Robust Low-Power Algorithm for Random Sensing Matrix for Wireless ECG Systems Based on Low Sampling-Rate Approach

doi:10.4236/jsip.2013.43B022

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Journal of Signal and Information Processing, 2013, 4, 125-131

doi:10.4236/jsip.2013.43B022 Published Online August 2013 (http://www.scirp.org/journal/jsip)

125

Robust Low-Pow er Al gori t hm f or Ran d om S ensin g Mat rix

for Wireless ECG Systems Based on Low Sampling-Rate

Approach

Mohammadreza Balouchestani*, Kaamran Raahemifar, Sridhar krishnan

Electri cal and C omputer Engineering Depart ment , Ryerson University, Toronto, Canada.

Email: mbalo uch@ee. r yer son. ca, kraahe [email protected], K r ishn a@ ee.ryerson.ca

Received April, 2013.

ABSTRACT

The main dra wbac k of curr ent E CG syst ems i s the loc atio n-specific nature of the systems due to the use of fixed/wired

applications. That is why there is a critical need to improve the current ECG systems to achieve extended patient’s mo-

bility and to cover security handling. With this in mind, Compressed Sensing (CS) procedure and the collaboration of

Sensing Matrix Selection (SMS) approach are used to provide a robust ultra-low-power approach for normal and ab-

normal ECG signals. Our simulation results based on two proposed algorithms illustrate 25% decrease in sampling-rate

and a good le vel of quali ty for the degree of incoherence between the random measurement and sparsity matrices. The

simulation resu lts also co nfirm that the Binar y Toeplitz M atrix (BT M) provides the best compressio n perfor mance with

the highes t energ y efficiency for r andom sensing matrix.

Keywords: Sensing Matrix; Power Consumption; Normal and Abnormal ECG Signal; Compre s sed Sensing; Block

Sparse Bayesian learning

1. Introduction

WBANs as a special purpose of Wireless Sensor Net-

works (WSNs) consist of tiny Biomedical Wireless Sen-

sors (BWSs) and a Gate Way (GW) to connect to the

external databases in the hospital and medical centers [1].

The WBANs are expected to be a breakthrough in

healthcare areas such as hospital and home care, Mobile

Health (MH), Electronic Health (EH), and physical reha-

bilitation. The GW could connect the BWSs, to a range

of wireless telecommunication networks. These wireless

telecommunication networks could be either mobile

phone networks, standard telephone networks, dedicated

medical center or using public Wireless Local Area

Networks (WLANs) nodes also known a Wi-Fi system

[2]. The compressed sensing is a revolutionary idea for

the acquisition and recovery of sparse signals that

enables sampling-rate significantly below the classical

Nyquist-rate (NR). The electrocardiogram (ECG) signals

are widely used in health care systems because they are

noninvasive mechanisms to establish medical diagnosis

of heart diseases. The current ECG systems suffer from

important limitations: limited patient’s mobility, limited

energy, limited on wireless applications. In order to fully

exploit the benefits of WBANs such as EH, MH, and

Ambulatory Health Monitoring Systems (AHMS) the

power consumption and sampling rate should be re-

stricted to minimum. Long-term records of ECG signals

in WBANs have become commonly used to collect in-

formation from the heart for diagnostic and therapeutic

purposes [3]. That is why the quantity of data grows sig-

nificantly and compression is required for reducing the

storage, trans missio n times, a nd p o wer consu mption. T he

ECG si gnals generally illustrate the redundancy bet ween

adjacent heartbeats due to its semi-periodic structure [4].

It is evident that this redundancy provides a high fraction

of common support between consecutive heartbeats that

is a good candidate for compression. Howe ver, the y have

low-frequency and non-stationary features and

processing noise setting strong characters, neither

time-demine nor frequency-domain based methods are

suitable for analyzing these signals. This paper presents

new algorithms with contribution of CS approach in

mind, and SMS procedure based on Dynamic Thre-

sholding Approach (DTA) to establish a robust ul-

tra-low-power for normal and abnormal ECG signals.

