In this paper we propose an efficient process of physiological artifact elimination methodology from brain waves (BW), which are also commonly known as electroencephalogram (EEG) signal. In a clinical environment during the acquisition of BW several artifacts contaminates the actual BW component. This leads to inaccurate and ambiguous diagnosis. As the statistical nature of the EEG signal is more non-stationery, adaptive filtering is the more promising method for the process of artifact elimination. In clinical conditions, the conventional adaptive techniques require many numbers of computational operations and leads to data samples overlapping and instability of the algorithm used. This causes delay in diagnosis and decision making. To overcome this problem in our work we propose to set a threshold value to diminish the problem of round off error. The resultant adaptive algorithm based on this strategy is Non-linear Least mean square (NL^{2}MS) algorithm. Again, to improve this algorithm in terms of filtering capability we perform data normalization, using this algorithm several hybrid versions are developed to improve filtering and reduce computational operations. Using the method, a new signal enhancement unit (SEU) is realized and performance of various hybrid versions of algorithms examined using real EEG signals recorded from the subject. The ability of the proposed schemes is measured in terms of convergence, enhancement and multiplications required. Among various SEUs, the MCN^{2}L^{2}MS algorithm achieves 14.6734, 12.8732, 10.9257, 15.7790 dB during the artifact removal of RA, EMG, CSA and EBA components with only two multiplications. Hence, this algorithm seems to be better candidate for artifact elimination.

Electroencephalogram (EEG) is the key tool to illustrates the functionality of various segments of the brain. Any physiological abnormality in the brain results abnormalities in the biopotentials generated in the neurons and causes medical ill conditions in the patient. As per the surveys of world health organization reported in [

In wireless EEG monitoring systems, the computational complexity is a major concern to be concentrated. If the received filter length is large, much time is required to perform the filtering operations, which are in terms of additions and multiplications. This cause overlapping of data values at the input of the SEU. To achieve less computational complexity, we develop the hybrid versions of MN^{2}L^{2}MS and clipped algorithms based on [^{2}MS). To improve convergence speed and to improve filtering capability we apply data normalization. The normalization with respect to data vector of Non-Linear LMS is termed as Normalized Non-Linear LMS (N^{2}L^{2}MS). This increase the number of computations of the denominator part of the algorithm equal to tap length. To avoid this, we modified the N^{2}L^{2}MS algorithm such that, the normalization is performed with respect to maximum of the input vector instead of all the values of the vector. As a result, the number of multiplication operations required in the denominator is only one. This algorithm is termed as Modified N^{2}L^{2}MS (M N^{2}L^{2}MS) algorithm. The resultant algorithms are Modified Clipped N^{2}L^{2}MS (MCN^{2}L^{2}MS) algorithm, Modified Sign (MSN^{2}L^{2}MS) algorithm and Modified Sign Sign N^{2}L^{2}MS (MS^{2}N^{2}L^{2}MS) algorithm. Using this adaptive FIR frame work we develop a signal enhancement unit (SEU) to eliminate various physiological components from brain wave in clinical scenario. The performance of various algorithms in SEU are tested experimentally using real EEG signals.

In the artifact elimination process the key element is the adaptive algorithm, which trains the FIR filter to change its coefficients. Let us consider ‘L’ to be the length of FIR filter. To facilitate ability to alter coefficients of filter in accordance to the artifact component this FIR filter is associated with an adaptive algorithm initially. Based on this strategy and using the framework of artifact elimination we develop an efficient adaptive artifact eliminator (AAE) which has better convergence, filtering ability, stability and less computational complexity.

A random component

Here, the step size parameter is written as,

In the next version of NLMS we normalize the step size with the maximum value of data vector E(n). This minimizes the number of computations in the denominator of the weight update recursion.

In physiological signal monitoring applications during critical conditions minute errors leads ambiguity in diagnosis. During critical conditions the decision has to be make instantaneously. To avoid this, a non-linear operation is combined with LMS algorithm, which results non-linear LMS (NL^{2}MS) and is able to eliminate the ambiguities of round-off errors [^{2}MS in the process of artifact elimination in EEG signals. This nonlinearity is defined as,

where d is threshold.

