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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The use of wireless body sensor networks is gaining popularity in monitoring and communicating information about a person's health. In such applications, the amount of data transmitted by the sensor node should be minimized. This is because the energy available in these battery powered sensors is limited. In this paper, we study the wireless transmission of electroencephalogram (EEG) signals. We propose the use of a compressed sensing (CS) framework to efficiently compress these signals at the sensor node. Our framework exploits both the temporal correlation within EEG signals and the spatial correlations amongst the EEG channels. We show that our framework is up to eight times more energy efficient than the typical wavelet compression method in terms of compression and encoding computations and wireless transmission. We also show that for a fixed compression ratio, our method achieves a better reconstruction quality than the CS-based state-of-the art method. We finally demonstrate that our method is robust to measurement noise and to packet loss and that it is applicable to a wide range of EEG signal types.

Healthcare consumes a large part of the gross domestic product of developed countries, and the trend is going upward ([

With respect to electrical brain activity, the electroencephalogram (EEG) signals are recorded using a collection of non-invasive wireless sensors located on a patient's scalp. These signals can then be used to detect different medical conditions, such as epileptic seizures [

Another important application of EEG signals in WBSNs is the use of a brain computer interface (BCI) that can detect the EEG patterns associated with a certain task performed by a patient [

Other common uses of EEG signals include sleep pattern studies and the diagnosis and treatment of strokes, infections (e.g., encephalitis, cerebral abscess), cerebral tumors and diseases (e.g., Alzheimer's) (see e.g., [

For an EEG-based WBSN, the EEG sensors are electrodes placed on a person's head, usually following an international convention (e.g., the international 10–20 system). An EEG sensor is also referred to as the EEG channel. The number of sensors depends on the application: some systems require few electrodes, while others require a few hundred. Every sensor is wired to a single central microprocessor unit that usually has three main components: a buffer (to store the EEG data stream coming from the different EEG channels; this buffer acts as memory), the microprocessor itself (to carry out computations needed before transmission) and a low-power radio (to wirelessly transmit the data). The combination of the EEG sensors and the microprocessor unit is referred to as the sensor node. This sensor node is battery powered. The sensor node transmits the EEG data to the server node wirelessly. The server node is comprised of two main blocks: a low-power radio receiver (to receive the transmitted EEG data) and a computing resource (to carry out any post-transmission computations, storage and any other desired operations). We assume that there is no constraint on the energy supply or the computational power at this server node. The complete system setup is shown in

The energy available in the battery powered sensor node in WBSNs is limited. This energy is needed for: (1) acquiring and digitizing the EEG samples; (2) carrying out the computations at the sensor node; and (3) wirelessly transmitting the data. Under current sensors technology, there is little that can be done to minimize the energy used for acquiring the signals; that is, the raw data must all be acquired and digitized. For computations carried out at the sensor node, energy savings could be realized by using algorithms that have low computational complexity. To minimize the amount of data transmitted, the acquired signals should be compressed before their transmission. A higher compression ratio will minimize the energy required for transmission. In other words, it is crucial to develop compression algorithms that do not require much computational energy.

Traditionally, measurements are collected by the sensors at the Nyquist rate. Then, lossy compression algorithms are directly applied to the raw data, prior to wirelessly transmitting them to the server node. This approach is undesirable for WBSNs, because of its high computational demand (and, thus, high energy consumption).

Recent research has demonstrated the advantages of using compressed sensing (CS) as an alternative compression scheme for physiological signals in the context of WBSNs [

The first study that applied CS to EEG compression used the multiple measurements vectors (MMV) approach to compress and reconstruct the signals of the different EEG channels (

For telemedicine applications, the first study that addressed the use of CS in EEG signal compression is found in [

More recently, Independent Component Analysis (ICA) was applied as a preprocessing step before using CS for compressing the EEG signals of newborn babies [

In [

The above studies resulted in some important questions: (i) What energy savings can be realized by using CS for EEG WBSN applications? (ii) Is it possible to exploit both the temporal correlations (intra-correlations) and the spatial correlations (inter-correlations between channels) to increase the compression performance of CS? (iii) How does CS compare with other state-of-the-art compression algorithms for EEG compression in WBSNs?

