Compressed Sensing and Classification of Cardiac Beats using

Patient Specific Dictionaries

Monica Fira

, Liviu Goras

1,2

, Victor-Andrei Maiorescu

1,2

and Mihaela Catalina Luca

1,3

Institute of Computer Science, Romanian Academy, Iaşi, Romania

“Gheorghe Asachi” Technical University of Iaşi, Iaşi, Romania

University of Medicine and Pharmacy, Iaşi, Romania

Keywords: ECG, Compressed Sensing, Classification.

Abstract: In this paper, we investigated the benefits of compressed acquisition for monitoring applications of patients

with various heart diseases. The possibility of heartbeat acquisition followed by classification into one of

two classes, namely, normal beats or pathological has been approached using patient-specific dictionaries.

Moreover, several types of projection matrices (matrices with random i.i.d. elements sampled from the

Gaussian or Bernoulli distributions, and matrices optimized for the particular dictionary used in

reconstruction by means of appropriate algorithms) have been compared. The dictionaries used in the

reconstruction phase were built with and without centred R waves.

1 INTRODUCTION

Based on the concept of signal sparsity in terms of

the atoms of a certain dictionary and making use of

classical decomposition algorithms the literature of

the latest years proposes and investigates the

interesting possibility of joining signal acquisition

and compression within the concept of compressed

sensing [Donoho 2006, Donoho 2004, Candes

2008]. It has been mathematically proved that if a

class of signals allow a representation in terms of a

small number of components in a properly selected

base (i.e., the signal is "sparse" in that specific base

or with respect to the atoms of a dictionary), the

signals can be reconstructed with a very good

precision from a reduced number of measurements

consisting of projections on random vectors by

solving a linear programming problem.

The decomposition of a signal in terms of an

over-complete dictionary it is not unique, and can be

obtained by means of general methods such as

method of frames (MOF), matching pursuit (MP)

and methods based on special dictionaries, such as,

the best orthogonal basis (BOB) or basis pursuit

(BP) [Elad 2007, Shaobing Chen 1998, Polania

2011, Zhang 2013].

2 BACKGROUND ON

COMPRESSED SENSING

Compressed sensing is a new concept in signal

processing basically consisting in minimizing the

number of measurements / projections to be taken

from signals that are sparse while still retaining the

information necessary to approximate them well.

Consider a family of signals

Rx ∈

known to

have sparse representations using at most T atoms

from a fixed dictionary

nxk

D ∈

. Such signals can

be described as

Dxj

=∀ ,

(1)

with

<<≤

where T is the sparsity of the

signals and the l

– norm counts the number of non-

zeros entries in

Compressed sensing consists of a joint sensing

and compression for such signals. Using a projection

matrix

pxn

P ℜ∈

with np

<<< , the

technique of compressed sensing seeks to represent

by p scalars y

given by

Pxy =

(2)

Fira, M., Goras, L., Maiorescu, V-A. and Luca, M.

Compressed Sensing and Classiﬁcation of Cardiac Beats using Patient Speciﬁc Dictionaries.

In Proceedings of the International Conference on Information and Communication Technologies for Ageing Well and e-Health (ICT4AWE 2016), pages 173-179

ISBN: 978-989-758-180-9

173

The original signal x

can be reconstructed from y

by exploiting the sparsity of it is representation so

that among all possible

satisfying

PDy

(3)

we seek the sparsest. If this representation coincides

with

, we get a perfect reconstruction of the

signal using equation 3.

(4)

In general this reconstruction is based on the

solution of

αα

PDy

min

(5)

which is known to be NP – hard even for moderate-

sizes of the linear system of the constraints.

Reconstruction algorithms are standard linear

programming algorithms with perhaps quadratic

constraints such as LARS, LASSO, SparseLab,

l1Magic, (Orthogonal) Basis Pursuit, (Orthogonal)

Matching Pursuit etc.

2.1 Compressed Sensed and

Key Problems

A key problem in CS is the choice or the

construction of the dictionary based on which the

compressed signal reconstruction is made. For many

classes of signals, dictionaries (time-frequency or

time-scale dictionaries) based on which good results

using the CS concepts have been obtained are

already known. Still, there are classes of signals for

which the use of standard dictionaries do not ensure

spectacular compression results, due to the fact that

the sparsity of these signals is not ensured. This

signal classes may require the construction of new

dictionaries to fit new types of data features. The

analytic construction of dictionaries such as

wavelets or curvelets stems from deep mathematical

tools from Harmonic Analysis. It may however be

difficult and time consuming to develop complex

mathematical theory each time a new class of data,

which requires a different type of dictionary, is met.

