Robust 3-way Tensor Decomposition and Extended State Kalman Filtering to Extract Fetal ECG

Transcription

1 Robust 3-way Tensor Decomposition and Extended State Kalman Filtering to Extract Fetal ECG Mohammad Niknazar, Hanna Becker, Bertrand Rivet, Christian Jutten, and Pierre Comon GIPSA lab, Grenoble, France

2 The Basic Problem Several sources of interference and noise Much lower amplitude of fecg compared with mecg

3 Multichannel Fetal ECG Extraction Current methods Adaptive filtering [Widrow et al. 1975] Independent component analysis (ICA) [De Lathauwer et al. 1995, Zarzoso & Nandi 21] Periodic component analysis (ΠCA) [Tsalaile et al. 29] Basic idea: Exploitation of the redundancy of the multichannel ECG to reduce mecg Drawback Exogenous noise cannot be totally canceled in this way Demand several channels 3

4 Outline of Fetal ECG Extraction and Denoising Using Only Two Electrodes ECGs estimation based on modifications of a tensor based parallel deflation procedure Weighted Canonical Polyadic decomposition Gaussian-shaped cost function Improvement of fecg and mecg estimates by a Kalman filtering Multichannel extension of dynamic ECG model for N ECGs Results on different data 4

5 Tensor Construction of Sources Having Different Symbol Rate A.L.F.D. Almeida, P. Comon, and X. Luciani, "Deterministic Blind Separation of Sources Having Different Symbol Rates Using Tensor-Based Parallel Deflation", in Proc. LVA/ICA, 21, pp

6 Third-Order Tensor Arrangement of an ECG Signal x 1 4 Y C ( n) M Tn Ln M: Number of sensors T : Number of ECG beats n L : Time samples per beat n ECG Amplitude ECG Beat 6 Time (Sample)

7 Third-Order Tensor Decomposition for n-th ECG Using the Canonical Polyadic (CP) min Y R n = A S H + N ( n) ( n) ( n) ( n) r r r r= 1 { ˆ ( n) ˆ ( n) ˆ ( n) A, S, H } A: Mixing matrix S: ECG beat amplitude H: ECG beat temporal pattern : Outer product R : Tensor rank R 2 n ( n) ( n) ( n) ( n) yijk air sjr hkr i, j, k r= 1 F n 7

8 Mixed ECGs on Two Electrodes

9 Maternal Tensor Two components 5 Maternal Tensor

10 Maternal Components Two extracted components.2 Maternal Components

11 Fetal Tensor fecg is weak: One component 5 Fetal Tensor

12 Fetal Component mecg prevents the algorithms to concentrate on fecg Fetal Component

13 Weighted CP Decomposition (WCPD) and Gaussian-shaped Cost Function (GCF) 5 min min ˆ ( n ) ˆ ( n) ˆ ( n) { A, S, H } { ˆ ( n ) ˆ ( n ) ˆ ( n) A, S, H } min ˆ ( n) ˆ ( n) ˆ ( n) { A, S, H } Rn ( n) ( n) ( n) ( n) ( n) wijk yijk air sjr hkr i, j, k r= 1 Rn ( n) ( n) ( n) ( n) ψ yijk air sjr hkr i, jk, r= 1 ( y µ ) ( n ) wijk = exp 2 σik R 2 n ( n) ( n) ( n) ( n) yijk air sjr hkr i, j, k r= 1 F 2 F ( n) 2 ijk ik 2 u ψ ( u) = 1 exp{ } 2 2σ 13

14 Fetal Components via Weighted Tensor Decomposition.15 Fetal Component

15 Extended Kalman Filter and Dynamic ECG Model A: Mixing matrix S: ECG beat amplitude H: ECG beat temporal pattern θk+ 1= ( θk+ ωδ )mod(2 π) 2 αω i θi zk+ 1= δ θ exp( ) 2 i + z 2 k+ η i { PQRST,,,, } bi 2bi ϕk 1 θk uk x [, ] T = + k = θk zk s k 1 z k v k R. Sameni, M. B. Shamsollahi, C. Jutten, and G. D. Clifford, A Nonlinear Bayesian Filtering Framework for ECG Denoising, IEEE Trans. Biomed. Eng., vol. 54, no. 12, pp , December

16 Multichannel Extension of Dynamical ECG Model for N ECGs x θ θ (1) ( N ) (1) ( N ) T k = [ k,, k, zk,, zk ] [ (1) ( ) (1) ( ),, N M,,, ] T k = ϕk ϕk sk sk y I y = x + u A k k k a11 a1 N A= =? am1 a MN ( ) ( ) ( ) ( ) { α n, n, n, n i bi ψi ω } i PQ,, RST,, =? 16

17 Using Loading Matrices for Mixing Matrix and Parameter Estimation A: Mixing matrix S: ECG beat amplitude H: ECG beat temporal pattern The mixing matrix is directly defined as the concatenation of the loading matrices A (n) related to the fetus and to the mother ( ) ( ) ( ) ( ) The state parameters { α n, n, n, n i bi ψi ω } are obtained by fitting, for each ECG, the sum of the Gaussian functions with the loading matrix H (n) The ECG variability is estimated using the third loading matrix S (n) 17

18 DaISy ECG Dataset 18

19 Twin MCG Dataset 19

20 Conclusions and Perspectives Robust 3-way tensor decomposition Extension of a synthetic dynamical ECG model within a Kalman filtering framework to model several ECGs Only two electrodes are utilized Deep comparison between tensor decomposition methods Application of the proposed method on other datasets 2

21 Thank You Arabic Russian Grazie Italian Mulţumesc Persian Hebrew Merci French Gracias Spanish Obrigado Portuguese Danke German Traditional Chinese Japanese Korean Simplified Chinese Thai 21