —ECG compression, wireless sensor network,compressive sensing, multi-channel ECG sensing, signal qualityanalysis.
I. I
NTRODUCTION
Due to increase in illnesses like diabetes and hypertension,the risk of cardiovascular diseases (CVDs) has recently seen asharp increase [1]. As a consequence, the need for continuousacquisition and real time monitoring of vital signs, such asECG, is needed for early detection of CVD so that earlyprevention modalities can be attempted. Internets of things(IoT) enabled Wearable sensor technology along with wirelessbody area networks (WBANs) offer continuous and real timeECG monitoring by continuously transmitting the acquiredECG measurements to a remote system for storage and furtherprocessing [2]–[4]. A study by Kadrolkar et al. showed thatapproximately of the small battery powered sensingdevices’ energy is consumed during data transmission forremote processing [5]; hence data transmission may have tobe done only on demand. As the wearable devices may not ©2020 IEEE. Personal use of this material is permitted. Permission fromIEEE must be obtained for all other uses, in any current or future media,including reprinting/republishing this material for advertising or promotionalpurposes, creating new collective works, for resale or redistribution to serversor lists, or reuse of any copyrighted component of this work in other works. have adequate memory to store the acquired measurements,a reduction in the number of samples of the acquired mea-surements may also be in order. Compressive sensing offers asolution that reduces the amount of measurements and datatransmission simultaneously. Thus compressive sensing hasrecently been proposed as signal acquisition technique andcan ensure continuous sensing without the need for frequentbattery replenishment.Compressive sensing (CS) acquires measurements far be-low the Nyquist rate and is recommended for compressiblesignals such EEG and ECG signals [6], [7], [8]. Although inliterature some alternative compression algorithms have beenproposed [9], CS based compression for ECG measurementshave an edge over other techniques because of encoder designsimplicity [10], [11]. To effectively monitor cardiac activity,single channel ECG measurements often are segmented duringacquisition through IoT enabled wearable sensors and recoveryof compressed signal is outsourced. To recover the loss ofquality due to segmentation during on-demand recovery, aKronecker-based method was proposed in [12], [8]. Also in[13], as part of analysis of this improved recovery technique,deterministic and random sensing approaches were compared.Often ECG is acquired on multiple channels when multipleleads are used (Holter monitoring). In such cases, althoughtraditional one channel CS approaches may be acceptable,it would be inefficient. As the measurements acquired bymultiple channels are generated by the electrical activity ofheart, there exists a strong correlation between these mea-surements. Hence, these multi-channel and non-independentECG measurements can be treated as jointly sparse. As aresult, CS theory for multiple measurement vector (MMV),an extension of single measurement vector (SMV), may be aneffective approach to acquire compressive ECG measurementscontinuously [14], [15].Qiao et al. used joint sparse model type 2 or JSM-2 todevelop a two-step reconstruction scheme for jointly sparsemeasurements [16]. In [17], compressive multiplexing ap-proach was proposed for multi-channel ECG sensing andrecovery. Sparse recovery algorithms exploiting joint sparsityof the ECG measurements, acquired by ‘resource-constrained’sensors, were shown in [18], [19]. While the current state-of-the-art research emphasizes the sparse recovery algorithm de-ign, analysis on the jointly sparse multi-channel compressedECG measurements (for the purpose of clinical evaluation) hasnot been widely reported.In this paper, we recommend and demonstrate compresseddomain analysis of multi-channel ECG measurements withoutthe need for recovery. A morphology preserving deterministicsensing model for acquiring multi-channel ECG measure-ments is presented in this paper. Deterministic sensing makesimplementation in hardware easier, unlike random sensingmatrices. As random sensing-based approach does not preservemorphology, it will require reconstruction of the compressivelyacquired signal for analysis. Unlike the existing methods in theliterature the sensing technique presented in this paper does notneed joint sparse recovery techniques for reconstruction. In or-der to demonstrate the preservation of morphology, structuralsimilarity is used in this work. The structural similarity of themeasurements in the compressed domain is compared with thatof the uncompressed measurements. A template-based corre-lation approach is used to quantify the structural similarity.The robustness of the sensing model is verified by detectingclinically significant feature, such as the R-peak from theQRS complex, in the compressed measurements. Performanceevaluation metrics are used to provide a statistical analysison pathologically significant ECG measurements chosen fromMIT-BIH Arrhythmia database.The rest of the paper is organized as follows: in SectionII background in CS has been discussed; CS based multi-channel ECG acquisition model has been presented in SectionIII; the quality evaluation metrics are introduced in SectionIV; Section V contains the details of results and analysis; thepaper ends in Section VI with a conclusion and scope of futurework.
