Development of Gradient Descent Adaptive Algorithms to Remove Common Mode Artifact for Improvement of Cardiovascular Signal Quality

Abstract

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.

Differences in Repeating Patterns of Complex Fractionated Left Atrial Electrograms in Longstanding Persistent Atrial Fibrillation as Compared With Paroxysmal Atrial Fibrillation

“…In contrast to RI and OI calculations that are used as measures of regularity in traditional DF analysis, 5,6 with linear prediction, the signal is not distorted before measurement because no filtering is applied. The linear predictive weights (coefficients) are adapted using the method of finite differences, which was previously tested and validated in a canine postinfarction model, 11 and later used to remove common mode artifact for improvement of cardiovascular signal quality 12 and for motion artifact cancellation in tonometric recordings. 13 Linear prediction was implemented using the following algorithm: $$\mathrm{v̲}=\mathrm{boldC}·\mathrm{w̲}$$ $$\mathrm{v̲}={false[{\mathrm{v}}_{\mathrm{j}}·{\mathrm{v}}_{\mathrm{normalj}-1}\dots {\mathrm{v}}_{\mathrm{normalj}-\mathrm{normaln}+1}false]}^{\mathrm{T}}$$ where v̲ is a vector of estimates of n future values of CFAE from discrete time epoch j to j−n+1, C is a matrix (linear transformation) of prior CFAE values, the elements of w̲ are the prediction coefficients (weights), and $$\mathrm{boldC}={false[{\mathrm{c̲}}_1{\mathrm{c̲}}_2\dots {\mathrm{c̲}}_{\mathrm{n}}false]}^{\mathrm{T}}$$ $${\mathrm{c̲}}_1=false[{\mathrm{c}}_{\mathrm{normalj}-1}{\mathrm{c}}_{\mathrm{normalj}-2}\dots {\mathrm{c}}_{\mathrm{normalj}-\mathrm{normaln}}false]$$ $${\mathrm{c̲}}_2=false[{\mathrm{c}}_{\mathrm{normalj}-2}{\mathrm{c}}_{\mathrm{normalj}-3}\dots {\mathrm{c}}_{\mathrm{normalj}-\mathrm{normaln}-1}false]$$ … $${\mathrm{c̲}}_{\mathrm{n}}=false[{\mathrm{c}}_{\mathrm{normalj}-\mathrm{normaln}}{\mathrm{c}}_{\mathrm{normalj}-\mathrm{normaln}-1}\dots {\mathrm{c}}_{\mathrm{normalj}-2\mathrm{normaln}+1}false]$$ where j−1, j−2, …, j−2n+1 are prior discrete time epochs, and the row vectors c̲ 1 , c̲ 2 , …, c̲ n are sequences of prior CFAE values.…”

A new LMS algorithm for analysis of atrial fibrillation signals

“…The step size depends on the position of the weights along a performance surface. In prior work, fixed step size has been used with finite differences to make adaptive updates with greater stability for simulated cardiologic data [21] as well as to cancel motion artifact from the blood pressure pulse obtained by tonometry [22]. The MSE is inversely proportional to the convergence coefficient μ [23].…”

“…Furthermore, the intrinsic signal shape of desired versus reference signals should be made to differ. For the new LMS, the step size for weight update was proportional to the finite difference in estimated signal, but updates using fixed increments [21,22,32] may also converge rapidly and stably. Initialization was set so that the path along the performance surface was within the concavity of the global minimum error.…”

“…Addition of a stochastic factor (random number) in Eq. 16 may be useful to overcome local minima during update of x-shift and x-scale as caused by presence of multiple signal deflections [21]. In the study it was supposed as a first approximation that for Widrow-Hoff, the delay line with 4 taps equals the unknown system impulse response; actual response should be tested for more accurate approximation [33].…”

P and R Wave Detection in Complete Congenital Atrioventricular Block

“…Figure 5c The algorithm used to update the weights of the adaptive filter is the classical LMS, in which the adaptation constant controls the speed of convergence and the stability of the system 5 . An simple explanation of the application of this algorithm to remove noise in cardiovascular signal can be found in 4 In our case, the adaptation constant controls the depth of the average, that is, the contribution of the latest pulses. Since the repetitive component must be cancelled, a linear averaging of the pulses would provide the greatest improvement in the SNR.…”