In this paper, we propose a novel CS framework that takes advantage of the inherent structure present in EEG signals (both temporal and spatial correlations) to improve the compression performance. To the best of our knowledge, this is also the first time that CS frameworks are compared with other state-of-the-art compression frameworks for EEG compression in WBSNs. It is also the first study where different types of EEG signals representing a variety of applications are used to test the performance of the proposed and existing frameworks, thus providing a more robust answer to the usefulness and validity of the systems.

The paper is organized as follows. Section 2 gives an overview of the theory underlying CS. Section 3 describes our algorithm and briefly introduces the benchmarking algorithms. Section 4 describes the experimental setup used for our experiments. Section 5 presents our results. Finally, Section 6 concludes the paper with suggestions for improvement and future work.

This section briefly discusses the key theoretical concepts behind compressing sensing: signal sparsity, signal acquisition and reconstruction, measurement incoherence and the extension to compressible signals.

Compressed sensing (CS) exploits the fact that most signals have a sparse representation in some dictionary. Denoting this dictionary by _{N}_{×}_{K}_{1}, _{2},…,_{K}

When the _{i}

The CS theory implies that instead of acquiring the

This system of equations is largely underdetermined. That is, given a _{0} optimization problem:
_{0} pseudonorm ‖ · ‖_{0} is the number of non-zero elements in a given vector. Unfortunately, this problem is non-deterministic polynomial-time hard (NP-hard), and as such, it is not tractable. Indeed, solving this problem requires an exhaustive search over all subsets of columns of

Fortunately, an _{1} optimization problem, a more practical problem due to its convexity, was shown to be equivalent under some conditions. It can be rewritten as follows:

This problem can be recast as a linear programming one, for which many practical solvers exist. It has also been shown that perfect recovery can be achieved, even when a small number of measurements (

The minimum acceptable value for

The number of measurements

Ideally, one should not need to know the sparsifying dictionary,

CS can further be extended to compressible signals (signals that are not purely sparse in a given dictionary, but whose coefficients,

Suppose that we are interested in recovering the

This section introduces the framework we developed to efficiently compress EEG signals using low energy. A brief overview of the state-of-the-art systems that will be used to compare our results with is also given.

Below, we present the different blocks and algorithms that make up our proposed system. We will discuss the preprocessing, the compression, the encoding, the wireless transmission, the decoding and the reconstruction. A block diagram of the proposed system is shown at the bottom of

The data is first divided into non-overlapping line segments of length _{1}, _{2},…, _{C}_{N}_{×}_{C}_{1}|_{2}| … |_{C}

The mean of each channel is then removed. The resulting matrix is _{1}|_{2}| … |_{C}]. The means will be added back in the reconstruction phase. Removing the means leads to a higher compression ratio, because the interchannel redundancy removal module (discussed later) performs better on demeaned EEG signals. It also reduces the total range of the signals, which makes it easier to quantize and encode them.

To compress the de-meaned EEG signals contained in one epoch, we first take their linear random projections and then apply an interchannel redundancy removal module.

As mentioned in Section 2, the chosen measurement matrix,

The use of a full Bernouilli matrix would reduce the challenges mentioned above (it is easier to generate its random entries, and it also has simpler multiplication operations), but this unfortunately would still require a high number of computations.

Instead, we use what is known as sparse binary sensing. This was first proposed in [

We propose the use of the same sparse binary sensing measurement matrix for each channel (sensor), so that we can further exploit the interchannel correlations (see the next section). We will test 2 different settings: the first uses a fixed sensing matrix (stored in the sensor node memory) for all epochs, and the second generates a new matrix for each epoch.

