[1] 15w Wavelet packet-based independent component analysis for feature extraction from motor imagery EEG of complex movements

[1] 311w h i g h l i g h t sThis study developed a wavelet packet-based independent component analysis (WPICA) method to extract the event-related de-synchronisation and synchronisation (ERD/ERS) patterns in different frequency bands during complex motor imagery of lower limb action. The criterion for principal independent component selection and the procedures of the WPICA method were demonstrated. The performance of the WPICA method was assessed by comparison with the traditional ICA method. a b s t r a c t Objective: The main goal of this study was to develop a novel spatial filtering method for better extracting the feature information underlying the event-related de-synchronisation and synchronisation (ERD/ERS) during complex motor imagery of lower limb action. Methods: The algorithm used a wavelet packet-based independent component analysis (WPICA) method to extract the ERD/ERS patterns in different frequency bands. Time-frequency decomposition in the wavelet packet domain was designed to avoid the statistical correlation between different electroencephalographic (EEG) rhythms. The subband-specific principal components were extracted after independent component analysis and projected back to the time-frequency domain of corresponding electrodes for better fitting the varying EEG spatial distributions. Results: The present method was tested with the EEG data from 10 human subjects performing three complex mental tasks (i.e., imagery standing up, imagery left/right foot movement combined with homolateral hand movement). A classification rate of about 80% was achieved using the WPICA-based technique, which is better than the traditional ICA method with the rate of 72.30% and the non-spatial filtering condition of 68.34%. Conclusions: We developed a novel spatial filtering method based on WPICA to extract the ERD/ERS patterns in different frequency bands. The overall performance of this algorithm was better than that of the conventional methods. Significance: The current method promised to provide an effective way for ERD/ERS patterns recognition and thus could improve the pattern classification performance of complex mental tasks from scalp EEGs.

[1] 254w Since the important work of Jasper and Penfield (1949), electroencephalographic (EEG) motor imagery has become a frequently used mental strategy for cognitive brain research or brain-computer interface (BCI) application (Pfurtscheller and Lopes da Silva, 1999;Qin and He, 2005). However, most efforts were converged to investigate the behaviour of brain activation induced during the execution or imagination of single motor tasks. These single motor tasks involved a restricted number of muscles such as single hand, foot or tongue movement (Pfurtscheller and Neuper, 1997;Pfurtscheller et al., 2005;Qin et al., 2004), while more complex movements, for example, standing up and walking were not addressed much so far. Only few researchers have investigated the brain activation during complex movements in the past decade. Vidailhet et al. performed the investigation of movement-related potentials during forward stepping (Vidailhet et al., 1993). Saitou et al. studied the brain dynamics preceding postural adjustments during standing (Saitou et al., 1996). do Nascimento et al. studied the influence of directional orientations during gait initiation and stepping on movement-related cortical potentials (do Nascimento et al., 2005). The reasons for fewer researches on imagery complex motor tasks, besides the logical one of prioritising basic functions, are mainly attributed to the complexity of EEG patterns and insufficiency of spatial resolution during complex movements. However, understanding the behaviour of motor imagery potentials (MRPs) during complex movement patterns is necessary for further cognitive brain research and successful application of BCI. Therefore, to capture the complex features of MRP is of special interest in cognitive brain research and BCI application.

[2] 173w It has been shown that independent component analysis (ICA) is especially suitable for removing a wide variety of artefacts in EEG recordings and separating MRP patterns generated in motor imagery. ICA is therefore a useful method for constructing spatial filters for preprocessing raw, multichannel EEG data. According to the ICA method, the original sources were assumed to be statistically independent and have non-Gaussian distributions. However, these were not true according to the practical EEG data. The real-world EEG data often build up complex, nonlinear structure; hence, applying ICA to global data may lead to poor results. Former EEG researchers have found a potential problem in using traditional ICA, that is, the independent components obtained after the application of this algorithm will contain EEG data in addition to artefacts (Ille et al., 2002;Frank and Frishkoff, 2007). Even remarkable artefact removal such as eye blinks was likely to result in the loss of some true EEG data when using the traditional ICA method to separate the blink artefacts (Barbati et al., 2004;Joyce et al., 2004).

[3] 96w Another important limitation of the traditional ICA model should be pointed out, that is, the spectral quality of EEG signals is neglected during its processing. However, the characteristics in the frequency domain are more important than those in the time domain. EEG researchers have reached a consensus that EEG signals have distinctive characteristics in different frequency bands that may be associated with different physiological sources (Pfurtscheller and Aranibar, 1977;Hjorth, 1975). Therefore, instead of allowing for a single mixing matrix in traditional ICA algorithms, a series of mixing matrixes should be remodelled for different feature frequency bands.