An alternative solution is dictionary learning, which

aims deduction the dictionary from a set of training

data [Fira 2010]. Dictionary learning, also known as

sparse coding, has the potential of ’industrialising’

sparse representation techniques for new data

classes.

Recent articles present the possibility of

combining the concepts of signal representation

using dictionaries with signal classification

concepts, solving the classification problems based

not on the concrete signal, but on a small number of

random measurements of the signal acquired using a

random projection matrix. Generally speaking, the

results of the classifications are influenced by two

important factors, namely the modality of

constructing the dictionary and the classifier used.

The possibility of classifying compressed signals

is extremely useful because it brings additional

information about the signal, information that will

allow the reconstruction of original signals using

specific dictionaries. In compressed sensing, in case

the sparsity of the signal cannot be ensured using a

single general dictionary, the use of specific

dictionaries will lead to a decrease of the

reconstruction error.

Starting from the mathematic fundaments of

compressed sensing, we aimed at the software

implementation of the compressed sensing for ECG

medical signals. The key element that appears in the

case of this type of signals is to find a dictionary that

would ensure the ECG signals sparsity in direct

connection to the reconstruction method.

2.2 Purpose and Objectives

Based on the results of the classification of acquired

heart rate compressed presented [Fira 2011a] and the

results for the patient-specific dictionaries presented

in [Fira 2011 b, Fira 2013], in this paper, we propose

a new method that combines the above previous

approaches. The aim is to develop and implement a

method for compressed sensed of ECG signal

together with the detection of the abnormal heart

beats and transmission of these beats to a center for

monitoring of people with heart diseases.

The proposed problem to solve is divided into the

following sub-problems:

• Construction of patient-specific dictionaries;

• Heartbeat classification;

• Compressed acquisition of abnormal heart

beats;

• Transmission of abnormally beats to a

surveillance center / recording of these beats for

further investigation by qualified personnel;

• Reconstruction of compressed sensed beats.

3 METHOD

Starting from ECG signals for which the position of

the R-wave is known exactly, we segment the ECG

signals in heart beats cycles. : A cardiac pattern

begins from the middle of an RR interval and

finishes at the middle of the next RR interval [Fira

ICT4AWE 2016 - 2nd International Conference on Information and Communication Technologies for Ageing Well and e-Health

174

2010]. Then, based on the ECG signal segmented in

cardiac cycles, we have developed two methods of

building patient-specific dictionaries, namely:

• Dictionary consisting in heart beats with

centered R wave;

• Dictionary with not centered R Wave.

3.1 Dictionaries Built from Cardiac

Beats with Centred R Wave

Each segment contains the P-wave, the QRS

complex and the T-wave and each cardiac segment

thus obtained was resampled at 301 samples so that,

after that all patterns will have the same dimension,

thus being possible to create a specific dictionary for

the ECG signals. To obtain cardiac patterns with

resampling and centred R wave, after segmentation

the peak of the R wave was positioned on sample

151 and then the whole beat was resampled such that

on the right and on the left of the R peak there will

be 150 samples i.e., the R wave will be positioned in

the middle.

NOTE: The resampling operation of the cardiac

segment on 301(150 samples on each side of the R

wave), which has as purpose to obtain cardiac

patterns with the same size, is a reversible

modification, as long as the information related to

the initial dimension is maintained.

50 100 150 200 250 300

900

950

1000

1050

1100

1150

1200

1250

Figure 1: Cardiac beat with centred R wave.

3.2 Dictionaries Built from Cardiac

Beats without Centred R Wave

When using segments with no R wave alignment,

the extracted segments are subsequently resampled

to 301 samples.

0 50 100 150 200 250 300

900

950

1000

1050

1100

1150

1200

1250

Figure 2: Cardiac beat without centred R wave.

