Adaptive energy-aware encoding for DWT-based wireless EEG tele-monitoring system

ADAPTIVE ENERGY-AWARE ENCODING FOR DWT-BASED WIRELESS EEG

TELE-MONITORING SYSTEM

1,2Ramy Hussein, 1Alaa Awad, 1,2Amr A. El-Sherif, 1Amr Mohamed, and 2Masoud Alghoniemy 1Dept. of CS & Engineering, College of Engineering, Qatar University, Doha, QATAR 2Dept. Electronics and communications, Alexandria University, Egypt

1{rhussein; aawad; amr.elsherif; amrm}@https://www.360docs.net/doc/3e5594626.html,.qa

2alghoniemy@https://www.360docs.net/doc/3e5594626.html,.eg

ABSTRACT

Recent technological advances in wireless body sensor networks (WBSN) have made it possible for the development of innovative medical applications to improve health care and the quality of life. Electroencephalography (EEG)-based applications lie at the heart of these promising technologies. However, excess power consumptions may render some of these applications inapplicable. Wireless (EEG) tele-monitoring systems performing encoding and streaming over energy-hungry wireless channels are limited in energy supply. Hence, energy efficient methods are needed to improve such applications. In this work, an embedded EEG encoding system that is able to adjust its computational complexity is proposed; which lead to energy consumption according to channel variations. We analyze the computational complexity for a typical Discrete Wavelet Transform (DWT)-based encoding system. We also propose a power-distortion-compression ratio (P-D-CR) framework. Using the developed P-D-CR framework, the encoder effectively reconfigures the complexity of the control parameters to match the energy constraints while retaining maximum reconstruction quality. Results show that by using the proposed framework, higher reconstruction accuracy can be obtained regardless of the power budget of the utilized hardware.

Index Terms—EEG; DWT; distortion-compression ratio analysis; P-D-CR model; convex optimization.

1. INTRODUCTION

Wireless body sensor networks (WBSN) technologies have a great potential to offer convenient solutions for some medical problems in cost-effective ways. WBSN addresses in particular the mobility problem while the patient is under medical supervision. In wireless EEG monitoring systems, EEG data detection, compression and radio transmission are performed on mobile motes with limited energy ?[1]. The most important factor to determine the sustainability of a wireless device is how efficiently it manages its energy consumption.

EEG encoding and radio transmission powers are the most dominant components in limiting the lifetime of a wireless EEG monitoring device. Many encoding algorithms have been reported in the literature, most of which do not take power consumption into consideration; they always study the tradeoff between the compression ratio and distortion. A lossy EEG compression algorithm based on the wavelet packets (WP) transform was developed in ?[2]?[3], which showed a good balance between compression ratio and residual distortion for different WP bases, however, it introduced a significant increase in the computational complexity. The work in ?[4] provides an exhaustive system level comparison between Compressive Sensing (CS)-based and DWT-based compression techniques. It quantifies the potential of CS for low-complexity energy-efficient compression. However, it has limited control on the encoder parameters, which in turn cannot achieve the best trade-off between power consumption and distortion. The work in ?[5]?[6] has investigated, in detail, the practical performance of different implementations of the CS theory when applied to scalp EEG signals; the reconstruction accuracy is studied for 18 different implementations using different dictionaries and reconstruction methods. In contrast, while the computational complexity of the compression on the portable EEG unit is low, the high computational complexity of the CS decoder might hinder the real time applications in addition to high storage demands and low reconstruction accuracies (the minimum distortion was 18.61%). A novel compression technique has been developed in ?[7] to achieve low distortion compared to other traditional compression methods such as the 1-D set partitioning in hierarchical trees (SPIHT) ?[8]?[9], Tucker and Parafac ?[10]. This technique makes use of the inter-channel redundancy present between different EEG channels of the same recording and the intra-channel redundancy between the different samples of a specific channel. It uses the DWT and SPIHT in 2-D to encode the EEG channels. The characteristics of the recordings vary a lot between different

patients which hinders the stability of the method when used with recordings of different characteristics.

From the power consumption and distortion viewpoints, the effect of EEG encoding is two-fold. First, modest EEG compression results in low distortion at the expense of high power consumption. Second, more efficient EEG compression considerably reduces the amount of data to be transmitted, which in turn reduces the power consumption but at the expense of higher distortion. So, there is always a tradeoff between the power consumption and distortion ?[4].