We apply the _{M}_{×}_{C}_{1}|_{2}| … |_{C}_{1}|_{2}| … |_{C}

Because all EEG channels collect information related to the same physiological signal, there exist large interchannel correlations amongst them. Indeed, channels that are spatially close to one another tend to collect signals that are highly correlated. Because we use the same measurement matrix for each channel, the linear projections of the signals of these channels are also correlated. To remove the redundancies inherent in the multi-channel EEG acquisition, we compute the differences between the compressed values of channel pairs (_{i}_{j}

1. Compute

_{max}, the maximum absolute value in matrix

_{k},j

_{k}

_{max}corresponding to the 2 channels used for the difference. Remove the channel pair (

_{k},j

_{k}

_{max}<

_{k}

_{k}

_{k},j

_{k}

The threshold,

We observed experimentally that for a given dataset, the best channel pairs are mostly stable over time (

The sensor node is only responsible for calculating the differences, which is computationally inexpensive. They are calculated for

After this stage, we obtain a matrix _{M}_{×}_{C}_{1}|_{2}| … |_{C}

After removing the interchannel redundancies, the signals are quantized and an entropy coding scheme is applied. The output of the encoding module is a stream of bits to be transmitted wirelessly.

For quantization, the columns of ^{T}

This type of vectorization ensures that the compressed samples of a single channel are interleaved,

After quantization, the resulting vector is _{q}

Entropy coding is then applied on _{q}_{q}

After compression and encoding, the EEG signals are wirelessly transmitted from the sensor node to the server node. As in [

Upon receiving the encoded compressed EEG signals, _{q}^{−}^{1}^{−1} is the Huffman decoding operator. We then form an _{q}_{q}_{1}|_{q}_{2}| … |_{q}_{C}

The final step is to reconstruct the original EEG signals from the decoded measurements, _{q}_{q}

As discussed above, one of the main elements of compressed sensing is the selection of a proper sparsifying dictionary,

The Gabor dictionary is a redundant dictionary that provides optimal joint time-frequency resolution [_{0} and _{0} are the centers of the Gabor atom, _{0}, _{0},

We now require a discretization over the _{0}, _{0} and _{0}, is proportional to the spread, and the frequency increment, _{0}, is inversely proportional to the spread. The size of the dictionary depends on the length of the EEG epoch considered in the time domain. To obtain the frequency step and the time step, we rely on the following equations:

These equations are based on the distance metric for Gabor atoms proposed in [_{0} and _{0} in this manner provides a dictionary with optimal distance between the atoms.

There exists a multitude of reconstruction algorithms for reconstructing the original signals. It is possible to use convex optimization to solve

In our framework, we use a convex optimization algorithm, the Basis Pursuit Denoise algorithm implemented in the SPGL1 package [_{q}_{rec} = [_{1}|_{2}| … |_{C}

The final step is to add back the means of each EEG channel.

Given that the problem under investigation (EEG compression in a WBSN setting) has only started to be studied recently, there is not a large body of existing literature around it, and identifying a proper benchmark is challenging. EEG compression has been studied quite extensively in the last two decades, but algorithms have not generally been designed for low energy consumption or for implementation on simple hardware. As such, some frameworks can achieve high compression ratios, but they require too many computations or some operations that are too complex given our target sensor hardware, making these frameworks prohibitive in WBSNs. Similarly, WBSNs started to gain momentum in the last decade, but few of them have addressed their applications to EEG signals. As a result, there only exist very few papers that have explicitly studied the problem of EEG compression for WBSNs. In order to identify state-of-the-art systems to compare the performance of our proposed framework, it is therefore necessary to extrapolate the results of this previous research in order to identify schemes that can offer good performance in the context in which we are interested.

We use the following requirements for selecting state-of-the-art systems to compare our system with:

low energy consumption: the system must not have a high computational requirement at the sensor node in order to conserve energy;

simple sensor hardware: the system must be simple enough to operate using inexpensive hardware;

high compression ratio: the achievable compression ratio must be high enough to justify the extra computations carried at the sensor node (as compared to wirelessly sending raw, uncompressed data).

Based on these requirements, we have selected 2 state-of-the-art compression methods to which we compare our proposed framework. These are described in some details below.

The JPEG2000-based EEG compression scheme was proposed in [

In contrast to CS schemes, this type of algorithm is adaptive in the sense that it relies on the exact knowledge of the signal to find its largest coefficients. Furthermore, the bulk of the computations is done at the sensor node. We will discuss the implications of these later.