[4] 79w Further, the standard ICA algorithms are not able to estimate statistically dependent original sources, that is, when the independence assumption is violated. Many cognitive brain researchers found out that there existed certain correlation between different EEG rhythms, such as alpha rhythm, beta rhythm and gamma rhythm (Suetsugi et al., 2002;Carlqvist et al., 2005;Lange et al., 2008). A natural extension and generalisation of ICA is multi-resolution subband decomposition ICA, which relaxes considerably the assumption regarding mutual independence of primarily sources.

[5] 170w Many researchers noticed some of the above limitations for traditional ICA and engaged in advancing the ICA algorithm into the extended subband ICA model (Hiroe, 2006;Zhang and Chan, 2006;Dyrholm et al., 2007). Three kinds of approaches can be used to realise the extended subband ICA, that is, the temporal filtering method, short time Fourier transform (STFT) and wavelet transform (or wavelet packet transform). Temporal filtering has a fatal defect that originates from its non-orthogonality. Subband signals obtained by this method would have great redundancy and dependency between each other. This makes it impossible for the reconstruction of the original signal. STFT-based extended subband ICA would lead to a well-known frequency permutation problem. Each subband signal decomposed by the STFT method would have a real part and an imaginary part. Then, the real and the imaginary parts of each subband signal would be performed by the ICA method, separately. How to fit the real components with associated imaginary ones became problematic when time domain signals were reconstructed (Mazur and Mertins, 2009).

[6] 231w In this article, we introduced a novel spatial filtering method based on wavelet packet ICA (WPICA) for better capturing the EEG dynamics during the mental imagination of complex movements. Because no imaginary part appeared during WPICA processing, the frequency permutation problem was avoided. WPICA had another merit. It transformed the original signal into sparse distribution, which would emphasise the non-Gaussian nature of the observed signals. According to this method, EEG data were recorded during three complex imagery movements (i.e., imagery standing up and imagery left/right foot movement combined with homolateral hand movement). Thereafter, the independent components of each characteristic frequency band were extracted by WPICA, and the principal ones including most ERD/ERS information were selected and projected back to the time-frequency domain of corresponding electrodes. To verify the effectiveness of this novel method, event-related (de-)synchronisation (ERD/ERS) patterns (Pfurtscheller and Aranibar, 1977) during complex mental tasks were studied in three cases of non-spatial filtering, traditional ICA spatial filtering and WPICA spatial filtering. Then, these cases were statistically compared according to ERD/ERS coefficients. Finally, ERD/ERS pattern recognition results were presented for distinguishing three complex mental task states and compared amongst the above three cases. To give more focus on the WPICA method, not the special kinds of tasks, we also adopted standard motor imagery tasks (left and right hand motor imagery) of the same subjects for further verifying the effectiveness of our method.

[1] 355w To obtain a representation of ERD/ERS patterns in different characteristic frequencies (covering the a and b bands), the wavelet packet analysis was applied along scales until the required subband components were obtained. Assume S ð0;0Þ i ði ¼ 1; 2; . . . ; 41Þ to be the preprocessed EEG signals of 41 standard leads with a 256-Hz sampling rate; the decomposed components at the 1st scale could be separately expressed as the lower frequency part S ð1;0Þ i (ranging from 0 to 64 Hz) and the higher frequency part S ð1;1Þ i (ranging from 64 to 128 Hz). Then, the components containing more than one characteristic frequency bands would be decomposed further in the following steps. For example, S ð1;0Þ i was the characteristic part with redundant bandwidth (containing frequencies in a and b rhythm) so that it should be divided further as S ð2;0Þ i (ranging from 0 to 32 Hz) and S ð2;1Þ i (ranging from 32 to 64 Hz). It should be pointed out that the component under decomposition in the mth subband of the nth scale, S ðn;mÞ i , would be split into two corresponding parts in the (m + n)th subband of the (n + 1)th scale, that is, the lower frequency part S ðnþ1;mÂ2Þ i and the higher frequency part S ðnþ1;mÂ2þ1Þ i . Similarly, the required 11 subband components S ð6;jÞ i ðj ¼ 4; 5; . . . ; 14Þ could be eventually obtained at the 6th scale, amongst which the first three components S ð6;jÞ i ðj ¼ 4; 5; 6Þ covered the a band and the remaining ones S ð6;jÞ i ðj ¼ 7; . . . ; 14Þ covered the b band. To be consistent with the symbols of EEG rhythms ðh; a; b; cÞ, we renamed the obtained components covering the a band as S ak i ðk ¼ 1; 2; 3Þ and the others covering the b band as S bk i ðk ¼ 1; 2; . . . ; 8Þ: The WP-based decomposing process and relationships between the nodes in different scales and subbands are shown in Fig. 3.

