This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2357841, IEEE Journal of Biomedical and Health Informatics
IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. XX, NO. XX, DD MMMM YYYY
1
A Novel ECG Data Compression Method Using Adaptive Fourier Decomposition with Security Guarantee in e-Health Applications JiaLi MA, TanTan ZHANG, and MingChui DONG Abstract—This paper presents a novel electrocardiogram (ECG) compression method for e-health applications by adapting adapti ve Fourier decomposition (AFD) algorithm hybridized with symbol substitution (SS ) technique. The compression consists of two stages: 1st stage AFD executes efficient lossy compression with high fidelity; 2nd stage SS performs lossless compression enhancement and built-in data encryption which is pivotal for e-health. Validated with 48 ECG records from MIT-BIH arrhythmia benchmark database, the proposed method achieves averaged compression ratio (CR) of 17.6 to 44.5 and percentage root mean square difference (PRD) of 0.8% to 2.0% with a highly linear and robust PRD-CR relationship, pushing forward the compression performance to an unexploited region. As such, this work provides an attractive candidate of ECG compression method for pervasive e-health applications. Index Terms—Adaptive Fourier decomposition, data encryption, ECG compression, e-health, information security.
T
I. INT RODUCT ION
HE ubiquitous deployment of body sensor network (BSN) and vigorous advance of information and communication technology (ICT) have dramat ically fostered the e-health development. With the aid of low cost portable or wearable embedded-link devices, e-health provides the accessibility to monitor and diagnose human wellness remotely and flexibly. In implementing and improv ing pervasive e-health, bio-informatics plays an important ro le through the management of bio medical informat ion acquisition, processing, storage, transmission, integration, and retrieval. Part icularly, the storage, transmission, and retrieval of massive bio-information should meet several co mpulsory requirements: 1) high efficiency for rap id transmission and prompt retrieval; 2) strict information security to guarantee users’ privacy; 3) high data fidelity to preserve the pathological information; 4) affordable cost for sustainable storage. Yet, vast amount of bio-signals generated by the long-term This work was supported by the research committee of University of Macau under grant No. MYRG2014-00060-FST and Science and Technology Development Fund (FDCT ) of Macau Government under Grant No. 016/2012/A1. JiaLi MA, TanTan ZHANG, and MingChui DONG are with Electrical and Computer Engineering Department, Faculty of Science and Technology, University of Macau (e-mail: [email protected], [email protected], [email protected]).
e-health pose a huge threat and unaffordable burden to the source-limited mobile devices regarding cost effective storage, economical rap id transmission, and timely retrieval feedback. To address this problem, e-health oriented bio-signals compression technique comes into play. During the past several decades, various methods have been proposed for electrocardiogram (ECG) co mpression, among which lossy methods are preferred to lossless methods in pursuit of high compression ratio (CR) [1]. Existing ECG compression schemes can be roughly classified into direct, transform, and parameter extract ion methods [2] where the first two types are prevalent due to their reversibility. For transform methods, the original signal is firstly deco mposed by means of a linear orthogonal transformat ion, and then the expansion coefficients are properly encoded for further co mpression. The commonly used transform methods include Fourier transform [3], Hermite transform [4], [20], d iscrete cosine transform [5], [18], Walsh transform [6], Karhunen-Loeve transform [7], and wavelet transform [8]-[10], [16], [17], [24]-[26]. Despite their performance in data volu me reduction, several challenges arise accordingly. First, most transform methods require p reprocessing (i.e. wave detection and/or beat segmentation) before compression, which leads to increased computation and might degrade the compression performance once incorrect preprocessing occurs. Second, the expansion basis is predetermined in general, which would limit the compression performance intrinsically. Third, since the compressed ECG signals still expose some of the crucial ECG features [12], [19], there exist risks of information disclosure and malicious abuse by unauthorized person with knowledge of the compression mechanism. Tackling these bottleneck problems, this paper presents a novel transform co mpression method based on adaptive Fourier decomposition (AFD) algorith m hybrid ized with symbol substitution (SS) technique. AFD has already been explo ited and validated for signals decomposition in Hardy H2 and Hilbert L2 space [11]. This work is the first attempt to adapt AFD algorith m fo r real-valued ECG co mpression. Unlike most transform methods, AFD relieves the requirement of preprocessing and generates input-dependent basis adaptively to achieve high efficiency and fidelity. Afterwards, the AFD compression results are encoded losslessly using SS technique to enhance CR wh ile maintain the reconstruction quality. Here, SS also serves the purpose of built-in encryption
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2357841, IEEE Journal of Biomedical and Health Informatics
IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. XX, NO. XX, DD MMMM YYYY
2
Compression 1 Original ECG Signal
st
Stage (lossy)
Hardy Projection
2nd Stage (lossless) SS Encoding
AFD
Compression Results
Decompression Reconstructed ECG Signal
Back Projection
Weighted Sum
SS Decoding
Fig. 1. Compression and decompression procedures of the proposed method.