The CS theor y indicate that s a small number of rando m

linear measurements of sparse signals contain enough

information to collect, process, transmit, and recover the

original signal [5]. This approach emphasizes that the

signal representing sparsity in any orthogonal basis can

Robust Low-Power Algorithm for Random Sensing Matrix for Wireless

ECG Systems Based on Low Sampling-Rate Approach

126

be well reconstructed usi ng ℓ1 norm minimization, while

satisfying the Restricted Isomerty Property (RIP) condi-

tion fo r ra nd om mea s ur e me nt ma tr i x

and or tho go nal

in any domain [6]. Our simulation results based on

two proposed algorithms illustrate 25% decrease in sam-

pling- rate and a good level of quality for the degree of

incoherence between the ra ndom measurement a nd spar-

sity matrices. The simula tion results al so c onfir m that th e

Binary Toeplitz Matrix (BTM) provides the best com-

pression performance with the highest energy efficiency

for rando m sensi ng matrix. The structure of this paper is

organized as follows: Section 2 gives an overview about

CS theory in general and specifically for WBANs. Sec-

tion 3 proposes the new algorithm based on combination

of CS theory, and SMS approach. The reminder of the

paper is categorized in the following way: the simulation

results are presented in Section 4. The conclusion is

drawn in Section 5.

2. Overview of Compressed Sensing

The conventi onal sampling app roaches have traditionally

relied on the Shannon sampling theorem. This theory

says a signal must be sampled at least twice its band-

width in order to be represented without error. The tradi-

tional approaches have two important drawbacks. First,

they generate huge samples for many applications with

large bandwidth that is not tolerated. Second, even for

low signal bandwidths such as ECG signals, they pro-

duced a large amount of redundant digital samples. That

is why it is desirable to reduce the number of acquired

ECG samples by using advantages of the sparsity. The

CS theory replaces the conventional sampling and

reconstruction operation with a general random linear

measurement process and an optimization scheme in

order to recover original signal from a small number of

rand o m mea sureme nt s.

2.1. Basic Theorem

The goal in the digital-CS theory as a new sampling

scheme is to reduce the load of sampling-rate by de-

creasing the number of samples after the Analog to Digi-

tal Convertor (ADC) required to completely describe a

signal by explo iting its compr essibility [7]. An important

aspect of CS theory is that the measurements are not

point samples but more general linear functions of the

signals. Any compressible or sparse signal



in ℝN can

be expressed as:

= Ψ

∑

. (1)

The compresses signal



can also be found as:

[][] []

MMN N

× ××

= Φ

. (2)

Thus, the c ompressed s ignal is found a s :

1 11

[][] [][][] []

MMNNN NMN N

×× ××××

=ΦΨ =Θ

. (3)

Fortunately,

[]Φ

and

[]Θ

have two interesting and

useful pro perties. First, they ar e incoherent with the basis

[]Ψ

. Second, they have the RIP with high probability

where is suitable condition to recover the original signal in

the receiver si de [8]. Thus , CS scen ario has two important

steps. First step i n CS offers a stable measure ment matr ix

[ ]

MN×

to ensure that the salient information in any

compressible signal is not damaged by the dimensionality

reduction from D ∈ℝN down to ℂ∈ℝM. 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. Therefore, we can

exactly reconstruct the original signal D with high prob-

ability via 1 norm by solving the following convex op-

timization pr oblem (

ss=

∑



min

s∈





subject to

S= ΦΨ

. (4)

There are two important conditions, which guarantee

the correctness of this recovery. Firstly, the number of

random linear measurements, the number of coefficients,

and the number of non-zero coefficients must satisfy the

following equatio n [9]:

/ (log)M KCN≤

. (5)

Secondly, for any vector

of the original signal

[]D

matrix

[]Φ

must satisf y the following co ndition for

some



1 /1aa

εε

− ≤Φ≤+ 

(6)