When applied to the error signal, it converts the LMS update recursion equation to

This is the mathematical recursion for NL^{2}MS algorithm. To achieve better convergence and enhancement we combine this NL^{2}MS algorithm with NLMS and results normalized non-linear LMS (N^{2}L^{2}MS). The mathematical expression for this algorithm is given as,

where

A generalized flow diagram for the proposed SEU for brain wave enhancement is shown in ^{2}L^{2}MS algorithm with sign-based algorithms. The three-familiar sign-based algorithms are clipped algorithm, sign algorithm and sign sign algorithm. The hybrid versions of N^{2}L^{2}MS and signed algorithms are named as, clipped N^{2}L^{2}MS algorithm (CN^{2}L^{2}MS), sign N^{2}L^{2}MS (S N^{2}L^{2}MS), sign sign N^{2}L^{2}MS (S^{2}N^{2}L^{2}MS) algorithms respectively. Again, these normalized versions of the algorithms suffer with a problem of computational complexity due to normalization. This is due to the normalization with respect to the input data vector of length ‘L’. In this operation ‘L’ number of multiplications are needed. To avoid this problem further N^{2}L^{2}MS is modified such that in the data normalization operation, the normalization is performed with respect to the maximum data value of the input vector. These versions of the proposed algorithms are called modified N^{2}L^{2}MS algorithm (MN^{2}L^{2}MS), modified clipped N^{2}L^{2}MS algorithm (MCN^{2}L^{2}MS), modified sign N^{2}L^{2}MS algorithm (MS N^{2}L^{2}MS), modified sign N^{2}L^{2}MS algorithm (MS^{2} N^{2}L^{2}MS) respectively.

The weight update recursions for modified N^{2}L^{2}MS algorithm is given as,

where

Here, ms(n) is the modified step size, which is the normalized version with respect to maximum value of data vector instead of normalization with respect to entire input data vector. This minimized computational complexity in the denominator by an amount ^{2}L^{2}MS algorithm we can minimize the number of computations for performing the filtering process. The theory and analysis of clipped algorithm is presented in [^{2}L^{2}MS algorithm (MCN^{2}L^{2}MS). Its weight update phenomenon mathematically can be written as,

where

Similarly, by combining Sign LMS (SLMS) and Sign Sign LMS (SSLMS) with MN^{2}L^{2}MS results MSN^{2}L^{2}MS and MS^{2} N^{2}L^{2}MS algorithms respectively. The weight update mechanism for these techniques can be written as,

Therefore, using these algorithms, namely, N^{2}L^{2}MS, MN^{2}L^{2}MS, MCN^{2}L^{2}MS, MSN^{2}L^{2}MS and MS^{2}N^{2}L^{2}MS we develop various signal enhancement units. The convergence curves for LMS algorithm and its signed algorithms versions are shown ^{2}L^{2}MS is just inferior than MN^{2}L^{2}MS.

The computational complexity of the above-mentioned enhancement techniques is shown in ^{2}L^{2}MS, MSN^{2}L^{2}MS and MS^{2}N^{2}L^{2}MS, MS^{2}N^{2}L^{2}MS has less computational complexity. But as the data vector and error component are undergoing clipping results in the much quantity of information will be missed in the signal enhancement operation. Hence, the filtering ability of the technique is poor. This is also evident form the filtering ability presented in the next section. The MN^{2}L^{2}MS has the complexity in terms of multiplications equal to MSN^{2}L^{2}MS, but due to error clipping its resolution is inferior than MN^{2}L^{2}MS. So, MSN^{2}L^{2}MS is also not a good candidate for artifact elimination process. Whereas, in MCN^{2}L^{2}MS the data vector is clipped and its computational complexity is nearly equal to conventional LMS in terms of multiplications with increased convergence characteristics. Also, the number of multiplications required in the second part of the weight update recursion is independent of filter length. Therefore, based on the analysis of various algorithms in terms of convergence characteristics and number of multiplications, the MCN^{2}L^{2}MS is seems to be a better candidate for brain wave analysis in wireless EEG monitoring devices as well as in remote health care monitoring systems.