simu ltaneously. In all, the proposed method provides an alternative for ECG co mpression with high co mpression efficiency, reconstruction fidelity, and information security. Rest of this paper is organized as follo ws. Section II introduces the proposed method in detail. In Section III, the method is validated by employing MIT-BIH arrhyth mia benchmark database and the results are listed out. Co mparisons and discussions are given in Section IV and V respectively. Finally, Section VI concludes the paper.
gives rise to Fourier system. The modified TM system distinguishes itself in selecting a n adaptively according to input signals rather than utilizing prescribed {a n } sequence in traditional TM system. Hence the system is capable of catering to various kinds of signals including ECG signals. AFD conducts expansion of signals from H2 and L2 space into weighted Bn components. For real-valued signal G decomposition, it should be firstly projected into H2 space to get the corresponding projection signal G+. Afterwards G+ will be decomposed as in (2).
II. M ET HOD AFD is the generalization of conventional Fourier decomposition method combined with greedy algorith m to expand input signal into a series of mono-co mponents in modified Takenaka -Malmqu ist (TM) system [11]. By pursuing maximal energy gain in each decomposition iteration, AFD generates tailor-made input-dependent basis adaptively. Hence several advantageous features are highlighted in AFD: 1) fast convergence in both energy and point-wise sense; 2) efficient computing time; 3) robustness [11]. Benefit fro m these merits, AFD possesses wide applicability for mu ltifarious signals decomposition as well as the potential for efficient data compression in e-health oriented applications . Fig. 1 depicts the procedures of ECG co mpression and decompression using the proposed method. The compression consists of two stages. The first stage carries out Hardy projection and AFD lossy compression, follo wed by the lossless encoding using SS technique in the second stage. Here, SS fulfills built-in data encryption simultaneously to guarantee informat ion security of the compression results. For the decompression, it is the inverse process of compression and possesses quite low co mputation comp lexity with simple calculations.
G z C p Bp z
where Cp is the pth coefficient of basis Bp . A complete expansion includes the calculation of coefficient Cp and the selection of a p in basis Bp under the princip le of greedy algorith m [11]. Since AFD endeavors to obtain the maximal energy gain at each iteration, a set of evaluators {ea } consisting of the elementary functions in (3) are emp loyed to facilitate computation and evaluate energy gain during decomposition. 1 | a |2 1 , a D (3) 2 1 az The first expansion starts with representation of G+ as G1 , and C1 is obtained by calculating inner product between G1 and ea1 in (4). ea z B1 z
C1 G1 , ea1 2 1 a1 G1 a1 , a1 D 2
1 | an |2 1 an z
z ak , n 1, 2, ... k 1 1 ak z
G ,e G a , a D
a1 arg max | C1 |2 arg max
arg max 2 1 a
2
2
1
2
a
(5)
1
Here, the result after the first decomposition is
AFD is based on the modified TM system {Bn } as in (1).
1 2
(4)
where a 1 is selected according to the maximal pro jection 2 principle (MPP) as in (5) that, for any G1 H there exists a 1 in 𝔻 such that energy |C1 |2 is maximal.