Block-Sparse Bayesian Learning (BSBL) is a reconstruction method that was proposed in [

The main difference between the BSBL framework and our framework is in how the reconstruction is carried. Whereas we assume that EEG signals are sparse in a transform domain (Gabor frames in our case) and use that information to reconstruct the original signals, the BSBL framework does not rely on this assumption. BSBL was first proposed to reconstruct signals that have a block structure, that is, signals that have few blocks containing nonzero entries, and the remainder of the blocks containing only zeros. It was then experimentally shown that the BSBL scheme was effective in reconstructing signals even if their block partition boundaries are unknown or if they do not have any clear block structure. Raw EEG signals fall in this last category.

To carry out the reconstruction, the BSBL framework uses a “sparsifying” matrix, Ψ, which is an inverse discrete cosine transform (DCT) operator (EEG signals are not sparse in the DCT basis, but as mentioned previously, BSBL does not rely on sparsity). We used the bounded-optimization variant of the BSBL family (BSBL-BO) with a block partition of 24 and 20 iterations, as we determined experimentally that these values were the optimal partition size and number of iterations for the best reconstruction accuracy.

We now introduce the experimental setup used to evaluate the selected frameworks. We start by presenting the datasets used, as well as defining the performance metrics selected. We then carry out our experiments to evaluate the choice of the measurement matrix.

In order to assess the performance of the different algorithms on a wide range of EEG cases, we selected 3 different databases.

The first one is Dataset 1 of the BCI Competition IV [

The 2 other databases are from Physionet [

Note that some files in these datasets contain dead channels (

The random selection algorithm used is straightforward. Each potential non-overlapping window in the current dataset under study is indexed. The desired number of windows is then drawn randomly, following a uniform distribution. We further ensured that the data used in the experimental setup (mainly for parameter setting) was entirely different from the data used for framework evaluation to avoid in-sample testing.

To quantify the compression performance, we used the compression ratio (CR), defined as follows:

To test the reconstruction quality, we used the normalized mean square error (NMSE), defined as follows:
_{x}

The NMSE measures the distance between 2 vectors. Of course, the lower the NMSE, the better the reconstruction. Note that in our formula, we remove the mean of the original signal, so that differences in means between datasets do not bias the results.

As mentioned in Section 3.1.2., we employ sparse binary sensing, where the measurement matrix, Φ, contains

As seen from this figure, the NMSE saturates relatively fast, which is a desirable property. Indeed, once the number of nonzero entries in each column,

We then set out to verify the performance of this sub-optimal measurement matrix by comparing the reconstruction performance with that obtained using an optimal random matrix (Gaussian or Bernouilli). We study the reconstruction error for different compression ratios using 4 different matrices: (1) an optimal Gaussian random matrix, in which each entry is formed by sampling an independent and identically distributed (i.i.d.) Gaussian random variable; (2) an optimal Bernouilli random matrix, in which each entry is formed by sampling an i.i.d. Bernouilli random variable; (3) a sparse binary sensing matrix (with

As seen from

We study the energy performance at the sensor node of the two CS schemes (BSBL and the proposed framework) and the JPEG2000 scheme.

After being acquired and digitized, the signals are compressed, encoded and transmitted. The sensing energy is constant for all schemes, since all samples must first be acquired. It was also shown in [

We implemented the code in Embedded C and simulated it on a MICAz target platform using the Avrora simulator ([

As expected, the CS-based schemes significantly outperform JPEG2000 in every category. In fact, even if we use the highest compression ratio for JPEG2000, it will never qualify from an energy perspective when compared with CS. JPEG2000, being an adaptive scheme, relies on a high amount of computations in order to efficiently compress the data while the random projections of CS require a much lower number of computations. It is also interesting to note that small gains (decrease in the number of cycles, run time and energy consumption) are obtained by the proposed framework when the compression ratio increases. This is due to a reduction in redundancy removal and encoding computations. We note that BSBL is slightly more energy efficient than the proposed framework. However, as we will see shortly, that comes at the expense of a worse reconstruction accuracy. We will argue that the small increase in energy consumption is well worth it in this case.

