Skin-Tone-Invariant Topological Signal Processing: A Framework for Bias-Reducing Optical Measurement Systems

Photoplethysmography (PPG, optical measurement of cardiac blood volume changes) is the foundation of wearable cardiac monitoring, but systematically fails on dark skin due to melanin absorption. We present the Melanin Absorption Invariance (MAI) framework: a label-free method that substantially reduces cross-skin-tone bias in cardiac feature extraction by preserving topological rather than geometric signal structure. We prove two theorems: Theorem 1 bounds attractor bias to O(SNR_eff^-1) under Z-normalization; Theorem 2 reduces residual bias to O(SNR_eff^-2) via SNR-adaptive correction. Empirical validation confirms these theoretical predictions on real dark-skin PPG signals. Comprehensive empirical validation on the complete MMPD dataset (Fitzpatrick III-VI, n = 656 recordings, 33 subjects, spanning all 4 lighting conditions and 5 motion types, Samsung Galaxy mobile phone) demonstrates MAI generalization across real-world deployment conditions. Results show substantial attractor bias reduction across all skin tone groups, with largest effects for Fitzpatrick IV and VI populations most affected by current systems. This work demonstrates a theoretically grounded, label-free, skin-tone-invariant cardiac monitoring framework.