[2] 158w According to the wavelet packet decomposition tree (Fig. 3), the EEG source signals were reconstructed by inverse wavelet packet transform. For the present study, the nodes representing EEG source signals covering the a and b band (separately expressed as Sak i ði ¼ 1; 2; . . . ; 41; k ¼ 1; 2; 3Þ and Sbk i ði ¼ 1; 2; . . . ; 41; k ¼ 1; 2; . . . ; 8Þ) were adopted to replace the nodes in the 6th scale (S ak i ðk ¼ 1; 2; 3Þ and S bk i ðk ¼ 1; 2; . . . ; 8Þ) for wavelet packet reconstruction, while the remained nodes falling outside the above frequency window were replaced by zero sequences during reconstruction. Following the steps of inverse wavelet packet transform, the EEG source signal Sð0;0Þ i ði ¼ 1; 2; . . . ; 41Þ was eventually reconstructed for further TF analysis.

[3] 177w To illustrate the effectiveness on spatial resolution enhancement of our proposed method, the comparisons on ERD/ERS values and classification results were given out amongst the cases of nonspatial filtering, traditional ICA spatial filtering and WPICA spatial filtering. Prior to these results, to make the reader have a good understanding about our novel method, we took imagery standing up as an example to give out the time-frequency map and Fig. 4a showed the averaged TF map (scalogram) of ERD/ERS at electrode C3 across all trials without a spatial filter during the mental task of imagery standing up. The scalogram represented the activities in the range of 1.5-30 Hz. An indistinct narrowband a-ERD around 12 Hz emerged from an unorderly background for a long period, and the mean ERD/ERS coefficient from 3.0 to 7.0 s was À2.3 referring to the 1 s interval before the prepare cue. However in the b band, the ERD phenomenon appeared as a diffuse distribution in 20-28 Hz, which made it difficult to distinguish the latency and characteristic frequency band of the ERD/ERS pattern.

[4] 128w Fig. 4b showed the averaged TF representation of all trials at electrode C3, as obtained by the traditional ICA spatial filter. From this figure, we could see that the a-ERD phenomenon around 12 Hz became more conspicuous with background noise suppressed, and the mean ERD/ERS coefficient during the interval between 3.0 and 7.0 s was decreased to À5.9. However, the TF resolution at the b band was still far from being satisfying. Although the diffuse distribution of pseudo-ERD was greatly weakened, the true ERD information was almost diminished after applying the traditional ICA spatial filter. Therefore, it was still difficult to effectively identify the time-frequency features from the b band because some true EEG data in the b band was lost when using traditional ICA to remove artefacts.

[5] 271w Fig. 5a illustrates the averaged TF representation of all trials during imagery standing up at electrode C3, as obtained by the WPICA method for the same subject (Fig. 4). From Fig. 5a we could see that the background noise with diffuse distribution was greatly suppressed. The a-ERD phenomenon around 12 Hz was enhanced further, and its ERD/ERS coefficient during the interval between 3.0 and 7.0 s was decreased to À8.7. More importantly, the b-ERD phenomenon around 22 Hz emerged eventually from an unorderly background and the mean ERD/ERS coefficient during the interval from 3.0 to 7.0 s was -6.5. Fig. 5a also presents the topographical plot of ERD/ERS maps across all 41 channels at four indicated points in the time-frequency plane. Before the implementation of the motor imagery task, no characteristic phenomenon of ERD or ERS was found in the sensorimotor area of the cerebral cortex (corresponding to C3, C4, Cz and their neighbouring electrodes) in the a-band (around 12 Hz) or the b-band (around 22 Hz). During imagination, a clear energy decrease, that is, ERD, appeared in the whole sensorimotor area corresponding to C3, C4 and Cz in the aband (around 12 Hz), along with similar notable ERD at electrodes C3 and Cz in the b-band (around 22 Hz). In particular, a short-lasting b-ERS was induced after imagination of standing up at C1A. Fig. 5b showed the power spectral density curve of the a-band at C3 obtained by the WPICA technique. This curve also illustrated the significant ERD phenomenon at C3, which was synchronised with the implementation of imagery standing up and corresponded to the TF representation in Fig. 5a.

[6] 150w In our study, during complex motor imagery of lower limb ac- were À8.7, À6.4 and À6.7 separately, and those in the b band at C3, Cz and C1A were À6.2, À5.2 and 7.7, respectively. The absolution values of ERD/ERS obtained by our method were higher than the other methods. Statistical analyses were applied on the averaged ERD/ERS values for the three methods. No significant differences were found in the b-ERD coefficients before and after the traditional ICA technique (P > 0.05) , although ERD responses in the a band were enhanced in comparison with the manner of non-spatial filtering (P < 0.05) and b-ERS patterns at electrode position C1A also got a few enhancement (P < 0.05). However, after WPICA spatial filtering, the values of ERD/ERS coefficients were significantly higher than that of traditional ICA spatial filtering or non-spatial filtering (P < 0.05) both in the a and b band.