A. Mathematical Foundation of AFD Algorithm
Bn z
(2)
p 1
G1 G1 , ea1 ea1 r1
n 1
(1)
where a n is a complex nu mber adaptively selected inside the open unit disc 𝔻 (𝔻 = {z∈ℂ: |z|
IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. XX, NO. XX, DD MMMM YYYY
1
A Novel ECG Data Compression Method Using Adaptive Fourier Decomposition with Security Guarantee in e-Health Applications JiaLi MA, TanTan ZHANG, and MingChui DONG Abstract—This paper presents a novel electrocardiogram (ECG) compression method for e-health applications by adapting adapti ve Fourier decomposition (AFD) algorithm hybridized with symbol substitution (SS ) technique. The compression consists of two stages: 1st stage AFD executes efficient lossy compression with high fidelity; 2nd stage SS performs lossless compression enhancement and built-in data encryption which is pivotal for e-health. Validated with 48 ECG records from MIT-BIH arrhythmia benchmark database, the proposed method achieves averaged compression ratio (CR) of 17.6 to 44.5 and percentage root mean square difference (PRD) of 0.8% to 2.0% with a highly linear and robust PRD-CR relationship, pushing forward the compression performance to an unexploited region. As such, this work provides an attractive candidate of ECG compression method for pervasive e-health applications. Index Terms—Adaptive Fourier decomposition, data encryption, ECG compression, e-health, information security.
T
I. INT RODUCT ION
HE ubiquitous deployment of body sensor network (BSN) and vigorous advance of information and communication technology (ICT) have dramat ically fostered the e-health development. With the aid of low cost portable or wearable embedded-link devices, e-health provides the accessibility to monitor and diagnose human wellness remotely and flexibly. In implementing and improv ing pervasive e-health, bio-informatics plays an important ro le through the management of bio medical informat ion acquisition, processing, storage, transmission, integration, and retrieval. Part icularly, the storage, transmission, and retrieval of massive bio-information should meet several co mpulsory requirements: 1) high efficiency for rap id transmission and prompt retrieval; 2) strict information security to guarantee users’ privacy; 3) high data fidelity to preserve the pathological information; 4) affordable cost for sustainable storage. Yet, vast amount of bio-signals generated by the long-term This work was supported by the research committee of University of Macau under grant No. MYRG2014-00060-FST and Science and Technology Development Fund (FDCT ) of Macau Government under Grant No. 016/2012/A1. JiaLi MA, TanTan ZHANG, and MingChui DONG are with Electrical and Computer Engineering Department, Faculty of Science and Technology, University of Macau (e-mail: [email protected], [email protected], [email protected]).
e-health pose a huge threat and unaffordable burden to the source-limited mobile devices regarding cost effective storage, economical rap id transmission, and timely retrieval feedback. To address this problem, e-health oriented bio-signals compression technique comes into play. During the past several decades, various methods have been proposed for electrocardiogram (ECG) co mpression, among which lossy methods are preferred to lossless methods in pursuit of high compression ratio (CR) [1]. Existing ECG compression schemes can be roughly classified into direct, transform, and parameter extract ion methods [2] where the first two types are prevalent due to their reversibility. For transform methods, the original signal is firstly deco mposed by means of a linear orthogonal transformat ion, and then the expansion coefficients are properly encoded for further co mpression. The commonly used transform methods include Fourier transform [3], Hermite transform [4], [20], d iscrete cosine transform [5], [18], Walsh transform [6], Karhunen-Loeve transform [7], and wavelet transform [8]-[10], [16], [17], [24]-[26]. Despite their performance in data volu me reduction, several challenges arise accordingly. First, most transform methods require p reprocessing (i.e. wave detection and/or beat segmentation) before compression, which leads to increased computation and might degrade the compression performance once incorrect preprocessing occurs. Second, the expansion basis is predetermined in general, which would limit the compression performance intrinsically. Third, since the compressed ECG signals still expose some of the crucial ECG features [12], [19], there exist risks of information disclosure and malicious abuse by unauthorized person with knowledge of the compression mechanism. Tackling these bottleneck problems, this paper presents a novel transform co mpression method based on adaptive Fourier decomposition (AFD) algorith m hybrid ized with symbol substitution (SS) technique. AFD has already been explo ited and validated for signals decomposition in Hardy H2 and Hilbert L2 space [11]. This work is the first attempt to adapt AFD algorith m fo r real-valued ECG co mpression. Unlike most transform methods, AFD relieves the requirement of preprocessing and generates input-dependent basis adaptively to achieve high efficiency and fidelity. Afterwards, the AFD compression results are encoded losslessly using SS technique to enhance CR wh ile maintain the reconstruction quality. Here, SS also serves the purpose of built-in encryption
2168-2194 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JBHI.2014.2357841, IEEE Journal of Biomedical and Health Informatics
IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. XX, NO. XX, DD MMMM YYYY
2
Compression 1 Original ECG Signal
st
Stage (lossy)
Hardy Projection
2nd Stage (lossless) SS Encoding
AFD
Compression Results
Decompression Reconstructed ECG Signal
Back Projection
Weighted Sum
SS Decoding
Fig. 1. Compression and decompression procedures of the proposed method.