3.3 Projection Matrices

It is known that the acquisition results are influenced

to some extent also by the type of matrix used for

acquisition. Therefore we analyzed the influence of

the compression matrix on acquisition and on the

classification of the compressed heartbeats, testing

three types of matrices, namely:

• Random matrix

• Bernoulli matrix

• Optimized matrix depending on dictionary

[Cleju 2011] - (product of random matrices and the

dictionary transposed)

3.4 KNN - k-Nearest Neighbours

The classifier used for heart beats classification is of

k-Nearest Neighbors (kNN) type. We opted for this

type of classifier since it is simple to implement in

practical applications even in hardware. For

improved results one can choose more complex

classifiers, but the results offered by this classifier

proved to be good enough; as a consequence we

selected it even for future hardware

implementations.

The kNN classifier was trained with normal and

abnormal heart beats evenly distributed on both

classes. The beats used to train the classifier were

extracted from the dictionary constructed for the

compressed acquisition.

3.5 Cardiac Patterns Reconstruction

For reconstructing the patterns we use the Basis

Pursuit algorithm to determine the coefficients. The

reconstruction of the compressed cardiac patterns is

based on using the above discussed patient specific

dictionary with or without centred R-wave. The

Compressed Sensing and Classiﬁcation of Cardiac Beats using Patient Speciﬁc Dictionaries

175

KNN

coef

> 6

min

< 6

min

ECG

cardiac

pattern

Compress

Recons.

ECG

Segment.

& resamp.

)(

Figure 3: Principle of the method.

patient specific dictionary consists of 700 cardiac

patterns.

3.6 Principle of the Method

Most of the methods proposed by different authors

do not capitalize the quasi periodic nature of the

ECG signal and the specific particularities of the

patient. Therefore, in this paper, we propose a

method that takes into account both advantages,

namely, working with heart beats (not with the ECG

signal as it is recorded) and secondly, the used

dictionaries are made of cardiac cycles taken from

the subject of acquisition. Thus, the first six minutes

of registration or previous recordings from the same

subject (if any) are used to build the dictionary

needed for reconstruction. Only after the dictionary

was built, the compressed sensing of the heart beats

starts, followed by the classification in normal or

pathological for each heartbeat and then the

transmission or storage of data when an abnormality

is detected.

For the implementation of the proposed method a

buffer memory is necessary. From the ECG recorded

samples that are stored in the processing buffer, full

cardiac beat cycles are extracted by detecting the

maxima of the R waves, followed by segmenting

between the midpoints of consecutive RR intervals.

When using segments with no R wave alignment,

the extracted segments are also subsequently

resampled to 301 samples. As already shown, for R

wave centred, each ECG segment is split in two

parts, one from the beginning of the segment to the

location of the R wave and the other one from there

to the end, and each part are independently

resampled to a length of 150 samples.

A block diagram of the proposed method is

shown in Figure 3.

3.7 Validation of the Compression

Method

We evaluated the distortion between the original and

the reconstructed signals by means of the percentage

root-mean-square difference (PRD) and its

normalized version, PRDN:

∑

−

nxnx

PRD

)(

))(

)((

100%

(6)

∑

−

xnx

nxnx

PRDN

))((

))(

)((

100%

(7)

where

)(nx

and

)(

are the samples of the

original and the reconstructed signals respectively,

is the mean value of the original signal, and N is

the length of the window over which the PRD is

calculated.

For compression evaluation we used the

compression rate (CR) defined as the ratio between

the number of bits needed to represent the original

and the compressed signal,

comp

orig

CR =

(8)

where

orig

and

comp

represent the number of bits

required for the original and compressed signals,

respectively.

ICT4AWE 2016 - 2nd International Conference on Information and Communication Technologies for Ageing Well and e-Health

176

4 EXPERIMENTAL RESULTS

To test the proposed method ECG segments from 14

ECG recordings (ID 100, 101, 102, 104, 105, 106,

119, 201, 202, 203, 210, 212, 217, 219) from the

MIT-BIH Arrhythmia [physionet] database were

used. The ECG signals were digitized through

sampling at 360 samples per second, quantized and

encoded with 11 bits. The MIT-BIH Arrhythmia

database, along the ECG signals, also contains

annotations of the cardiac beats for each of the

recordings.

0 50 100 150 200 250 300

900

950

1000

1050

1100

1150

1200

RED = Reconstructed Blue = Original *Black = Measured

Figure 4: Original and reconstructed cardiac beat.

Table 1 presents the mean results for 14 ECG

records for CR = 15:1 and tree types of confusion

matrices.

Table 1: Average Results for 14 ECG Records.

Projection matrix CR

Avg.

PRD

Avg.