Another interesting consideration would be to look at the comparison between sending compressed and uncompressed data. Sending uncompressed data requires 3.53 mJ of energy per channel (which is the energy required for wireless transmission, as no computations are carried out prior to transmission). We thus note that CS is more advantageous at any compression ratio, whereas JPEG2000 always consumes more energy than even sending uncompressed data.

The reconstruction performance of the different frameworks over the three datasets is shown at the bottom of

In terms of the NMSE, the proposed framework systematically outperforms BSBL. As expected, the reconstruction accuracy of the JPEG2000 framework is generally better than that of the CS-based frameworks, especially at high compression ratios. However, it is interesting to note that when the compression ratio decreases, the gap in reconstruction error quickly shrinks. At lower compression ratios, the proposed framework can even outperform the adaptive JPEG2000 scheme.

We then show that CS-based schemes are more robust to Gaussian noise and packet loss. Such studies have so far been omitted in EEG-based WBSN studies.

For this experiment, we arbitrarily fix the compression ratio to 2:1 and vary the signal-to-noise ratio (SNR) by introducing additive white Gaussian noise with varying standard deviations. The noise frequency is distributed between 0 Hz and 64 Hz. The results are shown in

The JPEG2000 framework is the most affected by Gaussian noise, especially when the SNR is low. Comparing our framework with BSBL, we notice that BSBL performs better at low SNRs, whereas our framework performs better for SNRs higher than 15 dB.

We then test the impact of packet loss on the reconstruction accuracy. Again, we arbitrarily select a compression ratio of 2:1. We vary the percentage of packets lost through a noisy channel by randomly choosing the lost packets, which then cannot be used to reconstruct the original signal. We assume that we know how many measurements are contained in each packet and that we know the packet sequence (

The important thing to note about this figure is the relationship between reconstruction accuracy and packet loss. What we notice is that for CS, the slope of the line is much less steep than for the JPEG2000 framework. This property is desirable, since it leads to a more graceful degradation in signal quality. In fact, we can see that as soon as packets are lost, JPEG2000 becomes worse than the proposed framework. Similarly, when the percentage of packets lost go above 9%, BSBL performs better than JPEG2000. Knowing that in WBSN, the packet loss rate can be high, we can see that CS becomes an attractive solution, even from the perspective of reconstruction accuracy. It is also important to understand the possible implications of packet loss for the different frameworks. Because JPEG2000 is adaptive and only sends the largest coefficients, we run the risk of losing the largest coefficients, and we have no control over that: it is simply a matter of luck. In contrast, because the measurements are nonadaptive random projections in the CS frameworks, no measurement bears more weight than another one. In a way, this provides a safety net: even if we have a noisy channel with a high packet loss rate, we know that in all cases, the degradation in signal quality will be proportional to the noise in the channel and will not depend on the timing or location of these losses.

In this paper, we propose a novel CS framework that exploits both the temporal correlations and the spatial correlations to efficiently compress EEG signals in WBSNs. By providing a simple, nonadaptive compression scheme at the sensor nodes, CS offers a solution to compress EEG signals in WBSNs that is energy efficient, robust to noise and packet loss and results in competitive reconstruction performance as compared to the energy-hungry JPEG2000 compression framework. On the energy front, our proposed CS framework is between five and eight times more energy efficient than the JPEG2000 framework in terms of sensor computations and wireless transmission. We also show that our method achieves a better reconstruction quality than the state-of-the art BSBL method, which also uses CS. This was also the first study in which a wide range of EEG signals are used to validate the performance of different frameworks.

The next steps to demonstrate the applicability of our proposed framework would be to build it in hardware, so as to be able to test its performance and energy consumption under real-life conditions instead of relying on simulations and assumptions. It would also be interesting to look at CS reconstruction algorithms that can directly exploit the spatial correlations by jointly reconstructing the channels. Along the same lines, it may be useful to look at the analysis prior formulation for the CS reconstruction problem, as it could yield an improvement in reconstruction accuracy. Finally, it might be worth looking for an optimal quantization and encoding strategy for CS measurements under a sparse binary measurement matrix. While this problem has been investigated for more traditional CS matrices (see, e.g., [

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Qatar National Research Fund (QNRF National Priorities Research Program 09-310-1-058).

The authors declare no conflict of interest.