S.No. | Algorithm | Multiplications | Additions | ASC | Divisions |
---|---|---|---|---|---|

1. | LMS | Nil | Nil | ||

2. | N^{2}L^{2}MS |
Nil | 1 | ||

3. | MN^{2}L^{2}MS |
Nil | 1 | ||

4. | MCN^{2}L^{2}MS |
2 | Nil | 1 | |

5. | MSN^{2}L^{2}MS |
Nil | 1 | ||

6. | MS^{2}N^{2}L^{2}MS |
Nil | Nil | 1 |

To demonstrate the ability of the signal enhancement scheme in health care monitoring contest we have recorded several brain waves in various physiological scenarios using the Emotive EPOC brain wave acquisition headset [^{2}L^{2}MS, MN^{2}L^{2}MS, MCN^{2}L^{2}MS, MSN^{2}L^{2}MS, MS^{2}N^{2}L^{2}MS algorithms. A typical noise generator is used in the experiments to facilitate reference signal to the signal enhancement unit. The filter length is chosen as 5. As the filter length increases the filtering process will be accelerated but excess mean square error also increases. This in turn decreases the signal to noise ratio. So, we have chosen filter length as 5. The experimental findings of artifact elimination are described case by case in the following sub-sections.

Artifacttype | Sample No. | SNRI due to various signal enhancement techniques | |||||
---|---|---|---|---|---|---|---|

