Sparse Multichannel Decomposition of Electrodermal Activity With Physiological Priors

Figures

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  Fig. 1.. Preprocessing pipeline for deconvolution Each SC signal passes through a noise calculation block which passes the estimated noise to the deconvolution algorithm. The SC Signals are then aligned, filtered, and downsampled before being fed to the main algorithm block.

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  Fig. 2.. Simplified overview of our algorithm. The algorithm has two stages to aid convergence - one for initial estimation and the next for fine-tuning output.

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  Fig. 3.. Adaptive Threshold Update Rule For FOCUSS+. The update rule for the adaptive FOCUSS algorithm before eliminating impulses below the threshold in each step is shown in (a). The blue impulse is an impulse that is not eliminated in the update step as they are above the threshold and the yellow impulse will be eliminated in the following step. In contrast to the regular GCV-FOCUSS+ algorithm, we amplify the blue impulse instead of leaving it as is. If we draw the wave (marked by a red dotted line) generated by convolving the system model with the blue impulse, the part of the yellow nullified impulses that intersect the wave (marked red) is added to the blue impulse as shown in (b).

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  Fig. 4.. Estimated Deconvolution of the Experimental Multichannel SC Signals of Two Female and Two Male Participants: In each of the panels, the top sub-panel (i) shows the actual SC signal (orange \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\ast$\end{document} markers) versus the reconstructed SC signal (represented by the solid green line) and the tonic component of the signal (solid blue line) for the 1st channel. The timings of the actual stimulation events are shown as gray vertical lines in all panels. (ii) shows the recovered phasic component for channel 1. (iii), (iv), (v), and (vi) show the same figures for channel 2 and channel 3 respectively, and finally (vii) shows the estimated ANS activations.

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  Fig. 5.. Comparison of Single Channel Methods with Ours. Panels (i)–(iii) show the deconvolution results of cvxEDA for channels 1–3 respectively, panels (iv)–(vi) show the deconvolution results of Ledalab for channels 1–3 respectively and panel (vii) shows the deconvolution results of our proposed algorithm.

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  Fig. 6.. Reconstruction Performance of Our Algorithm with Simulated Noise The solid line in the above panels shows the mean value and the vertical limits are variances of the metric for a particular noise level overall simulated subjects. Panel (i)–(iii) shows the change in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $R^{2}$\end{document} value between the recovered signal and original signal for SC signal, phasic component, and tonic component respectively. Panel (iv) shows the difference between the non-zero count of the recovered sparse signal to the original. Panel (v)–(viii) shows the percentage error of recovered parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\tau _{r}$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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  Fig. 7.. ROC Curves for Single vs Multichannel Decomposition. ROC curves of single channel deconvolution done previously in [39] (indicated by dashed lines) compared to multichannel deconvolution (indicated by solid lines) are shown above for lookback durations 3 s (red), 4 s (green) and 5 s (blue). The average ROC for all subjects is also marked.

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  Fig. 8.. Analysis of Rise and Decay Times. A segment of skin conductance data for subject 1 is shown. Note how the delay between channel 1 (red) and channel 2 (blue) indicated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\beta _{2}$\end{document} decreases from 1.01 s to 0.51 s whereas the delay between channel 1 and channel 3 (yellow) indicated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\beta _{3}$\end{document} decreases from 1.66 s to 1.34 s. There is also a missing impulse in channel 3 that is present in both channel 1 and channel 2.

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  Fig. 9.. Estimated Deconvolution of the Experimental Multi-Channel SC Signals of Two Female and Two Male Participants: In each of the panels, the top sub-panel (i) shows the actual SC signal (orange \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\ast$\end{document} markers) versus the reconstructed SC signal (represented by the solid green line) and the tonic component of the signal (solid blue line) for the 1st channel. The timings of the actual stimulation events are shown as gray vertical lines in all panels. (ii) shows the recovered phasic component for channel 1. (iii), (iv), (v), and (vi) show the same figures for channel 2 and channel 3, respectively, and finally (vii) shows the estimated ANS activations.

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  Fig. 10.. Estimated Deconvolution of the Experimental Multi-Channel SC Signals of Two Female and Two Male Participants: In each of the panels, the top sub-panel (i) shows the actual SC signal (orange \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\ast$\end{document} markers) versus the reconstructed SC signal (represented by the solid green line) and the tonic component of the signal (solid blue line) for the 1st channel. The timings of the actual stimulation events are shown as gray vertical lines in all panels. (ii) shows the recovered phasic component for channel 1. (iii), (iv), (v), and (vi) show the same figures for channel 2 and channel 3, respectively, and finally (vii) shows the estimated ANS activations.

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  Fig. 11.. Estimated Deconvolution of the Experimental Multi-Channel SC Signals of Two Female and Two Male Participants: In each of the panels, the top sub-panel (i) shows the actual SC signal (orange \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\ast$\end{document} markers) versus the reconstructed SC signal (represented by the solid green line) and the tonic component of the signal (solid blue line) for the 1st channel. The timings of the actual stimulation events are shown as gray vertical lines in all panels. (ii) shows the recovered phasic component for channel 1. (iii), (iv), (v), and (vi) show the same figures for channel 2 and channel 3, respectively, and finally (vii) shows the estimated ANS activations.

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  Fig. 12.. Estimated Deconvolution of the Experimental Multi-Channel SC Signals of Two Female and Two Male Participants: In each of the panels, the top sub-panel (i) shows the actual SC signal (orange \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\ast$\end{document} markers) versus the reconstructed SC signal (represented by the solid green line) and the tonic component of the signal (solid blue line) for the 1st channel. The timings of the actual stimulation events are shown as gray vertical lines in all panels. (ii) shows the recovered phasic component for channel 1. (iii), (iv), (v), and (vi) show the same figures for channel 2 and channel 3, respectively, and finally (vii) shows the estimated ANS activations.