where satisfies RIP property for the random dictionary

matr ix. In order to recover K-sparsity of t he origi nal sig-

nal, now we have

MK×

system of linear equations,

with M equations and K unknowns. It is possible to find

out the K-sp arsity of the original signal, because of

MK≥

2.2. Compressed Sensing in WBANs

The CS theory says sparse or compressible signals such

as ECG; signals can be well recovered using to minimize

ℓ1 norm optimization, while satisfying the RIP condition

for the random measurement matrix Ф and orthogonal

basis ψ. Basically, the biomedical signals are sparse or

near sparse. To verify this condition, we exploit a con-

ventional Fast Fourier transformation (FFT) to check

signal sparsity. These signals have K non-zero coeffi-

cients and (N-K) zero coefficients with K N and can

be well recovered using M projects or measurements

Robust Low-Power Algorithm for Random Sensing Matrix for Wireless

ECG Systems Based on Low Sampling-Rate Approach

127

such as K≤ M<<N. As the result, the small number of

non-zero coefficients is small; the CS theory can be ap-

plied to reduce the load of sampling. Figure 1 illustrates

CS theory in WBANs .

Figure 1. CS in WBANs.

As it can be seen the biomedical signals are com-

pressed by wireless sensors. The collected compressed

biomedical data are then transmitted wirelessly to Access

Points (APs) at hospital, ambulance, and helicopter [10,

11]. The APs recover compressed biomedical data for

diagnostic and therapeutic purposes. Further mor e, the D

data vector in WBANs is a sparse vector, because the GW

needs to collect only M bits instead of N bits of data

(M≈K– spa rs e) t hr ou gh the ne t wor k. In t he W B AN s wit h

N wireless senso r, senso r

is acquiring a sa mple i

d of

the hum an body [9]. Th e final goal in WBANs for medical

applications is to collect Data's vector D of N wireless

senso rs in a s uit able basis Ψ= [Ψ1][Ψ2]…[ΨN] like:

= Ψ

∑

. (7)

CS suggests that, under certain conditions, instead of

collecting data vector D, we can collect compressed ve c-

tor

[][][]D= Φ

 where Φ is (K×N) sensing matrix

whose entries are i.i.d random variables. In non-CS sce-

nario a node is receiving N-1 packets and sends out N

packets ((N-1) received packets plus its data) each packet

corresponding to data sample from a node. In WBANs

with CS theory the GW needs only to receive M

(M≈K-sparse) packets [9]. In order to use CS, each node

needs to know the value of Compressed Ratio (CR=N/ K)

that is constant and value of N [16]. The node i compute

K=N/CR and generate K values Φji (1≤ j ≤k) and creates a

vector Di [Φ1 i, Φ2 i… Φk i], where Di is its own data. Typ-

ically, node i would wait to receive from all its down-

stream neighbors. Each received packet carries its index

from 1 to K, so that it can be added to the data already

waiti ng in i with the same index (either locally produced

or received from a neighbor). Then node i would send

exactly K-Packets corresponding to the aggregated col-

umn vec tor s . Now the diff erence between CS and non-CS

operation becomes clear [10]: CS operation requires each

node to send exactly M packets irrespective of what it has

received, and each node needs to know CR and N and then

computes the value of (M≈K). The received vector in GW

can be written as:

[][] []

MMN N

× ××

= Φ. (8)

Consequently, the received vector in GW is a con-

densed representation of the sparse events and can be

expressed like:

1111 1

MMMN N

ΦΦ

 

 

ΦΦ

 



 



. (9)

Our simulation r esults sho w that b y emplo ying the C S

the WBANs can achieve a higher transmission, a lower

time delay and higher probability of success of data

transmission. Therefore, a combination of CS theory to

WBANs is an optimal solution for achieving robust

WBAN with low sampling rate and power consumption.

As it can be seen the biomedical signals are compressed

by wireless sensors. The collected com pressed biomedical

data are then transmitted wirelessly t o Access Points (APs)

at hospital, ambulance, and helicopter [10, 11]. The APs

recover compressed biomedical data for diagnostic and

therapeutic purposes.

3. Proposed Approach

To validate the performance of the considered compres-

sion schemes three performance measurements are de-

fined in this section first. Then, the proposed algorithm

for selecting the best fit for random sensing matrix is

proposed.

3.1. Performance Measure

The Compression Ratio (CR), the Structural Similarity

Index (SSI), and Percentage Root-mean-square Differ-

ence (PRD) are employed as performance measures in

our approach. The CR is found as follows [12]:

/ 100CRN M= ×

, (10)

where M and N are the number of random linear mea-

surements and number of samples in ECG signals re-

spectively. Further, our simulation results indicate that

satisfying quality of SR can be achieved when CR does

not exceed of 35%. The SSI metric is defined as [13]:

(/)100SSI D= ×

, (11)

where

and



are the original and recovered ECG

signals respectively. This metric measure the similarity

between the recovered and original ECG signals [14].