Notation:
In this work, boldfaced lower-case letters, e.g. x ,denote vectors, whereas the boldfaced upper-case letters, e.g. X , denote matrices. Letter n denotes index of the measurementand [ . ] T denotes the transpose operation. cov ( . ) signifiescovariance measure whereas σ stands for standard deviation.II. B ACKGROUND
A. CS for Single Channel system
In classical CS theory, a k -sparse 1-D signal x N can besimultaneously sensed and compressed by a linear map onto y M , also called measurement vector, for M << N , where, y M × = Φ M × N x N × (1)Here, Φ is called the sensing matrix. Signal x is assumedto have a sparse representation in a basis, (sparsifying basis), Ψ . Equation (1) can be represented in the following form, y M × = Φ M × N Ψ N × N s N × (2)where s is the sparse vector. Numerous algorithms have beendeveloped to recover x from the compressed measurementvector y [20]–[22]. These are single measurement vector(SMV) recovery. B. CS for Multi-channel System
Mathematically, a t -channel ECG measurement can berepresented as, X N × t = [( x N ) T , ( x N ) T , . . . , ( x tN ) T ] (3)where x N represents the ECG measurements acquired byindividual channels and the superscripts (from . . . t ) identifythe respective channels. Similarly, t measurement vectors canbe obtained in the following way (forming MMV), Y M × t = Φ M × N Ψ N × N S N × t (4)Few recovery algorithms that exploit the temporal structureof the jointly sparse MMV are available [23]–[25]. Unfor-tunately, such algorithms are computationally expensive andcannot be carried out on a resource constrained wearabledevice.It was reported in [26], [27] that certain signal processingproblems like, detection, classification, filtering can be per-formed on the compressed measurements itself, without theneed to perform signal reconstruction. However, the assump-tion was that compression was achieved using random Φ M × N .In Section III we explore the idea of CS based morphologypreserving jointly sparse ECG compression that may to leadto further signal processing in the compressed domain.III. D ETERMINISTIC S ENSING FOR M ULTI - CHANNEL
ECGM
EASUREMENTS
Restricted isometry property (RIP) of Φ , introduced in[28], may be used for designing sensing matrices. Randommatrices satisfy RIP condition and recovery can be guaranteedwith overwhelming probability [29]. While random matricesoffer a probabilistic notion in guaranteeing recovery of thecompressed measurements, hardware realization for acquir-ing measurements is not straightforward. Hence, determin-istic construction of the sensing matrices is recognized asa viable alternative [30]. In literature, several deterministicmatrix construction techniques were proposed based on codingtheory [31]–[33]. In this work, we use linear filtering baseddeterministic binary block diagonal (DBBD) matrix as Φ , asit is easily implementable in a measurement system [34].The DBBD sensing matrix can be viewed as a linear filterblock followed by a decimation of NM . Order of the filter anddecimation is determined by CR. For example, for CR = ,sensing matrix would be a second order linear phase filterfollowed by decimation of factor . Accordingly, appropriaterepresentation can be found for higher CRs.IV. Q UALITY E VALUATION M ETRICS
To evaluate the quality of the compressed measurements,structural similarity and ability to detect fiduciary points areconsidered. In this work, R peak is used as fiduciary point forevaluation purposes. . Structural Similarity
In order to compare the structural similarity of the com-pressed measurements with that of the uncompressed ones,a block-based correlation approach was applied. Each com-pressed measurement was segmented into smaller blocks oflength equal to individual beat length. Correlation betweenindividual segments were obtained using Pearson’s correlationcoefficient (CC). Pearson’s CC between two segments A and B is determined as follows, corr ( A, B ) = cov ( A, B ) σ A σ B (5)Note that σ A and σ B represented standard deviations of A and B respectively.Pearson’s CC of compressed and original measurementswere compared to quantitatively infer about the structuralsimilarity between both the measurements. B. Fiduciary Point Detection: R-peak Detection
In order to demonstrate the ability to analyze ECG signal,R-peak detection is considered in this work. Pan-TompkinsQRS detection algorithm is applied on the compressed ECGmeasurements [37]. True R-peak is considered as detected, ifthe estimated location of the peak falls exactly on the peak ofthe QRS complex and is considered as true positive (TP). Ifthe estimated peak location is different from the actual peaklocation (obtained through visual inspection), then the peakis declared as false and taken as false positive (FP). If nopeak is detected when it should be, then it is declared as falsenegative (FN). To evaluate the performance of QRS detectionalgorithm on the compressed measurements, the followingmetrics in terms of number of TP, FP and FN were chosen forthe evaluation purpose: sensitivity ( Se ), positive predictivity( P + ), F measure ( F ) and detection error rate ( DER ). Theyare given below: Se (%) = T PT P + F N × (6) P + (%) = T PT P + F P × (7) F (%) = 2 × T P × T P + F N + F P × (8) DER (%) =
