Comparing Numerical Optimization Algorithms for On-Device Luminescence Lifetime Analysis

Luminescence sensing is widely used in biomedical applications, including transcutaneous oxygen monitoring in wearable devices, tumor hypoxia detection, and real-time monitoring of specific biological analytes. It employs two readout techniques: intensity-based and lifetime-based measurements, with the latter offering greater resilience to confounding factors, making it the preferred choice for robust and reliable measurements. Computing the lifetime requires solving a nonlinear optimization problem to extract exponential decay rates from time-resolved measurements. While various optimization algorithms exist for this problem, their implementation on low-power wearable platforms remains challenging due to strict energy and computational constraints. This work presents a systematic comparison of non-linear optimization algorithms for on-device lifetime computation, evaluating Gauss-Newton, gradient descent variants, Levenberg-Marquardt, and Broyden-Fletcher-Goldfarb-Shanno methods in terms of energy usage, computation time, convergence reliability, and error on an STM32WB35 microcontroller based transcutaneous oxygen sensing board. Experimental results show that while fixed step size gradient descent with optimal initial parameters offers minimal execution time, the Levenberg-Marquardt and BFGS algorithms provide superior convergence reliability and loss with moderate computational cost.