A Stable Operating Point for Lipschitz-Regularized PPG Denoising

Lipschitz regularization controls how strongly a denoising autoencoder propagates an input perturbation to its output, and has been used for photoplethysmography (PPG) denoising. We revisit the gradient-norm penalty that applies this constraint. The stability principle that motivates such regularization makes the constraint intrinsically an upper bound on a Lipschitz-related sensitivity of the reconstruction map, which implies a one-sided penalty. The two-sided squared penalty used in the previous formulation additionally penalizes already-contractive maps and therefore drives the measured sensitivity upward, away from the stability objective. We show, by analysis and by a controlled ablation on a PPG semi-simulation, that the two-sided penalty has an empirical instability mode that the one-sided penalty removes: under matched settings the one-sided penalty lowers reconstruction error (MSE) by about 23%, with no divergent runs. We further find that, in our experiments, this operating point depends on the penalty form rather than on how the Lipschitz target is parameterized. We recommend an anchored constant target with a one-sided penalty as a simple and stable operating point for this task.