LMS | N^{2}L^{2}MS |
MN^{2}L^{2}MS |
MCN^{2}L^{2}MS |
MSN^{2}L^{2}MS |
MS^{2}N^{2}L^{2}MS |
||

RA | EEG1 | 7.8476 | 16.3562 | 15.7870 | 14.6734 | 12.7342 | 10.6472 |

EEG2 | 7.2387 | 16.2794 | 15.5632 | 14.1979 | 12. 0637 | 10. 6422 | |

EEG3 | 7.1343 | 16.1133 | 15.3254 | 14.0256 | 12. 0364 | 10. 6241 | |

EEG4 | 7.5372 | 16.3511 | 15.6334 | 14.6232 | 12. 6523 | 10. 6456 | |

EEG5 | 7.9362 | 16.7231 | 15.9343 | 14.9454 | 12. 9342 | 10. 7643 | |

EMG | EEG1 | 6.2187 | 15.9572 | 13.9448 | 12.8732 | 10.9245 | 8.8421 |

EEG2 | 6.3654 | 15.7810 | 13.8437 | 12.5742 | 10.8920 | 8.6433 | |

EEG3 | 6.7382 | 15.5631 | 13.5351 | 12.4265 | 10.6342 | 8.4531 | |

EEG4 | 6.8365 | 15.5372 | 13.4523 | 12.3721 | 10.2755 | 8.1791 | |

EEG5 | 6.8436 | 15.0863 | 13.4437 | 12.0728 | 10.0264 | 8.1257 | |

CSA | EEG1 | 4.9953 | 13.9872 | 12.9196 | 10.9257 | 9.8647 | 7.7742 |

EEG2 | 4.9643 | 13.7995 | 12.8743 | 10.8430 | 9.8270 | 7.5631 | |

EEG3 | 4.5218 | 13.7436 | 12.6319 | 10.7341 | 9.6036 | 7.4972 | |

EEG4 | 4.3142 | 13.2432 | 12.5871 | 10.5631 | 9.5542 | 7.3268 | |

EEG5 | 4.0402 | 13.1151 | 12.4537 | 10.1547 | 9.0564 | 7.0146 | |

EBA | EEG1 | 8.7531 | 18.7536 | 16.9114 | 15.7790 | 14.8749 | 11.8321 |

EEG2 | 8.6563 | 18.7091 | 16.8542 | 15.6972 | 14.5967 | 11.7127 | |

EEG3 | 8.5546 | 18.5896 | 16.5826 | 15.5411 | 14.5163 | 11.5937 | |

EEG4 | 8.2761 | 18.4342 | 16.2745 | 15.3380 | 14.3164 | 11.4741 | |

EEG5 | 8.1598 | 18.3592 | 16.2531 | 15.1917 | 14.2364 | 11.1414 | |

Noise | Measure | LMS | N^{2}L^{2}MS |
MN^{2}L^{2}MS |
MCN^{2}L^{2}MS |
MSN^{2}L^{2}MS |
MS^{2}N^{2}L^{2}MS |
---|---|---|---|---|---|---|---|

RA | Excess MSE | −17.7383 | −36.8376 | −34.6194 | −32.5537 | −30.0053 | −27.9637 |

Misadjustment | 0.1868 | 0.08649 | 0.0975 | 0.1063 | 0.1366 | 0.1649 | |

Coherence | 0.5687 | 0.9694 | 0.9248 | 0.8785 | 0.6003 | 0.5951 | |

EMG | Excess MSE | −16.5456 | −32.5791 | −30.1873 | −29.3341 | −28.8792 | −26.6649 |

Misadjustment | 0.7456 | 0.1137 | 0.2434 | 0.3438 | 0.4582 | 0.5342 | |

Coherence | 0.4562 | 0.8872 | 0.8464 | 0.7982 | 0.5478 | 0.4864 | |

CSA | Excess MSE | −15.3754 | −29.5742 | −27.8467 | −26.7591 | −25.7539 | −23.1586 |

Misadjustment | 0.8945 | 0.1554 | 0.3564 | 0.4627 | 0.5225 | 0.6847 | |

Coherence | 0.5478 | 0.8295 | 0.7946 | 0.7727 | 0.6651 | 0.5975 | |

EBA | Excess MSE | −18.4268 | −39.3572 | −37.8524 | −35.1866 | −32.7841 | −30.1379 |

Misadjustment | 0.6196 | 0.1452 | 0.2392 | 0.3315 | 0.4287 | 0.5205 | |

Coherence | 0.6573 | 0.9349 | 0.8974 | 0.8659 | 0.7579 | 0.6876 |

This experiment proves the RA elimination process from EEG component. The raw brain wave component is taken as input to the SEU as shown in ^{2}L^{2}MS and its signum based variants. Again, by examine the performance measures in terms of convergence rate, SNR, excess mean square error, misadjustment, among the various algorithms N^{2}L^{2}MS based SEU achieves highest performance measures. But, among all the algorithms MCN^{2}L^{2}MS based SEU requires less amount of computational complexity in terms of multiplications by an amount of filter length, in this case it is ‘L’, shown in ^{2}L^{2}MS is little bit inferior than N^{2}L^{2}MS algorithm based SEU. This fact is depicted by examine ^{2}L^{2}MS based SEU could be tolerated than SEU based on N^{2}L^{2}MS, as MCN^{2}L^{2}MS needs lesser number of multiplications by an amount ‘L’, which is filter length in this case. Hence, MCN^{2}L^{2}MS based SEU is suitable for elimination of artifacts from brain waves for EEG analysis in remote health care monitoring applications.

This experiment proves the respiration artifact elimination process from EEG signal. The raw brain wave component is taken as input to the SEU as shown in ^{2}L^{2}MS and its variants. Again, by examine the performance measures in terms of convergence rate, SNR, excess mean square error, misadjustment, among the various algorithms N^{2}L^{2}MS based SEU achieves highest performance measures. But, among all the algorithms MCN^{2}L^{2}MS based SEU requires less amount of computational complexity in terms of multiplications by an amount of filter length, in this case it is ‘L’, shown in ^{2}L^{2}MS is little bit inferior than N2L2MS algorithm based SEU. This fact is depicted by examine ^{2}L^{2}MS based SEU could be tolerated than SEU based on N^{2}L^{2}MS, as MCN^{2}L^{2}MS needs lesser number of multiplications by an amount ‘L’, which is filter length in this case. Hence, MCN^{2}L^{2}MS based SEU is suitable for elimination of artifacts from brain waves for EEG analysis in remote health care monitoring applications.

