title: Development of gradient descent adaptive algorithms to remove common mode artifact for improvement of cardiovascular signal quality.
abstract: BACKGROUND
  Common-mode noise degrades cardiovascular signal quality and diminishes measurement accuracy. Filtering to remove noise components in the frequency domain often distorts the signal.
  
  
  METHODS
  Two adaptive noise canceling (ANC) algorithms were tested to adjust weighted reference signals for optimal subtraction from a primary signal. Update of weight w was based upon the gradient term of the steepest descent equation: [see text], where the error epsilon is the difference between primary and weighted reference signals. nabla was estimated from Deltaepsilon(2) and Deltaw without using a variable Deltaw in the denominator which can cause instability. The Parallel Comparison (PC) algorithm computed Deltaepsilon(2) using fixed finite differences +/- Deltaw in parallel during each discrete time k. The ALOPEX algorithm computed Deltaepsilon(2)x Deltaw from time k to k + 1 to estimate nabla, with a random number added to account for Deltaepsilon(2) . Deltaw--> 0 near the optimal weighting.
  
  
  RESULTS
  Using simulated data, both algorithms stably converged to the optimal weighting within 50-2000 discrete sample points k even with a SNR = 1:8 and weights which were initialized far from the optimal. Using a sharply pulsatile cardiac electrogram signal with added noise so that the SNR = 1:5, both algorithms exhibited stable convergence within 100 ms (100 sample points). Fourier spectral analysis revealed minimal distortion when comparing the signal without added noise to the ANC restored signal.
  
  
  CONCLUSIONS
  ANC algorithms based upon difference calculations can rapidly and stably converge to the optimal weighting in simulated and real cardiovascular data. Signal quality is restored with minimal distortion, increasing the accuracy of biophysical measurement.
authors.affiliation: Department of Pharmacology PH7W318, Columbia University, 630 W 168th Street, New York, NY 10032, USA. ciaccio@columbia.edu
authors.forename: Edward J
authors.initials: EJ
authors.lastname: Ciaccio
authors.forename: Evangelia
authors.initials: E
authors.lastname: Micheli-Tzanakou
mesh_terms: D000465:Algorithms; D016477:Artifacts; D002319:Cardiovascular System; D004562:Electrocardiography / Q000379:methods; D005583:Fourier Analysis; D012815:Signal Processing, Computer-Assisted