Optimal local polynomial regression of noisy time-varying signals
We address the problem of local-polynomial modeling of smooth time-varying\nsignals with unknown functional form, in the presence of additive noise.\nThe problem formulation is in the time domain and the \npolynomial coefficients are estimated in the pointwise minimum mean square\nerror (PMMSE) sense. The choice of the window length for local modeling\nintroduces a bias-variance tradeoff, which we solve optimally by using the\nintersection-of-confidence-intervals (ICI) technique. The combination\nof the local polynomial model and the ICI technique gives rise to an\nadaptive signal model equipped with a time-varying PMMSE-optimal window\nlength whose performance is superior to that obtained by using a fixed\nwindow length. We also evaluate the sensitivity of the ICI technique with\nrespect to the confidence interval width. Simulation results on\nelectrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio\n(SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo\nperformance analysis shows that the performance is comparable to the basic\nwavelet techniques. For 0 dB SNR, the adaptive window technique yields\nabout 2-3dB higher SNR than wavelet regression techniques and for SNRs\ngreater than 12dB, the wavelet techniques yield about 2dB higher SNR.