PRDN

Classific

ation

rate

Patient specific dictionary with un-centered R-wave

Gaussian distribution

Random*Dict†(20*301)

15:1 0.78 11.98 92.24%

0 and 1 (with controlled

arrangement)(20*301)

15:1 0.94 16.06 84.71%

Gaussian distribution

Random (20*301)

15:1 0.82 13.82 91.14%

Patient specific dictionary with centered R-wave

Gaussian distribution

Random*Dict†(20*301)

15:1 0.51 9 93.41%

0 and 1 (with controlled

arrangement)(20*301)

15:1 0.71 12.4 88.06%

Gaussian distribution

Random (20*301)

15:1 0.72 12.51 89.70%

Since many authors report besides the average

results obtained on the MIT-BIH databases results

on record no. 117 we have presented such results in

Table 2. Heart beat rate classification of this record

is not calculated because it is not relevant. There are

mostly normal heart beats, so a classification in such

a situation is senseless.

Table 2: Average Results for the 117 Record.

Projection matrix CR

Avg.

PRD

Avg.

PRDN

Patient specific dictionary with un-centered R-wave

Gaussian distribution

Random*Dict†(20*301)

15:1 0.38 8.82

0 and 1 (with controlled

arrangement)(20*301)

15:1 0.56 12.81

Gaussian distribution

Random (20*301)

15:1 0.53 12.27

Patient specific dictionary with centered R-wave

Gaussian distribution

Random*Dict†(20*301)

15:1 0.38 8.73

0 and 1 (with controlled

arrangement)(20*301)

15:1 0.49 11.25

Gaussian distribution

Random (20*301)

15:1 0.48 11.15

In Table 3 we present results for reconstructed

cardiac patterns with and without centered R-wave

for CR = 4:1, 10:1 and 15:1 for Gaussian

distribution Random*Dict† projection matrix.

Table 3: Average Results for the 117 Record for CR = 4:1,

10:1, respectively 15:1 and matrix projection by type

Gaussian distribution Random*Dict†.

Projection matrix CR

Avg.

PRD

Avg.

PRDN

Patient specific dictionary with un-centered R-wave

Gaussian distribution

Random*Dict†(20*301)

4:1 0.19 4.36

10:1 0.29 6.77

15:1 0.38 8.82

Patient specific dictionary with centered R-wave

Gaussian distribution

Random*Dict†(20*301)

14:1 0.19 4.54

10:1 0.29 6.80

15:1 0.36 8.43

Table 4: Average Results for the 100 Record for CR = 4:1,

10:1, respectively 15:1 and matrix projection by type

Gaussian distribution Random*Dict†.

Projection matrix CR

Avg.

PRD

Avg.

PRDN

Classifi

cation

rate

Patient specific dictionary with un-centered R-wave

Gaussian distribution

Random*Dict†(20*301)

4:1 0.19 4.36 99.12%

10:1 0.29 6.77 98.17%

15:1 0.38 8.82 98.83%

Patient specific dictionary with centered R-wave

Gaussian distribution

Random*Dict†(20*301)

14:1 0.19 4.54 99.85%

10:1 0.29 6.80 96.27%

15:1 0.36 8.43 99.56%

Compressed Sensing and Classiﬁcation of Cardiac Beats using Patient Speciﬁc Dictionaries

177

In Table 4 we present results for record no. 100

for reconstructed cardiac patterns with and without

centred R-wave for CR = 4:1, 10:1 and 15:1 for

Gaussian distribution Random*Dict† projection

matrix and for classification witk KNN.

Table 5: Results for ECG Records for compression ratio

CR= 15:1 and centred R wave.