Higher SSI means better recovery quality. Our simulation

results will show the proposed approach has this ability to

achieve SSI with value close to 100%. The PRD is com-

puted as [14]:

Robust Low-Power Algorithm for Random Sensing Matrix for Wireless

ECG Systems Based on Low Sampling-Rate Approach

128

(/) 100PRD DD

=−×

 . (12)

The value of PRD shows the quality of reconstruction

approach. The relationship between the measured PRD

and diagnostic distortion is recognized on the weighted

diagnostic data for ECG signals, which classi fies the dif-

ferent va lues o f PRD based o n the signal quality obtained

by a specialist. Table 1 illustrates the resulting different

quality classes and corresponding PRD values. As de-

picted in Table 1, lower PRD means better recovery

quality.

Table 1. Different Quality Classes.

PRD

Quality of recovery

0 1%

Excellent

1 2%

Very good

2 0.85%

Good

0.85%≥

Poor

3.2. Proposed SMS Algorithm

The random measurement matrix

[]Φ

is a key compo-

nent of CS theory. Two key features are needed for a

successful implementation of CS approach: Sparsity of

the biomedical signal and incoherence between the ran-

dom sensing matrix and the sparsity basis [15]. That is

why; the random sensing matrix must exhibit a high de-

gree of incoherence with the sparsity basis

[]Ψ

. In this

part, the new SMS procedure is presen ted to select the best

fit for the random sensing matrix

[]Φ

. Herein, Bernoulli

Toeplitz, Gaussian Circulant, and Binary Toeplitz ma-

trices are examined to find out the best fit for random

sensing matrix [16]. The Toeplitz matrix is a matrix in

whic h eac h de sce ndi ng dia go nal fro m left to right is co n-

stant. The random sensing matrix in Binary form is ex-

pressed as:

01 1

1 10

− −+

−

ΦΦ Φ





ΦΦ Φ



Φ=



Φ ΦΦ





 



(13)

The Circulant matrix is a special kind of Toepliz ma-

trix where each row vector is rotated on element to the

right relative to the preceding row vector [17]. The ran-

dom sensing matrix in Circulant form is illustra te d as:

01 1

10 2

1 10

−

ΦΦ Φ





ΦΦ Φ



Φ=



Φ ΦΦ





 



(14)

In the simulation part, CS approach is applied on the

ECG data obtained from MIT-BIH database for three

sensing matrix possibilities: (1) Bernoulli Toeplitz matrix,

(2) Gaussion Circulant matrix, and (3) Binary Toeplitz

matrix. Our simulation results will further confirm that the

Binary Toeplitz matrix shows the best performance for the

random sensing matrix

. Table 2 illustrates our new

algorithm to select the best fit for random sensing ma-

trix

Table 2. The best fit for sensing matrix.

Algorithm: The Best Fit for Random Sensing Matrix

Enter: Raw ECG data

1: Apply Dynamic Thresholding Approach to Raw ECG data

2: Select Initial Square Matrix

3: Apply Row Se l ection Schem e (select the fir st M ro ws as the in it ia l

sensing matrix

)

4: Compare with Binary Toeplitz Matrix

5: If

is Binary Toeplitz Matrix Stop, the Algorithm is completed

6: M=M+1

7: Go to Step 4

In the step 1 of the proposed algorithm, the DTA pro-

cedure is applied to the raw ECG data. The princip al ob-

jective of the DTA is to vary the sparsity level of a raw

ECG signal to convenient level [18]. 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 [19]. In the step 3, a Row

Selection Scheme (RSS) is applied to reduce the number

of rows from N to M [20]. Two RSSs approaches are

compared: (1) select first M rows from the initial

NN×

matrix, and (2) randomly select M rows from

the initial

NN×

matrix. The first RSS approach de-

monstrates better performance than the second RSS ap-

proach. So only the first RSS approach is utilized in the

proposed algorithm.

