Frequencydomain Criterion for Speech Distortion Weighted Multi Channel

Frequency-domain Criterion for Speech Distortion Weighted Multi. Channel Wiener Filtering 1 1 2 Simon Doclo , Ann Spriet 1, 2, Marc Moonen , Jan Wouters 1 Dept. of Electrical Engineering (ESAT-SCD), KU Leuven, Belgium 2 Laboratory for Exp. ORL, KU Leuven, Belgium HSCMA-2005, 17. 03. 2005

Overview • Adaptive beamforming: GSC o Not robust against signal model errors • Spatially-preprocessed SDW-MWF: o Increase robustness of adaptive stage by taking speech distortion into account o Implementation: stochastic gradient algorithms o Frequency-domain criterion o Experimental validation in hearing instruments • Audio demonstration • Conclusions 2

Hearing instruments § Introduction § Adaptive beamforming § Experimental validation § Audio demo § Conclusions • Hearing problems effect more than 10% of population hearing aids and cochlear implants • Digital hearing instruments allow for advanced signal processing, resulting in improved speech understanding • Major problem: (directional) hearing in background noise o o reduction of noise wrt useful speech signal multiple microphones + DSP in BTE current systems: simple fixed and adaptive beamforming robustness important due to small inter-microphone distance design of robust multi-microphone noise reduction scheme 3

GSC = Adaptive MVDR-beamformer § Introduction § Adaptive beamforming -GSC -SP-SDW-MWF -Implementation Spatial pre-processor (Fixed beamforming) 0° 0° G Adaptive stage (Adaptive Noise Canceller) speech reference + speech + noise § Experimental -- validation § Audio demo § Conclusions 0° noise references noise + speech leakage Avoids speech distortion Filter w 1 speech + noise distorted speech + noise Filter w 2 Minimises output noise power Relies on assumptions known mic characteristics, known speaker position, no reverberation Violated in practice Speech distortion ! 4

Robustness against model errors § Introduction • § Adaptive beamforming -GSC -SP-SDW-MWF -Implementation Spatial pre-processor and adaptive stage rely on assumptions that are generally not satisfied in practice: o Distortion of speech component in speech reference o Leakage of speech into noise references, i. e. Speech component in output signal gets distorted § Experimental validation § Audio demo § Conclusions • Design of robust noise reduction algorithm: 1. Reduce speech leakage contributions in noise references: • Robust fixed spatial filter [Nordebo 94, Doclo 03] • Adaptive blocking matrix [Van Compernolle 90, Hoshuyama 99, Herbordt 01] • Estimate relative acoustic transfer functions [Gannot 01] 2. Reduce effect of present speech leakage: • Only update adaptive filter during low-SNR periods/frequencies • Quadratic inequality constraint, leaky LMS [Cox 87, Claesson 92, Tian 01] • Take speech distortion explicitly into account, SDW-MWF [Spriet 04] 5

Design of robust adaptive stage § Introduction • Distorted speech in output signal: § Adaptive • Robustness: limit beamforming -GSC -SP-SDW-MWF -Implementation § Experimental validation by controlling adaptive filter o Quadratic inequality constraint (QIC-GSC): = conservative approach, constraint f (amount of leakage) o Take speech distortion into account in optimisation criterion (SDW-MWF) § Audio demo § Conclusions noise reduction speech distortion – 1/ trades off noise reduction and speech distortion (1/ = 0 GSC, 1/ = 1 MMSE estimate) – Regularisation term ~ amount of speech leakage Limit speech distortion, while not affecting noise reduction performance in case of no model errors QIC 6

Implementation § Introduction § Adaptive beamforming -GSC -SP-SDW-MWF -Implementation § Experimental • Algorithms: o Recursive matrix-based (GSVD, QRD) – too expensive o Stochastic gradient algorithms (time vs. frequency domain) • Stochastic gradient algorithm (time-domain): o Cost function validation § Audio demo § Conclusions results in LMS-based updating formula Classical GSC regularisation term o Practical computation of regularisation term using data buffers o Reduce complexity by frequency-domain implementation [Spriet 04] Still large memory requirement due to data buffers o Memory reduction by approximating FD regularisation term [Doclo 04] 8

Frequency-domain criterion (1) § Introduction § Adaptive • Extension of block-based frequency-domain criterion for multi -channel AEC [Benesty 01, Buchner 03] beamforming -GSC -SP-SDW-MWF -Implementation § Experimental validation § Audio demo § Conclusions • Set derivative wrt time-domain filter coefficients w to zero normal equations in FD • Recursive algorithm (details cf. book “Speech Enhancement”) 9