There are three major contributions in this work. First, based on the complexity analysis of typical EEG encoding systems, we have developed a parametric encoding architecture which is fully scalable in power consumption. Second, we have successfully extended the conventional distortion-compression ratio (D-CR) analysis by considering

another dimension, the power consumption, and established the P-D-CR analysis framework for energy-constrained portable EEG devices. Third, and more importantly, at run-time, the proposed compression technique changes its parameters in real time according to the state of the channel based on the feedback signal from the receiver.

The rest of the paper is organized as follows; Section II describes the system model. The encoding complexity and its accompanied power consumption of a typical EEG encoder are explained in Section III. Section IV describes the conventional D-CR model; also, it studies the power and distortion behavior of the complexity control parameters. Section V introduces the proposed optimization scheme and explains the proposed energy-aware optimum algorithm. Section VI presents the simulation environment and results. Section VII concludes the paper.

2. SYSTEM MODEL

The general structure of a typical EEG encoder is illustrated in Fig. 1. It has the following encoding modules; amplifier ?[11]?[12], sampling, DWT, quantization, encoding of the quantized DWT coefficients and transmitter (RF module). Here, the distortion is measured as the Percentage Root Difference (PRD) between the recovered EEG data and the original one, also called the source coding distortion which can be written as follows,

(1) where x is the original signal, and is the reconstructed signal.

The compression ratio (CR) is evaluated as,

( )(2) Where, M is the number of samples that have absolute values greater than a threshold (in case of utilizing DWT compression technique) and N is the length of the original signal.

In this work, the EEG database in ?[13] is used. The database consists of five sets (denoted A-E), each containing

Fig. 1. General structure for a typical wireless EEG encoder

100 single-channel EEG segments; each one of them consists of 23.6 sec. Sets A and B represent healthy subjects, with eyes open and closed, respectively. Sets C and D represent non-active subjects diagnosed with epileptic disorder. Set E is taken from patients currently experiencing the epileptic seizure.

3. ENCODER COMPLEXITY ANALYSIS AND

POWER CONSUMPTION

For power scalable EEG encoder, encoding and transmission power consumptions can be estimated based on a set of parameters which control the computational complexity of each module for the system model in Fig. 1.

3.1. Encoding Power Calculation

With the aid of the block diagram in Fig. 1, the encoding power denoted by can be measured as follows,

(3) Where is the fixed power consumed by the amplifier [11], is the power consumed during the DWT compression, and is the power consumption in the sampling, quantization and encoding processes.

For threshold-based DWT, compression can be applied using one of the wavelet families, orders and decomposition levels ?[14]; samples that have absolute values greater than a predefined threshold are selected, and those below the threshold are discarded.

It should be noted that the wavelet series expansion for a function () is [14],

()∑()()∑∑()() (4) Where are the approximation coefficients. The scaling function ()is used to provide an approximation of ( )at a scale ; where is an arbitrary scale. The

approximation coefficients can be calculated using the inner product:

()? ()()?(5) ()are the details coefficients which provide the fine resolution. The wavelet function, ( ), is used in the computation of the details of ( ) as follows,

()? ()()? (6) The DWT implements eqns. (5) and (6) using a tree composed of low pass and high pass finite impulse response (FIR) filters.

It should be noted that the computational complexity (measured in number of instructions) of the DWT, denoted by , is

∑ (7) where F is the filter length of the utilized wavelet family and equals to (2*family order), L is the number of decomposition levels, and N is the length of the original signal. Therefore,

()(8) where is the power consumed per instruction.

The figure of merit (FOM) of the utilized analog-to-digital converter (ADC) is a design specification. In a subsequent analysis, the FOM used to obtain the power and distortion values is 100 nJ/conversion step, which is consistent with the general performance of modern ADCs ?[15]. For the sampling, quantization and encoding, the power consumption depends on the number of conversion steps (from samples to bits), which in turn depends on the input rate of the quantization and encoding modules (()sample/sec) and the energy consumed for each conversion step (). Therefore, the total power consumption in sampling, quantization and encoding denoted by can be computed as

()(9) where is the consumed energy at each conversion step. The signal length, N, can be represented as a function of the sampling rate, , as follows,

(10) where is the signal duration, ( seconds) ?[13]. From eqn. (3) and substituting with eqns. (8) and (9), the encoding power is

[∑ ]

() (11) 3.2. Transmission Power Calculation

The transmission power denoted by can be calculated directly as

()(12) where [ () is the transmission rate, n is the number of bits/sample, and is the energy consumed to transmit only one bit.

