Experiment of Self-paced Finger Movement 77

Time−frequency Spectrum Map of Reference Signal

Time (sec.)

Frequency (Hz)

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

8 10 12 14 16 18 20 22 24

(a)

(b)

Figure 4.15: Time-frequency Coherence map of the estimated sources by maximum nor-malized correlation beamformer with the recordings from left index finger finger move-ments experiment. The map is normalized and truncated the parts that their coherence is lower than 0.2. We use the estimation at the location with the maximum F-statistic value as reference signal and then exploits the procedure introduced in 3.3.4 to imaging the time-frequency coherent sources. (a)Power spectrum of Morlet wavelet representation of reference signal (ROI of the wavelet coefficients) (b)Viewing coherent level in whole source space slice by slice.

78 Experiment Results

Time (sec.)

Frequency (Hz)

−1 −0.5 0 0.5 1

10 15 20 25

(a)

0 23.9

(b)

Figure 4.16: Time-frequency Coherence map of the estimated sources by maximum nor-malized correlation beamformer with the recordings from right index finger finger move-ments experiment. The map is normalized and truncated the parts that their coherence is lower than 0.2. We use the estimation at the location with the maximum F-statistic value as reference signal and then exploits the procedure introduced in 3.3.4 to imaging the time-frequency coherent sources. (a)Power spectrum of Morlet wavelet representation of reference signal (ROI of the wavelet coefficients) (b)Viewing coherent level in whole source space slice by slice.

Chapter 5

Conclusions

80 Conclusions

In 3.2.4, we proposed maximum contrast beamformer which determines a meaning-ful source orientation that maximizes the F-statistic value. The criteria is similar with SAM such that it has no probability of miss-detection that LCMV-based approaches may encounter. Rather than (exhaustively) searching, our method determines the source ori-entation via solving an eigen problem of a 3 × 3 matrix. The problem can be solved by deterministic steps including just primary arithmetic and matrix computational operations, that is, the computational complexity is merely O(1).

In 3.3.3, we proposed another algorithm, maximum normalized correlation beamformer, to image the coherent sources. The algorithm is like DICS but, first, we use the technique that is similar to maximum contrast beamformer to analytically determine a proper di-rection (maximum normalized correlation) for probing and, second, it, theoretically, can image the sources which correlate in the domain where the auto- and cross- correlation are defined.

In 3.3.4, we utilized maximum normalized correlation beamformer and provide a pro-cedure to image the time-frequency coherent sources that may be coherent cross multi-ple band by computing the auto- and cross- correlation on the selected Morlet wavelet domain. First we transform the reference signal from time course representation to the time-frequency representation by Morlet wavelet coefficients among which we select the interesting coefficients. After the same step is applied to the recordings, we estimate the auto- and cross- correlation matrix by average that of very trials. Finally, feed auto- and cross- correlation matrix into the maximum normalized correlation beamformer to estimate the coherence between the target position and the reference signal.

In Chapter 4, the simulation, phantom experiments were conducted to generate record-ings with the ground truth for verification and demonstration of the proposed methods. Ac-cording to the results, we can find that, indeed, they can accurately find the orientation of the targeted source with low computational cost. Table 5.1 gives a summarized comparison between our, LCMV-based, SAM methods in the issues of accuracy and efficiency. Also, proposed methods respectively image reasonable maps of the significance of the source power and coherent sources in the head by feeding the simulated recordings. Besides, we apply our method to the recordings measured from real finger movement experiment and the results approximates fit the already-known neuropathological knowledge.

Conclusions 81

Table 5.1: Comparison of SAM, LCMV and our methods in both computational cost and robustness. ”Our” stands for our methods including maximum contrast and maximum normalized correlation beamformers. ”SAM 3D” stands for the extension of the SAM that probing the direction in 3D space, that is, with two degree of freedom like the ability of

”Our” and ”LCMV”.

Comparison of different methods Accuracy Our ≥ SAM 3D > LCMV Efficiency LCMV > Our > SAM >> SAM 3D

82 Conclusions

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