[7] 26w According to the same processes presented above, we can similarly obtain the enhanced ERD/ERS patterns during imagery left/ right foot movement combined with homolateral hand movement.

[8] 115w Thereafter, to test the feasibility and effectiveness of our proposed technique for extracting the feature information underlying in the ERD/ERS patterns, classification results of complex mental tasks were obtained and compared between three kinds of processing manners (i.e., non-spatial filtering; traditional ICA spatial filtering; and WPICA spatial filtering). Four typical non-overlapping 1-s intervals (3.0-4.0 s, 4.0-5.0 s, 5.0-6.0 s and 6.0-7.0 s) were separately selected for ERD/ERS coefficient calculation in relation to a 1-s reference interval before the preparation cue. Then, all ERD/ERS values (four electrodes, two frequency bands) according to these intervals were adopted for pattern recognition, and the support vector machine (SVM) technique based on RBF core function was selected as the classifier.

[9] 171w Table 2 lists the classification results of all the subjects according to three kinds of processing manners. Based on 10-fold crossvalidation, the recognition rates achieved by the WPICA-based technique were more satisfying with an average accuracy of 79.19%, which was better than that achieved by the other two techniques (non-spatial filtering: 68.34%; traditional ICA spatial filtering: 72.30%). Paired t-tests with the Bonferroni correction were used at the 5% level of significance to determine if there were any significant differences between the classification accuracies obtained by the above-mentioned three techniques. The significance test shows that the classification accuracies according to the WPICA-based approach are significant higher than that of the non-spatial filtering or the traditional ICA method (P < 0.05).This result is quite promising because it is based on single trials, not averaged values. We also did not use any training procedure, and the feature information for classification was extracted from only four electrode positions. Using more scalp electrodes for classification may further improve the results as obtained from the proposed approach.

[10] 418w To give more focus on the WPICA method, not the special kinds of tasks, we also adopted standard motor imagery tasks (left-and right-hand motor imagery) of same subjects for further verifying the effectiveness of our method. The same experimental paradigm as Fig. 1 was used for the experiments of single motor imaginary tasks (left-hand movement imagination and right-hand movement Fig. 6. Comparison of ERD/ERS coefficients during imagery standing up across three kinds of processing manners. The marker ''*'' represented that there was a significant difference in ERD/ERS coefficients between non spatial filtering method and traditional ICA method or WPICA method, and the marker ''Â'' represented the significant difference in ERD/ERS coefficients between traditional ICA method and WPICA method. imagination) except for a few differences on execution cues, that is, at second 3, the arrow pointing left or right was presented that indicated the imagination of left-or right-hand movement imagination. Table 3 gave out the comparison of averaged ERD/ERS values of all 10 subjects during left and right motor imagery across three kinds of processing manners. We applied statistical analyses on the averaged ERD/ERS values for these three methods. Significant difference (P < 0.05) was found in both a-ERD and b-ERD coefficients between WPICA and traditional ICA or between WPICA and non-spatial filtering. For example, during right-hand motor imagery, b-ERD at electrode C3 became enhanced by the WPICA method (À4.8) relative to traditional ICA (À2.6) or non-spatial filtering (À1.9). To give an illustrative explanation about the effectiveness of the WPICA method, topographical plots for b-ERD values of one typical subject during right-hand motor imagery are given in Fig. 7. With non-spatial filtering, b-ERD values at C3 and C4 were À1.8 and À1.7, respectively. After traditional ICA, b-ERD values at C3 and C4 were À1.4 and À1.1, respectively. The ERD phenomenon seemed weakened after traditional ICA. This meant that some true EEG data were lost when using the traditional ICA method to remove the artefacts. After applying WPICA, b-ERD values at C3 and C4 were À4.7 and À2.2 respectively. The ERD phenomenon at C3 and C4 was enhanced in comparison to no spatial filtering or traditional ICA. The diffusion of the ERD pattern around C3 or C4 was greatly suppressed, because WPICA removed the artefacts and retained the true EEG data of the ERD pattern. Here, we should point out that the diffusion of the ERD pattern around C3 or C4 was also suppressed by the traditional ICA method; however, this method lost some valuable ERD signals when removing artefacts.