4. POWER-DISTORTION-COMPRESSION RATIO

(P-D-CR) MODEL ANALYSIS

The conventional distortion-compression ratio model does not consider the processing power of the encoder. As a consequence, choosing the CR based on the desired distortion only is not efficient for energy-constrained systems since it does not take the consumed power into consideration. In contrast, in the proposed model, both distortion and power consumption are studied versus the dominant encoder’s control parameters.

Fig. 2 shows how the power consumption and distortion are affected by the complexity control parameters, which include , and . In particular, Fig. 2-(a) and (b) illustrate how the power and distortion are affected by the compression ratio and filter length. Fig. 2-(d) and (e) illustrate the same parameters with compression ratio and sampling rate. Fig. 2-(c) and (f) show the integrated P-D-CR model for different filter lengths and sampling rate respectively. One can deduce that increasing the CR affects negatively the distortion but saves power. Regarding and , increasing them proposes a significant enhancement in the distortion but at the expense of increasing power consumption. As shown in Fig. 2, it is worthwhile mentioning that an underlying trade-off among the distortion and power consumption always exist regardless of the encoding parameters choices are. The optimization technique proposed in section V illustrates how to control the aforementioned encoder’s parameters in order to obtain the optimal distortion according to a typical power constraint. For a typical EEG dataset, the distortion can be obtained in a polynomial form of the encoder parameters () as follows,

(13) where are constants. Simulation results show that the Mean Square Error (MSE) between the real distortion and the fitted one was 0.1935%.

5. OPTIMUM DISTORTION ENERGY-AWARE EEG

ENCODING

From eqns. (11) and (12), the total power denoted by can be calculated as the summation of the encoding and transmission powers,

() (14) where , ∑, and Instead of representing the source coding distortion in eqn.

(13) and the total power in eqn. (14) as functions of the dominant encoding control parameters, the optimal encoding parameters will be computed. The objective of the

(b) (c)(d) (e) (f)

Fig. 2. (a) P-CR-F, (b) D-CR-F, (d) P-CR- , (e) D-CR- , (c) and (f) Integrated P-D-CR model for different filter lengths and sampling rates respectively

proposed optimization problem is to minimize the source coding distortion, D, under a constraint that the transmitted rate is less than the maximum-allowable transmitted rate and the total power consumption does not exceed the available power budget at the transmitter. Therefore, the problem of minimizing the source coding distortion can be formulated as

{ } ( )

{

(15)

where is the threshold power and it mainly depends on the resource-constrained utilized platform. is the transmission rate threshold, according to the channel state and is the Nyquist sampling rate.

In real world applications, transmission impairments, such as attenuation, free space loss, slow fading, fast fading, refraction, noise and atmospheric absorption, affect line of sight (LOS) transmissions. Due to channel dynamics, the system adaptively changes the utilized compression algorithm parameters according to the channel conditions to minimize the source coding distortion and conserve the reliability of the system. To maintain the reliability of the system, there is a constraint on the maximum transmitted rate at the transmitter. Because at bad channel state, the CR

should be increased in order to decrease the transmitted rate significantly and to maintain the bit error rate at a specific level, and vice versa at good channel state. As it is assumed that the sensor nodes transmit their information at a constant power. Therefore, according to the channel variations the encoding parameters should be updated to minimize the source coding distortion at the transmitter side.

The parameters ( ) can be obtained by solving the convex optimization problem in eqn. (15) using typical convex optimization techniques ?[16]. The general form of the optimization scheme represents a three dimensional optimization problem. The resultant distortion in this case is called three dimensional optimal distortion (3D-OD). Some applications sometimes have constraints on one or more of the encoding control parameters ( ). Therefore, as a special case of the optimization scheme is to assign a typical value for one of these parameters. In this case, the problem is converted into two dimensions and the resultant distortion is called two-dimensional optimal distortion (2D-OD). 2D-OD represents a sub-optimal solution. The idea here is that one of the complexity control parameters is assumed to equal a typical value and the other two parameters are tuned in order to obtain the optimal distortion subject to a typical power constraint. Another special case represents the traditional DWT compression approach which represents the baseline algorithm against which the performance, computational complexity, and energy consumption of the

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utilized compression technique are benchmarked. No optimization is proposed, a typical distortion is obtained whatever the power constraints. The obtained distortion called Arbitrary Distortion (AD).

