Independent Component Analysis Algorithm for Adaptive Noise Cancelling 적응 잡음 제거를 위한 독립 성분 분석 알고리즘 Hyung-Min Park, Sang-Hoon Oh, and Soo-Young Lee Brain Science Research Center and Department of Electrical Engineering and Computer Science Korea Advanced Institute of Science and Technology

2 Contents  Adaptive Noise Cancelling (ANC)  Least mean squares algorithm  ANC based on independent component analysis (ICA)  Learning rule  Extention to transform-domain adaptive filtering (TDAF) methods  Experimental results  Conclusion

3 Adaptive Noise Cancelling  Adaptive noise cancelling  An approach to reduce noise based on reference noise signals  System output  The LMS algorithm

4 Independent Component Analysis  Recover independent sources from linear mixtures  Sensor signals  Problem  To recover the original sources by estimating unmixing matrix  Information theoretical approach  Maximizing the entropy of s u x A W where y g

5 ICA-based Approach to ANC (1)  Maximizing entropy  Set dummy output  Learning rules of adaptive filter coefficients in ANC where u x w(k)w(k) y n 1 v s n 1 y 2

6 ICA-based Approach to ANC (2)  The difference between the LMS algorithm and the ICA-based approach  Existence of the score function  The LMS algorithm Decorrelate output signal from the reference input  The ICA-based approach Make output signal independent of the reference input  Independence  Involve higher-order statistics including correlation  The ICA-based approach  Remove the noise components using higher-order statistics and correlation

7 Transform-Domain Adaptive Filtering  LMS algorithm  The most widely used real time adaptive filtering algorithm  Convergence speed of the LMS algorithm  Controlled by the spread of eigenvalues of the autocorrelation matrix of the input data  Enhanced by reducing the eigenvalue spread  TDAF methods  Pre-whiten the input data using unitary transform  The best transform -> Karhunen-Loéve transform (KLT) Depend on the signal -> usually cannot be computed in real time –Replaced by simpler transforms

8 TDAF approach to ANC  Normalized LMS algorithm  Normalized ICA-based algorithm where

9 Experimental Setup  Measure  SNR in the system ouput  Input signals  Artificially generated i.i.d. signals  Recorded sources Signal -> speech Noise -> car noise, speech noise, music noise

10 Experimental Results (1)  Experiments for artificially generated i.i.d. signals  SNRs of output signals for the simple simulation mixing filter (dB) Signal and Noise Initial SNRs SNRs after convergence LMS algorithm ICA-based approach Laplacian Gaussian

11 Discussion on the experiments for artificially generated i.i.d. signals  The Laplacian source signals  The performances of the ICA-based approach Better than those of the LMS algorithm –There may be many components which have dependency through higher-order statistics –Cancelled by the ICA-based approach  The Gaussian source signals  The ICA-based approach Almost the same SNRs as or a little worse than the LMS algorithm  Described by only the first and second-order statistics  The score function is not adequate to the original signal  The performances can be degraded.

12 Experimental Results (2)  Experiments for recorded signals  Signal waveforms for the car noise and the simple simulation filter Signal sourceNoise source Primary input signalSystem output signal

13 Experimental Results (3)  Experiments for recorded signals  SNRs of output signals for the measured filter

14 Experimental Results (4)  Comparison of learning curves with and without TDAF  Car noise The ICA-based approachThe LMS algorithm

15 Discussion on the experiments for the extension to the TDAF method  Convergence speed  The ICA-based algorithm Significantly improved by TDAF with the almost same SNR after convergence  The LMS algorithm No obvious difference with TDAF –Relatively large step sizes gave higher SNRs after convergence –Fast convergence speed in the beginning  The ICA-based algorithm with TDAF Comparable with the LMS algorithm in the beginning with better SNR after convergence

16 Conclusion  A method to ANC based on ICA was proposed.  The ICA-based learning rule was derived.  The ICA-based approach  Include higher-order statistics  Make the output independent of the reference input The LMS algorithm –Make the output uncorrelated to the reference input  Gave better performances than the LMS algorithm  TDAF method was applied to the ICA-based approach.  Derived the normalized ICA-based learning rule  Improved convergence rates