General block diagram for the electroencephalography (EEG) wireless body sensor network (WBSN) system.

Block diagrams of the sensor node for (1) the JPEG2000-based framework (

Block diagrams of the server node for (1) the JPEG2000-based framework (

Probability density functions of the raw CS measurements and of the difference signals.

NMSE vs. d for different CRs.

Normalized mean square error (NMSE)

Reconstruction performance under Gaussian noise for a fixed CR (2:1), with varying signal-to-noise ratio (SNR).

Reconstruction performance under packet loss for a fixed CR (2:1).

Energy consumption and reconstruction accuracy for all frameworks. BCI, brain computer interface.

| |||||||||
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502,200 | 507,690 | 512,448 | 519,402 | 524,526 | 531,480 | 542,757 | 557,477 | ||

429,486 | 429,486 | 429,486 | 429,486 | 429,486 | 429,486 | 429,486 | 429,486 | ||

4,908,731 | 4,908,367 | 4,908,055 | 4,907,535 | 4,907,171 | 4,906,703 | 4,905,975 | 4,904,831 | ||

| |||||||||

68.11 ms | 68.86 ms | 69.50 ms | 70.45 ms | 71.14 ms | 72.08 ms | 73.61 ms | 75.61 ms | ||

58.25 ms | 58.25 ms | 58.25 ms | 58.25 ms | 58.25 ms | 58.25 ms | 58.25 ms | 58.25 ms | ||

665.8 ms | 665.7 ms | 665.7 ms | 665.6 ms | 665.6 ms | 665.5 ms | 665.4 ms | 665.3 ms | ||

| |||||||||

1.55 mJ | 1.56 mJ | 1.58 mJ | 1.60 mJ | 1.61 mJ | 1.64 mJ | 1.67 mJ | 1.72 mJ | ||

1.32 mJ | 1.32 mJ | 1.32 mJ | 1.32 mJ | 1.32 mJ | 1.32 mJ | 1.32 mJ | 1.32 mJ | ||

15.11 mJ | 15.11 mJ | 15.11 mJ | 15.11 mJ | 15.11 mJ | 15.11 mJ | 15.10 mJ | 15.10 mJ | ||

| |||||||||

1.99 mJ | 2.15 mJ | 2.29 mJ | 2.48 mJ | 2.62 mJ | 2.82 mJ | 3.08 mJ | 3.49 mJ | ||

1.76 mJ | 1.91 mJ | 2.03 mJ | 2.20 mJ | 2.33 mJ | 2.50 mJ | 2.73 mJ | 3.09 mJ | ||

15.55 mJ | 15.70 mJ | 15.82 mJ | 15.99 mJ | 16.12 mJ | 16.29 mJ | 16.51 mJ | 16.87 mJ | ||

| |||||||||

| |||||||||

0.3136 | 0.2171 | 0.1661 | 0.1127 | 0.0856 | 0.0580 | 0.0328 | 0.0108 | ||

0.5012 | 0.3723 | 0.3124 | 0.2273 | 0.1910 | 0.1554 | 0.1251 | 0.0919 | ||

0.1159 | 0.0910 | 0.0770 | 0.0612 | 0.0527 | 0.0435 | 0.0333 | 0.0220 | ||

| |||||||||

0.6471 | 0.5049 | 0.4247 | 0.3244 | 0.2746 | 0.2106 | 0.1410 | 0.0743 | ||

0.6689 | 0.5381 | 0.4610 | 0.3538 | 0.3076 | 0.2613 | 0.2126 | 0.1597 | ||

0.1967 | 0.1504 | 0.1246 | 0.0971 | 0.0825 | 0.0675 | 0.0517 | 0.0351 | ||

| |||||||||

0.3048 | 0.1754 | 0.1133 | 0.0628 | 0.0430 | 0.0248 | 0.0125 | 0.0036 | ||

0.4260 | 0.2983 | 0.2352 | 0.1514 | 0.1189 | 0.0913 | 0.0644 | 0.0404 | ||

0.0568 | 0.0344 | 0.0243 | 0.0156 | 0.0118 | 0.0084 | 0.0055 | 0.0030 |