[11] 127w Fig. 8 presents classification results of left-or right-hand motor imagery across three methods. ERD/ERS values of alpha and beta rhythm at two electrodes (C3 and C4) of eight intervals (3.0-3.5 s, 3.5-4.0 s, 4.0-4.5 s, 4.5-5.0 s, 5.0-5.5 s, 5.5-6.0 s, 6.0-6.5 s and 6.5-7.0 s) were adopted as the input data for classification; 90% of total data samples of each subject were adopted as training data. Paired t-tests with the Bonferroni correction were used at the 5% level of significance to determine if there were any significant differences between the classification accuracies obtained by the above-mentioned techniques. The significance test shows that the classification accuracies according to the WPICA-based approach are significantly higher than that of the non-spatial filtering or traditional ICA method (P < 0.05).

[1] 67w The task-related activities induced in complex mental movements involve more complicated ERD/ERS patterns than that of single motor tasks, which makes them vulnerable to spontaneous brain activity and non-task related activity. Although little is still unknown about cortical behaviour during complex movements, it is undoubted that understanding the behaviour of event-related potentials during complex movements is necessary for further cognitive brain research and successful application of BCIs.

[2] 161w In the present study, we have proposed a WPICA method for the analysis of the ERD/ERS response induced during three complex mental tasks (i.e., imagery standing-up and imagery left/right foot movement combined with homolateral hand movement). A few previous imaging studies addressed brain activity during imagery or observation of standing (Jahn et al., 2004;Iseki et al., 2008), which seemed similar to our study on the mental task of imagery standing up. However, there were two key differences. First, Jahn and Iseki investigated the blood oxygenation level-dependent (BOLD) signal during motor imagery tasks using functional magnetic resonance imaging (fMRI). In our study, we investigated the brain activity using conventional EEG techniques. The fMRI had the ability of identifying the involved brains regions with high spatial resolution, but it had a low or absent temporal resolution. The conventional EEG techniques can obtain the information on the timing of activation and the correlations between different areas of activation, but with a low spatial resolution.

[3] 261w Second, in Jahn and Iseki's works, participates were asked to perform standing imagery, that is, they imagined that they were maintaining a standing posture or an upright posture. However in our study, participants were asked to perform standing-up imagery, that is, they should imagine that they were performing the process of standing up. After the comparison of Jahn and Iseki's works and our study, similar major activated regions including the left supplementary motor area and premotor cortex area were found in both imagery standing and imagery standing up. However, some significant difference should be pointed out. In our study, the activated process of the left supplementary motor area and premotor cortex area could also be obtained from the information of ERD/ERS pattern variation, for example, the premotor cortex area was activated before the left supplementary motor area during standing-up imagery. However, similar information on the activated process of brain area was not provided in Jahn and Iseki's works, which might be on account of the low temporal resolution of fMRI. Furthermore, we should point out that the relationship between the BOLD signal and ERD/ERS signal was complicated. Formaggioa et al. (2010) studied the relationship between the EEG signal and BOLD signal during the imagery of a right-hand thumb adduction. They found that the correlation is negative in the contralateral side and positive in the ipsilateral side of the sensory motor area. Visani et al. (2011) found that the patients with Unverricht-Lundborg disease had abnormal ERD/ERS but unaffected BOLD response. The relationship between ERD/ERS and BOLD signal is still an open problem.

[4] 228w In comparison with the traditional ICA technique, four aspects of the WPICA method were improved for modelling dynamic EEG signals. First, the WPICA method could transform the original signal into sparse distribution, which emphasised the non-Gaussian nature of the observed signals. Second, EEG source superposition might be frequency dependent, the WPICA technique allowed for the existence of different functionally independent sources in different frequency bands. Moreover, the WP-based time-frequency analysis could realise the TF decomposition of EEG data allowing for interindividual differences, as Klimesch suggested (Klimesch et al., 1998;Doppelmayr et al., 1998). Third, in this technique, functional independent EEG sources were projected back to the corresponding time-frequency domain electrode voltages, which made a better understanding of the resulting time-varying spatial distributions. Lastly, many cognitive brain researchers found out that there existed a certain correlation between different EEG rhythms, such as alpha rhythm, beta rhythm and gamma rhythm. The standard ICA algorithms are not able to estimate statistically dependent original Fig. 8. Classification results of left or right hand motor imagery in three cases of non spatial filtering, traditional ICA spatial filtering and WPICA spatial filtering. The marker ''*'' represented that there was a significant difference in classification rates between non spatial filtering method and traditional ICA method or WPICA method, and the marker ''Â'' represented the significant difference in classification rates between traditional ICA method and WPICA method.

[5] 13w sources, but WPICA relaxes considerably the assumption regarding mutual independence of primary sources.