4. Simulation Results

The following assumptio ns w e r e made for simulation:

► Experiments are carried out over a 10-minute s E CG

signal from MIT-BIH database [21] .

► One hundred repletion’s are averaged for our simu-

lation results. To validate the simulation results ECG

signals from records 100,107,115 and 117 of MIT-BIH

are investigated.

►The mean of ECG blocks is rounded in the sliding

window to the nearest multiple of

, where

is the

BSBL level [22].

►To simulate SNR for ECG signals the follo wing eq-

uation is used [23].

20log (0.01)SNR PRD= −

. (15)

►Three sensing matrix possibilities are examined for

rand om sens ing mat rix

: (1) Bernoulli To eplitz matrix,

(2) Gaussian Circulant matrix, and (3) Binary Toeplitz

Robust Low-Power Algorithm for Random Sensing Matrix for Wireless

ECG Systems Based on Low Sampling-Rate Approach

129

matrix [24].

►The SPARCO toolbox is used for testing sparse re-

const ructio n algorithm.

►The SPGL1 (Spectral Projected Gradient for 1

mi-

nimization) toolbox is used to determine Large-scale

one-norm regularized least squares in the following equ-

ation:

min 1

c∈





subject to

D= Φ

. (16)

►To validate the simulation results, the BPBQ (Basis

Pursuit DeQuantizer) toolbox is used for recovery of

sparse signals from quantized random measurements to

solve [25]:

argmin 1

c∈





subject to

D−Φ 

for

2p≥

. (17)

►The simulation results were obtained for an input

signal of N=512 samples and a 12-bits resolution for the

input signal and t he me asure ment signal



►To simulate the SMS approach, the DTA framework

is used to vary the sparsity level [26].

Figure 2 illustrates the sampling-rate for random bi-

nary matrix with CS theory for different values of

non-zero entries

for specific records of ECG sig na ls.

Figure 2. Sampling-rate.

Based on the results of Figure 2 and suitability of the

rand om bina ry matri x, the sampling rate can be reduced

by 75% of NR without sacrificing the performance. Fig-

ure 3 shows simulation results on power consumption

for random binary matrix with CS theory in terms of

Compressed Ratio (CR) for specific records of ECG sig-

nals.

As depicted in the Fig. 3, the power consumption can

be reduced by 65% by employing CS theory. Table 3

compares the simulation results on sampling rate and

power consumption for random binary matrix with CS

theory.

Figure 3. The pow er consumpti on.

Table 3. Comparing SR and PC.

N in ECG CR SR PC

1024 10.24 25%*(NR) 30%*(PC in non-CS)

2048 20.48 28%*(NR) 35%*(PC in non-CS)

3074 30.74 32%*(NR) 40%*(PC in non-CS)

Table 2 indicates that satisfying quality on sampling

rate and power consumption can be achieved when CR

does not exceed of 30.

5. Future Work

We have simulated the benefit of CS to wireless ECG

systems for some recodes of ECG signals. Our future

work involves developing the CS theory to other records

of ECG signal, including abnormal records for wireless

ECG syst ems.

6. Conclusions

The ECG signal is widel y used in WB ANs becau se it is a

noninvasive way to provide medical diagnosis of heart

disea ses. This paper has presented new algorithm with a

contribution of CS approach, and SMS procedure based

on DTA aapproach to establish a robust ultra -low-power

for normal and abnormal ECG signals. The works by

Alvarado [2] and Baheti [14] focus only CS theory for

normal ECG signal with only random Gaussian matrix.

While the present study offers a new algorithm to select

the best fit for random sensing matrix of the CS approach

for normal and abnormal ECG signals. Our simulation

results validate the suitability of a new algorithm for a

real-time energy-efficient ECG compression on re-

source-constrained in WBANs. The simulation results

also confirm that t he Binary Toep litz matrix pro vides the

best compression performance with the highest energy

efficiency for random sensing matrix. Advanced ECG

Robust Low-Power Algorithm for Random Sensing Matrix for Wireless

ECG Systems Based on Low Sampling-Rate Approach

130

systems based on CS will be able to deliver healthcare

not only to patients in hospita l; but also in t heir homes.

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