Accelerated curve fitting for diffuse correlation spectroscopy using variable projection

As diffuse correlation spectroscopy (DCS) scales to many channels, standard two-parameter curve fitting becomes a computational bottleneck for real-time embedded processing. We evaluated variable projection (VarPro) as a fast, predictable alternative. Because the Siegert relation is separable in the coherence factor ( β ), VarPro solves this linear parameter analytically, reducing nonlinear optimization for the blood flow index (BFI) to a bounded one-dimensional search. We compared VarPro with 2D nonlinear least-squares fitting using simulations, liquid-phantom measurements, and an ESP32-C3 microcontroller. VarPro produced nearly identical accuracy to the 2D solver across all tested flow and noise ranges. Furthermore, it reduced objective-function evaluations, achieving up to an 18-fold desktop speedup relative to a standard MATLAB nonlinear least-squares implementation and a 10-fold speedup on embedded hardware with highly consistent fit times. This platform-agnostic reduction enables real-time processing for portable, high-channel-count DCS instrumentation.