[6] 117w Our results obtained from the three kinds of complex mental tasks strongly supported the feasibility of this novel WPICA method. As shown in Figs. 4 and 5, the traditional ICA technique was not fully satisfactory in acquiring ERD/ERS patterns. The independent components obtained by the traditional ICA method will contain EEG data in addition to artefacts. Therefore, it was likely to result in the loss of some true EEG data when using the traditional ICA method to separate the artefacts. To overcome this problem, the WPICA technique was designed that adopted different mixing matrices in each feature frequency band when modelling for corresponding functional independent sources. This relaxes considerably the assumption regarding mutual independence of primary sources.

[7] 241w In the following results, we examined the spatio-frequency distribution of ERD/ERS patterns and further investigated the significance of ERD/ERS coefficients separately obtained by three proceeding ways. ERD/ERS values according to the complex imagery movements of low limb action were compared between non-spatial filter, traditional ICA and WPICA conditions. Results identified the applicability of the WPICA technique on ERD/ERS enhancement (see Fig. 6). However, as many researches show, ERD/ERS phenomenon is varied with time during the process of motor imagery movements (Pfurtscheller and Neuper, 1997;Pfurtscheller et al., 2005;Qin et al., 2004;Vidailhet et al., 1993;Saitou et al., 1996;do Nascimento et al., 2005); hence, using a single ERD/ERS coefficient representing the whole imagery process (see Fig. 7) may lose some useful information. Therefore, we separately calculated the ERD/ERS values in four non-overlapping intervals along the time index for EEG pattern recognition according to the above-mentioned three methods (non-spatial filtering, traditional ICA spatial filtering and WPICA spatial filtering). The WPIC-A-based technique achieved about 80% classification accuracy using all trials without training, which is better than the traditional ICA method with the rate of 72.30% and the non-spatial filtering condition of 68.34%. To give more focus on the WPICA method, not the special kinds of tasks, we also adopted standard motor imagery tasks (left-and right-hand motor imagery) of the same subjects for further verifying the effectiveness of our method. Classification results showed that WPICA had superior performance on EEG spatial filtering than the traditional ICA method.

[8] 130w In summary, we have developed a novel WPICA spatial filtering technique under a convoluted mixing model combined with power spectral density (PSD) analysis for brain dynamics capture from complex mental tasks. The mathematic model presented here indicated that this WPICA technique allowed for the spatio-temporal dynamics in EEG data that the traditional ICA method ignores. To verify the effectiveness of this technique, the ERD/ERS patterns during imagery standing up was studied, and the present results suggested that this technique could take consideration of the timespace-frequency characteristics of motor imagery EEG, which made it more effective in capturing the EEG features than traditional methods. However, to confirm the relevance of the new method for understanding brain data, further investigation should be made based on more extensive analysis across subjects and experiments.

[1] 255w Ten right-handed healthy young volunteers (4 females and 6 males, age with 24.3 ± 3.1 years) participated in the experiment. Informed consent was obtained from all participants prior to their participation in each experiment. The experiments were performed in accordance with the Declaration of Helsinki (last adopted at the 52nd World Medical Association General Assembly 2000 in Edinburgh). During the performance of the experiment, the subjects sat in a semi-reclining armchair and watched a 19-inch monitor from a distance of about 1 m. The participants were instructed to perform the indicated motor imagery task without overt motor output. Each trial (8 s) began with a blank screen for 2 s. At the 2nd second, a fixation cross (preparation cue, lasting 1 s) appeared at the centre of the monitor. Then at the 3rd second, an up, left or right pointing arrow (execution cue, lasting 4 s) appeared indicating that it was time to begin the mental task of imagery stand-up or imagery left/right foot movement combined with homolateral hand movement. The subjects were instructed to perform the indicated motor imagery task up to the 7th second. At the end of imagination, a blank screen was presented for 1 s before the next trial (Fig. 1). Each experiment was divided into 6 runs, consisting of 30 trials each. There were breaks of 3-5 min between the runs. In each experiment (for each subject), there were 60 trails performed for each task. The presentation of all trails (180 trails) of each task was in a pseudo-random sequence.

[2] 128w Scalp EEG data (band pass between 0.5 and 70 Hz) were recorded from 41 Ag/AgCl scalp electrodes (Fig. 2) placed according to the International 10/20 System with a sampling rate of 256 Hz. Activity produced primarily by eye movements and blinks (plus EEG activity) was obtained by sensors positioned at the left outer canthus and below the right eye. The electrode grid covered the line crossing C3-Cz-C4 and adjacent regions anterior and posterior to it and was referenced to the left mastoid. During data collection, an additional 50-Hz notch filter was used to eliminate power-line interference. After recording, orthogonal source derivations were calculated to obtain reference-free data (Hjorth, 1975). Thereafter, all raw EEG trials were visually controlled, and trials severely contaminated with ocular or muscle artefacts were discarded.