6. SIMULATION RESULTS

In this section, the optimal distortion is obtained at first for a typical channel condition and different hardware implementation choices, i.e., different threshold power. The simulation results are generated using the block diagram shown in Fig. 1. The simulation parameters are assigned for typical values as shown in Table I.

The number of decomposition levels ( ) is determined based on the dominant frequency components of the signal ?[15]?[18]. In this study, EEG signals were decomposed into subbands by using the wavelet Daubechies family (D) because it yields efficient results in terms of the classification accuracy [19]. According to the highest success of the model, the decomposition level was chosen as two levels. The dominant frequency interval was determined between 43.40Hz and 86.80Hz, and its most important component was second level detail coefficients.

Based on the aforementioned premises, the proposed 3D-OD is tested at different threshold power. Also, all cases of 2D-OD are tested as a sub-optimal solution. First, CR is assigned a value of 50% and both of and are tuned subject to different threshold power values. Second, is assumed to be 242Hz and both of CR and F are tuned. Third, a typical value for filter length is assumed and the optimal distortion is studied versus the threshold power in case of tuning CR and . Interestingly, as shown in Fig. 3, our results show that 3D-OD represents a competitive alternative to both sub-optimal 2D-OD and state-of-the-art AD DWT-based EEG compression solutions in the context of WBSN-based EEG tele-monitoring systems. More specifically, while expectedly exhibiting inferior compression performance than its AD DWT-based counterpart for a given reconstructed signal quality, its substantially lower complexity and CPU execution time enables it to ultimately outperform DWT-based EEG compression in terms of overall energy efficiency. More interestingly, Fig. 3 provides a practical guideline in system

Table I. Model Parameters

design for wireless EEG encoding and communication under energy constraints. An EEG platform of a typical power budget can be selected such that it achieves the minimum distortion. For such platform, the system adaptively changes the configuration of the control parameters based on the channel variations. As shown in Fig. 4, the user who has bad channel conditions should decrease the transmission rate significantly to maintain the required constraint (channel distortion). Therefore, the encoding parameters should be updated to satisfy the new constraint (new threshold rate). CR is one of these parameters which should be increased to decrease the rate. Source encoding distortion is influenced negatively by increasing CR.

Fig. 4 illustrates the gained reduction in the distortion by using our proposed algorithm. In this figure, we compare the proposed adaptive solution with the conventional distortion (CD) solution. In our proposed solution, at bad Fig. 3. Comparison between 3D-OD, 2D-OD and AD performance

Fig. 4. CD and 3D-OD at different threshold rate

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channel state the transmitted rate should be decreased to maintain the performance. Therefore, by using the proposed optimization problem we get the optimal encoding parameters that satisfy the transmitted rate constraint and at the same time minimize the distortion. On the other side, in the CD solution, it increase the CR only to satisfy the transmitted rate constraint and that will lead to significant increase in the distortion, compared with our solution, as shown in Fig. 4.

7. CONCLUSIONS

We have developed an EEG encoding architecture which is fully scalable in power consumption. Specifically, we have introduced several control parameters into the EEG encoder to control the power consumption of the major encoding modules. Based on the proposed P-D-CR model, we have developed a quality optimization scheme called 3D-OD to determine the best configuration of source encoder according to pre-defined power budget to minimize the EEG source distortion. Such optimization model can be very effective to try to attain the best sensor’s encoding quality with pre-defined encoding power level in a WBSN, in addition to effectively choose the optimal system parameters to adapt to the varying channel conditions. The P-D-CR analysis establishes a theoretical basis and provides a practical guideline in system design and performance optimization for wireless EEG encoding and communication under energy constraints. In our future work, we will extend this model to consider the channel distortion. ACKNOWLEDGEMENT

This work was made possible by NPRP 09 - 310 - 1 - 058 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

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