PPV_

class1%

PPV_

class2%

k-Nearest

Neighbors

ID_

ECG

Total

Classification

rate %

99.9 96.4 1

100

99.8

99.9 85.7 2 99.6

99.6 92.9 3 99.4

88.8 100.0 1

101

88.8

99.4 100.0 2 99.4

96.4 100.0 3 96.4

100.0 99.5 1

102

99.5

100.0 97.6 2 97.6

100.0 97.7 3 97.7

68.8 99.1 1

104

98.0

75.0 96.9 2 96.2

56.3 99.8 3 98.2

95.4 87.5 1

105

95.3

98.2 87.5 2 98.1

97.5 87.5 3 97.4

99.6 97.7 1

106

98.9

99.9 95.7 2 98.4

99.9 95.7 3 98.4

100.0 100.0 1

119

100.0

100.0 100.0 2 100.0

100.0 100.0 3 100.0

51.4 83.5 1

201

59.0

65.7 77.1 2 68.4

61.3 79.9 3 65.7

49.3 80.0 1

202

50.3

66.2 75.0 2 66.5

57.5 80.0 3 58.2

97.3 94.8 1

203

50.3

98.6 90.5 2 66.5

97.7 94.4 3 58.2

98.7 93.3 1

210

98.2

99.6 87.7 2 98.5

99.2 89.0 3 98.3

97.2 100.0 1

212

99.0

98.4 99.7 2 99.2

96.9 100.0 3 98.9

0.0 100.0 1

217

82.9

0.0 100.0 2 82.9

0.0 100.0 3 82.9

90.0 62.9 1

219

89.3

99.3 54.3 2 98.1

93.8 60.0 3 92.8

The positive predictive value (PPV) is defined as

FPTP

PPV

(9)

where a "true positive" (TP) is the event that the test

makes a positive prediction, and the subject has a

positive result under the gold standard, and a "false

positive" (FP) is the event that the test makes a

positive prediction, and the subject has a negative

result under the gold standard.

Table 6 contains the average results for 14

records from the database and also record no. 117

reported in [Polania et al. 2011a, b] and

[Mamaghanian et al. 2011].

Table 6: Other results for Average Values for 24 Records

and 117 Record.

Record /

Ave.

Avg.

PRD

Avg.

PRDN

Other Compression Algorithms

POLANIA [Polania

2011a,b]

117 8:1 2.18 Notspec.

POLANIA [Polania

2011a,b]

117 10:1 2.5 Notspec.

MAMAGHANIAN

[Mamaghanian

2011] for before and

after inter-packet

redundancy removal

and Huffman coding

Ave. for

14 recs

4:1

(75)

Before Huffman 35

After Huffman 15

10:1

(90)

Before Huffman >45

After Huffman >45

15:1

(93)

Before Huffman >45

After Huffman >45

Note that Mamaghanian in [Mamaghanian 2011]

presents a compression method followed by

Huffman coding. Thus the final CR is increased by

using Huffman coding. In [Mamaghanian 2011]

results are presented both before and after Huffman

coding. Therefore, for a relevant comparison our

results should be compared to those before Humman

coding reported in [Mamaghanian 2011].

Moreover, in the above work the compression

ratio expressed as

100*

orig

comporig

−

(9)

that is different from the formula used in this paper.

In Table 7 we presented the number of bits

required for the original and compressed signals

difference between the two formulas used

Mamaghanian in [Mamaghanian 2011] and by us in

this paper.

ICT4AWE 2016 - 2nd International Conference on Information and Communication Technologies for Ageing Well and e-Health

178

Table 7: Correspondence between CR used in

[Mamaghanian 2011] and in this paper.

100*

orig

comporig

−

used by Mamaghanian

comp

orig

CR =

used by us in this paper

Mamaghanian in this

paper

Mamaghanian in this

paper

10 1.11 91 11.11

20 1.25 92 12.50

30 1.43 93 14.29

40 1.67 94 16.67

50 2 95 20

60 2.5 96 25

70 3.33 97 33.33

80 5 98 50

90 10 99 100

5 CONCLUSIONS

In this paper the possibility to build and use patient-

specific dictionaries for compressed sensing heart

beats that are classified by a KNN type classifier as

normal and abnormal. The presented principle has

several significant features, namely:

• gives very good results for the classification in

two classes (normal and abnormal), i.e., detection of

abnormal compressed sensed heartbeats

• allows reconstruction for the compressed

sensed heartbeats

• needs few calculations in the compressed

acquisition stage

• uses a k-NN type classifier for the classification

stage, which also implies less complex calculations.

Taking into account all these aspects, this work

can be considered relevant for a first step in the

implementation of an algorithm for monitoring and

management of cardiac crisis situations.

ACKNOWLEDGEMENTS

This work was supported by a grant of the Romanian

National Authority for Scientific Research and

Innovation, CNCS – UEFISCDI, project number

PN-II-RU-TE-2014-4-0832 “Medical signal

processing methods based on compressed sensing;

applications and their implementation"

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Compressed Sensing and Classiﬁcation of Cardiac Beats using Patient Speciﬁc Dictionaries

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