F P + F NT B × (9)where TB stands for total number of beats.V. R ESULT AND A NALYSIS
To evaluate performance in compressed domain, ECGmeasurements, representing ‘large variety of pathologicalcases’, from MIT-Arrhythmia database were chosen [38], [39].Two channel ECG measurements were digitized at a rate of360 samples/second over 10 mV range and 11-bit resolution[40]. In our analysis, samples of measurements, for eachchannel, were compressed using DBBD matrix. To verify the structural similarity, while implementing thedeterministic sensing model, we segmented the measurements(each of length ) into smaller measurements (eachof length for original measurement and of length or or compressed measurements with CRs = or or . respectively). Segmentation was based on averagebeat length calculated by RR intervals (duration ≈ templates . Pearson’s CC, described inSection-IV (A) , was calculated for each of these templates andan average estimate obtained for each measurement, which isused as a metric. Fig. 1 shows the structural similarity betweenthe original and compressed ECG measurements for differentCRs (CR = , and . ) for both the channels.From analysis, it can be inferred that the deterministic sensingmodel preserves the morphology of the original measurements,which might be useful for application of signal processingalgorithms on the compressed measurements itself (withoutfurther processing). However, for higher CRs, such as CR = . , slight degradation in similarity measure was observed.We carried out statistical analysis, mentioned in Section-IV (B) , to verify the possibility of performing signal process-ing, like anomaly detection, on the compressed measurements.Fig. 2 shows the analytical results, representing average sta-tistical analysis on detection of R-peak from the compressedmeasurements (without designing any algorithm dedicated tocompressed domain R-peak detection), for CRs = , and . . Analysis was performed on individual compressedECG measurements, for both channels. An average over all ECG measurements for channel-1 has been reported in thispaper. Analysis for channel-2 has not been shown because ofspace constraint. Analytical results of the average values ofsensitivity, positive predictivity and F-measure indicate thatthe clinically significant features of the ECG measurementsremain unaffected using the deterministic sensing scheme.Low values of detection error rate signify the possibility ofcorrect detection of R-peak, from the compressed measure-ments. From analysis, it is evident that with the increase ofCR, detection performance decrease.VI. C
ONCLUSION
In this paper, we presented a model for continuous multi-channel ECG sensing and analysis based on deterministiccompressive sensing approach. Linear filtering based DBBDdeterministic matrix, easily implementable in hardware, wasused as sensing matrix. We formed templates and used corre-lation between the compressed and the uncompressed ECG templates to quantify the structural similarity between thetwo, for varying CRs. We also performed R-peak detection onthe compressed ECG measurements and presented statisticalanalysis. The analysis was performed without designing ormodifying any new algorithm for compressed domain process-ing. Moreover, the analysis was presented for varying CRs, byavoiding a computationally expensive joint sparse recovery formulti-channel ECG measurements.
04 107 111 112 115 116 118 119 201 207 208 209 212 213 214 228 231 232
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Fig. 1: Structural similarity analysis at (a) CR = , (b) CR= , (c) CR = . (two channels are marked with CH-I and
CH-II ).
40 50 60 70 80 90 100
CR (%) S e ( % ) (a)
40 50 60 70 80 90 100
CR (%) P + ( % ) (b)
40 50 60 70 80 90 100
CR (%) F ( % ) (c)
40 50 60 70 80 90 100
CR (%) -0.2-0.100.10.20.30.40.5 D E R ( % ) (d) Fig. 2: Performance of R-peak detection on the compressedmeasurements (of CH-I) for varying CRs (CR = , and . ). (a) Sensitivity analysis, (b) Positive predictivityanalysis, (c) F-measure and (d) DER analysis.lthough, the proposed sensing model preserves the mor-phology of the measurements in the compressed domain,for some applications measurements are required to be en-crypted for privacy purposes. Future studies would includethe application of anomaly detection using machine learningalgorithms on the compressive measurements, sensed usingrandom sensing, to preserve privacy. Effectiveness of thesensing model in presence of measurement noise would alsobe studied. Dimensionality reduction, offered by compressivesensing, would enable hardware based implementation ofanomaly detection for continuous and long-term multi-channelECG monitoring.VII. A CKNOWLEDGEMENT
The authors would like to acknowledge the financial supportfrom NSERC. R
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CR (%) -0.2-0.100.10.20.30.40.5 D E R ( % ))