[3] 43w According to the subband ICA model presented above, we engaged in designing a novel WPICA technique to avoid the statistical correlation between different EEG rhythms and the well-known frequency permutation problem. The main processing stages for the WPICA method are listed as follows.

[4] 108w The normalised power spectrum from the 3.0-and 7.0-s intervals was averaged to calculate REP according to Formula 6 in relation to the 1-s reference interval before the prepared cue. For each subject, differences in ERD/ERS coefficients across three kinds of processing manners (non-spatial filtering, traditional ICA spatial filtering and WPICA spatial filtering) were examined by analysis of variance (ANOVA) with characteristics electrodes (C3, C4, Cz and C1A) and corresponding frequency bands (a-band and b-band) as repeated measures. Paired t-tests with the Bonferroni's correction were used at the 5% level of significance to determine if there were any significant differences between the ERD/ERS values obtained by the above-mentioned techniques.

[1] 78w Traditional ICA is a computationally efficient technique for blind source separation. The traditional ICA model presently is a simple linear and instantaneous mixing one. In this model, we have some observable variables x ¼ ½x 1 ðtÞ; x 2 ðtÞ; . . . x M ðtÞ T . They are assumed to be a linear mixture of some mutually statistically independent variables s ¼ ½s 1 ðtÞ; s 2 ðtÞ; . . . s N ðtÞ T ,

[2] 51w where the operator T stands for the transpose operator of the matrix. The M Â N matrix A ¼ ½a 1 ; a 2 ; . . . a N is called the mixing matrix, and it is assumed that at most one of the sources s i is Gaussian distributed.

[3] 41w In the traditional ICA model, A and s are both unknown. By using some linear transform, the task of the ICA is to find the signals y ¼ ½y 1 ; y 2 ; . . . y N T ,

[4] 87w which are as mutually independent as possible, such that they provide an estimate of s. The M Â N matrix W is called the demixing matrix. Here, the presentation is restricted to square-mixing, that is, M ¼ N. However, the traditional ICA method has three defects. First, in the traditional ICA, the original sources are assumed to be statisti-cally independent and have non-Gaussian distributions. However, these are not true according to practical EEG data. Therefore, we should find an adequate representation when the signal distributions are non-Gaussian.

[5] 38w Second, the standard ICA algorithms are not able to estimate statistically dependent original sources, that is, when the independence assumption is violated. However, many cognitive brain researchers found out that there existed certain correlation between different EEG rhythms.

[6] 39w Third, EEG researchers have reached a consensus that EEG signals have distinctive characteristics in different frequency bands, which may be associated with different physiological sources. Therefore, a series of mixing matrixes should be remodelled for different feature frequency bands.

[7] 35w To solve the above three problems, the basic ICA model should be extended to subband decomposition ICA. In this novel model, all sources s i can be represented as the sum of several subcomponents as,

[8] 39w where s k i , k ¼ 1; . . . ; L are narrow-band subcomponents. The goal of subband decomposition ICA was to estimate the original sources in the kth subband from the observations in the corresponding subband:

[9] 42w To obtain the original sources s ðkÞ ¼ ½s k 1 ðtÞ; s k 2 ðtÞ; . . . ; s k N ðtÞ in each subband, we should first apply some transform C to the observations x to get subband observations,

[10] 14w x ðkÞ ¼ CðxÞ ¼ A ðkÞ ½CðsÞ ¼ A ðkÞ s ðkÞ ð5Þ

[11] 33w In the next step, we just needed to apply an ICA algorithm to the subband observations, and we could obtain the demixing matrix W ðkÞ associated with the mixing matrix A ðkÞ .

[12] 96w To realise the subband ICA, three methods seems to be applicable, that is, temporal filtering method, STFT and wavelet (or wavelet packet) transform. However, temporal filtering has a fatal defect originating from its non-orthogonality, which makes it impossible for the reconstruction of the original signal. The STFT-based subband ICA will be confronted with a well-known frequency permutation problem originating from the imaginary part of Fourier transformation; this is still an open problem. In addition, to make a good trade-off between time and frequency resolution, the interval length selection will be another inevitable problem for STFTbased methods.

[13] 58w In this article, we adopted the wavelet packet-based ICA method. This method can emphasise the non-Gaussian nature of the observed signals and obtain the orthogonal subband sources without the frequency permutation problem. In addition, compared to the wavelet-based ICA method, the wavelet packet-based ICA band can have a narrower subband; this can increase the independence of source signals.

[14] 42w ICA was separately applied on the 11 subband components S ak i ðk ¼ 1; 2; 3Þ and S bk i ðk ¼ 1; 2; . . . ; 8Þ: The main procedures of the ICA spatial filter are presented as follows.