Frequency-domain criterion (2) § Introduction • Practical calculation of regularisation term averaging § Adaptive beamforming -GSC -SP-SDW-MWF -Implementation § Experimental validation • Approximations for reducing the computational complexity: o Approximate and by block-diagonal (or diagonal) correlation matrices : § Audio demo § Conclusions (block-)diagonal matrices can be easily inverted Ensure that is positive-definite: eigenvalues of (block-)diagonal matrix can be easily computed o Constrained vs. unconstrained update : corresponds to setting derivate wrt frequency-domain filter coefficients to zero 10

Experimental results mic 1 mic 2 § Introduction Configuration § Adaptive • 3 -mic BTE on dummy head (d = 1 cm, 1. 5 cm) beamforming • Speech source in front of dummy head (0 ) § Experimental • 5 speech-like noise sources: 75 , 120 , 180 , 240 , 285 • Gain mismatch validation -Performance -Complexity § Audio demo mic 3 = 4 d. B at 2 nd microphone Reverberation time = 500 msec § Conclusions Noise 5 Noise 1 H. A. Noise 4 Noise 3 11

Performan ce measures § Introduction § Adaptive beamforming • Improvement in speech intelligibility [d. B] speech noise § Experimental validation -Performance -Complexity f § Audio demo - § Conclusions [d. B] Importance of i-th band for speech intelligibility • Speech distortion [d. B] input speech output speech - f [d. B] 12

Experimental validation (1) § Introduction § Adaptive beamforming § Experimental • SDR-GSC (unconstrained update) o Results after convergence (L=32, =0. 5, =0. 995, BD/D stepsize) o GSC (1/ = 0) : degraded performance if significant leakage o 1/ > 0 increases robustness (speech distortion noise reduction) validation -Performance -Complexity § Audio demo § Conclusions GSC 13

Experimental validation (2) § Introduction § Adaptive beamforming § Experimental • Convergence behaviour: o Convergence speed: block-diagonal step size > diagonal step size o large fast convergence o large slow convergence, better performance upon convergence validation -Performance -Complexity § Audio demo § Conclusions 14

Complexity + memory § Introduction • Parameters: M = 3 ( mics), N = 2 (a), N = 3 (b), L = 32, fs = 16 k. Hz, Ly = 10000 § Adaptive • Computational complexity: beamforming Algorithm Complexity (MAC) MIPS QIC-GSC (FD) (3 M-1)FFT + 16 M - 9 2. 16 SDW-MWF (FD-buffer) (3 N+5)FFT + 30 N + 10 3. 22(a), 4. 27(b) § Audio demo SDW-MWF (FD-matrix-diag) (3 N+2)FFT + 8 N 2 + 13 N 2. 46(a), 3. 89(b) § Conclusions SDW-MWF (FD-matrix-BD) (3 N+2)FFT + 14 N 2 + 10 N + 12 2. 94 (N=2 !) § Experimental validation -Performance -Complexity • Memory requirement: Algorithm Memory k. Words QIC-GSC (FD) 4(M-1)L + 6 L 0. 45 SDW-MWF (FD-buffer) 2 NLy + 6 LN + 7 L 40. 61 SDW-MWF (FD-matrix-all) 4 LN 2 + 6 LN + 7 L 1. 12 (a), 60. 80 1. 95 (b) Complexity and memory comparable to QIC-GSC 15

Audio demonstration § Introduction Algorithm No deviations Deviation (4 d. B) § Adaptive beamforming Noisy microphone signal § Experimental validation § Audio demo Speech reference § Conclusions Noise reference Output GSC (1/ = 0) Output SDR-GSC (1/ = 0. 5) (L=32, =10, =0. 99875, block-diagonal stepsize, unconstrained update ) 16

Conclusions § Introduction • Spatially pre-processed SDW-MWF: § Adaptive o Take speech distortion explicitly into account improve robustness of adaptive stage § Experimental o Encompasses GSC and MWF as special cases beamforming validation § Audio demo § Conclusions • Implementation: o Stochastic gradient algorithms in time- and frequency-domain o Frequency-domain criterion: block-based processing natural derivation of different adaptive algorithms o Block-diagonal vs. diagonal, constrained vs. unconstrained o Comparable implementation cost as QIC-GSC • Experimental results: o SP-SDW-MWF achieves better noise reduction than QIC-GSC, for a given maximum speech distortion level o Faster convergence speed for block-diagonal step size matrix 17