This experiment proves the cardiac signa artifact elimination process from EEG component. The raw brain wave component is taken as input to the SEU as shown in ^{2}L^{2}MS and MCN^{2}L^{2}MS algorithms. Again, by examine the performance measures in terms of convergence rate, SNR, excess mean square error, misadjustment, among the various algorithms N^{2}L^{2}MS based SEU achieves highest performance measures. But, among all the algorithms MC N^{2}L^{2}MS based SEU requires less amount of computational complexity in terms of multiplications by an amount of filter length, in this case it is ‘L’, shown in ^{2}L^{2}MS is little bit inferior than N^{2}L^{2}MS algorithm based SEU. This fact is depicted by examine ^{2}L^{2}MS based SEU could be tolerated than SEU based on N^{2}L^{2}MS, as MCN^{2}L^{2}MS needs lesser number of multiplications by an amount ‘L’, which is filter length in this case. Hence, MC N^{2}L^{2}MS based SEU is suitable for elimination of artifacts from brain waves for EEG analysis in remote health care monitoring applications.

This experiment proves the EBA elimination process from brain wave component. The raw brain wave component is taken as input to the SEU as shown in ^{2}L^{2}MS and its variant algorithms. Again, by examine the performance measures in terms of convergence rate, SNR, excess mean square error, misadjustment, among the various algorithms N^{2}L^{2}MS based SEU achieves highest performance measures. But, among all the algorithms MCN^{2}L^{2}MS based SEU requires less amount of computational complexity in terms of multiplications by an amount of filter length, in this case it is ‘L’, shown in ^{2}L^{2}MS is little bit inferior than N^{2}L^{2}MS algorithm based SEU. This fact is depicted by examine ^{2}L^{2}MS based SEU could be tolerated than SEU based on N^{2}L^{2}MS, as MCN^{2}L^{2}MS needs lesser number of multiplications by an amount ‘L’, which is filter length in this case. Hence, MCN^{2}L^{2}MS based SEU is suitable for elimination of artifacts from brain waves for EEG analysis in remote health care monitoring applications.

This research demonstrates a new method for developing adaptive artifact eliminator to facilitate high-resolution brain waves for wireless EEG monitoring, remote health care monitoring applications in the contest of BCI. The proposed N^{2}L^{2}MS based SEUs achieved good filtering ability, convergence rate, less computational complexity of the adaptive algorithms. To examine these characteristics various SEUs based on N^{2}L^{2}MS, MN^{2}L^{2}MS, MCN^{2}L^{2}MS, MSN^{2}L^{2}MS, MS^{2}N^{2}L^{2}MS algorithms are developed and demonstrated the brain wave enhancement. These implementations are compared with the performance of SEUs based on conventional LMS algorithm. Among these implementations N^{2}L^{2}MS based SEU achieved highest values of performance measures like SNR, EMSE, misadjustment, convergence, except computational complexity. This is evident from ^{2}L^{2}MS and M N^{2}L^{2}MS based SEUs the N^{2}L^{2}MS out performs. Again, when comparing N2L2MS and its hybrid versions of sign algorithms the performance of MS^{2}N^{2}L^{2}MS, diverges more than MN^{2}L^{2}MS due to error clipping, data error clipping. When we compare the performance measures of N^{2}L^{2}MS and MCN^{2}L^{2}MS based SEUs in terms of SNR, EMSE, misadjustemnt convergence rate, the performance of MCN^{2}L^{2}MS is little inferior than N^{2}L^{2}MS. But, the computational complexity of MCN^{2}L^{2}MS is ‘L’ times less than N^{2}L^{2}MS. Hence, it becomes more attractive for wireless and remote health care monitoring applications.