simu ltaneously. In all, the proposed method provides an alternative for ECG co mpression with high co mpression efficiency, reconstruction fidelity, and information security. Rest of this paper is organized as follo ws. Section II introduces the proposed method in detail. In Section III, the method is validated by employing MIT-BIH arrhyth mia benchmark database and the results are listed out. Co mparisons and discussions are given in Section IV and V respectively. Finally, Section VI concludes the paper.
gives rise to Fourier system. The modified TM system distinguishes itself in selecting a n adaptively according to input signals rather than utilizing prescribed {a n } sequence in traditional TM system. Hence the system is capable of catering to various kinds of signals including ECG signals. AFD conducts expansion of signals from H2 and L2 space into weighted Bn components. For real-valued signal G decomposition, it should be firstly projected into H2 space to get the corresponding projection signal G+. Afterwards G+ will be decomposed as in (2).
II. M ET HOD AFD is the generalization of conventional Fourier decomposition method combined with greedy algorith m to expand input signal into a series of mono-co mponents in modified Takenaka -Malmqu ist (TM) system [11]. By pursuing maximal energy gain in each decomposition iteration, AFD generates tailor-made input-dependent basis adaptively. Hence several advantageous features are highlighted in AFD: 1) fast convergence in both energy and point-wise sense; 2) efficient computing time; 3) robustness [11]. Benefit fro m these merits, AFD possesses wide applicability for mu ltifarious signals decomposition as well as the potential for efficient data compression in e-health oriented applications . Fig. 1 depicts the procedures of ECG co mpression and decompression using the proposed method. The compression consists of two stages. The first stage carries out Hardy projection and AFD lossy compression, follo wed by the lossless encoding using SS technique in the second stage. Here, SS fulfills built-in data encryption simultaneously to guarantee informat ion security of the compression results. For the decompression, it is the inverse process of compression and possesses quite low co mputation comp lexity with simple calculations.
G z C p Bp z
where Cp is the pth coefficient of basis Bp . A complete expansion includes the calculation of coefficient Cp and the selection of a p in basis Bp under the princip le of greedy algorith m [11]. Since AFD endeavors to obtain the maximal energy gain at each iteration, a set of evaluators {ea } consisting of the elementary functions in (3) are emp loyed to facilitate computation and evaluate energy gain during decomposition. 1 | a |2 1 , a D (3) 2 1 az The first expansion starts with representation of G+ as G1 , and C1 is obtained by calculating inner product between G1 and ea1 in (4). ea z B1 z
C1 G1 , ea1 2 1 a1 G1 a1 , a1 D 2
1 | an |2 1 an z
z ak , n 1, 2, ... k 1 1 ak z
G ,e G a , a D
a1 arg max | C1 |2 arg max
arg max 2 1 a
2
2
1
2
a
(5)
1
Here, the result after the first decomposition is
AFD is based on the modified TM system {Bn } as in (1).
1 2
(4)
where a 1 is selected according to the maximal pro jection 2 principle (MPP) as in (5) that, for any G1 H there exists a 1 in 𝔻 such that energy |C1 |2 is maximal.
A. Mathematical Foundation of AFD Algorithm
Bn z
(2)
p 1
G1 G1 , ea1 ea1 r1
n 1
(1)
where a n is a complex nu mber adaptively selected inside the open unit disc 𝔻 (𝔻 = {z∈ℂ: |z|