[15] 209w First, by applying ICA algorithm in the wavelet packet domain, independent components C ak i ði ¼ 1; 2; . . . ; 41; k ¼ 1; 2; 3Þ and C bk i ði ¼ 1; 2; . . . ; 41; k ¼ 1; 2; . . . ; 8Þ corresponding to the 11 subspaces covering the a and b band (S ak i ðk ¼ 1; 2; 3Þ and S bk i ðk ¼ 1; 2; . . . ; 8Þ), were obtained with their corresponding separating matrices W ak i ðk ¼ 1; 2; 3Þ and W bk i ðk ¼ 1; 2; . . . ; 8Þ; After that, principal components were separately selected amongst the independent components of each wavelet packet subspace; those with notable ERD/ERS phenomena were retained while the others were set as zero sequences. Finally, EEG source signals dominating the a and b band (separately expressed as Sak i ði ¼ 1; 2; . . . ; 41; k ¼ 1; 2; 3Þ and Sbk i ði ¼ 1; 2; . . . ; 41; k ¼ 1; 2; . . . ; 8Þ were separately reconstructed by projecting the principal components back into the EEG signals corresponding to EEG electrodes.

[16] 91w To capture the ERD/ERS patterns with high spatial resolution, principal component selection was crucial amongst the above steps. The parameters related to the ERD/ERS phenomenon should be adopted as the primary basis for component selection. Therefore, referring to the quantitative principles for ERD/ERS patterns presented by Pfurtscheller and Lopes da Silva (1999) and combining these principles with the characteristics of WPICA technique, ERD/ERS coefficients defined by logarithm power spectrum in the wavelet packet domain were introduced as the foundation for principal component selection. The definition for ERD/ERS coefficients was expressed as:

[17] 52w where REP represented the normalised mean power spectrum in some subband with notable ERD/ERS phenomenon during the mo- higher than the mean absolute ERD/ERS value of the a or the b band were retained. Thereafter, the retained components with notable ERD/ERS patterns were projected back to their corresponding time-frequency domain electrode voltages.

[18] 87w The support vector machines (SVM) technique based on RBF core function was selected as the classifier. A simple description is provided as following. Suppose we have a set of training data, T ¼ fðx 1 ; y 1 Þ; . . . ; ðx j ; y j Þ; . . . ; ðx N ; y N Þg; x j 2 R n , y j 2 fÀ1; þ1g; j ¼ 1; 2; . . . ; N: The decision function f ðxÞ has the form,

[19] 24w where fa j g are embedding coefficients and kðx; x j Þ is the radial basis function (RBF) kernel in our research, that is:

[20] 11w The optimal decision function is computed by the following quadratic programming:

[21] 15w subject to a j P 0; j ¼ 1; . . . ; N and

[22] 50w In our research work, three kinds of mental tasks (imagery stand-up, imagery left/right foot movement combined with homolateral hand movement) should be classified. Because the ERD/ERS features of these three tasks are separable between each other, the three-class classification task can be transformed into three oneagainst-one classification tasks, that is,

[23] 102w The final classification results were decided by the voting of three one-against-one classifiers, and the voting rules were presented in Table 1. For example, if the output of SVM1 (left hand/foot imagination against right hand/foot imagination) was '+1' (indicates imagery of left foot movement combined with homolateral hand movement, denoted as 'left hand/foot') and the output of SVM2 (left hand/foot imagination against stand-up imagination) was '+1' (left hand/foot), the final classification result must be 'imagery left foot movement combined with homolateral hand movement' whether the output of SVM3 (right hand/foot imagination against stand-up imagination) be '+1' (right hand/foot) or 'À1' (stand up).

[24] 171w In our research, ERD/ERS values of alpha and beta rhythm at four electrodes (C3, C4, Cz and C1A) of four intervals (3.0-4.0 s, 4.0-5.0 s, 5.0-6.0 s and 6.0-7.0 s) were adopted as the input data for classification. The proportion of training data has great influence on classification results: when the training data are only 10% of the total data samples, the recognition rates is low for both methods; when it is increased to more than 80%, the recognition rates tends to be stabilised. In this article, 90% of the total data samples of each subject were used as training data. A 10-fold cross-validation experiment was carried out to evaluate the performance of the SVM models. The total data samples of each subject were randomly divided into 10 subsets. According to the total trails of each subject (equal to or lesser than 180), there were about 162 trails used in the training sets and the remaining trails (equal or lesser than 18) were used in the testing set during cross validation.

[25] 38w The training and testing were carried out 10 times for each model using one distinct set for testing and the remaining nine for training. The performance of the model was reported as the average performance over 10 sets.