Fast blood flow index reconstruction of diffuse correlation spectroscopy using a back-propagation-free data-driven algorithm

This study introduces a fast and accurate online training method for blood flow index (BFI) and relative BFI (rBFI) reconstruction in diffuse correlation spectroscopy (DCS). We implement rigorous mathematical models to simulate the auto-correlation functions (𝑔2) for semi-infinite homogeneous and three-layer human brain models. We implemented a fast online training algorithm known as random vector functional link (RVFL) to reconstruct BFI from noisy 𝑔2. We extensively evaluated RVFL regarding both speed and accuracy for training and inference. Moreover, we compared RVFL with extreme learning machine (ELM) architecture, a conventional convolutional neural network (CNN), and three fitting algorithms. Results from semi-infinite and three-layer models indicate that RVFL achieves higher accuracy than the other algorithms, as evidenced by comprehensive metrics. While RVFL offers comparable accuracy to CNNs, it boosts training speeds that are 3900-fold faster and inference speeds that are 19.8-fold faster, enhancing its generalizability across different experimental settings. We also used 𝑔2 from one- and three-layer Monte Carlo (MC)-based in-silico simulations, as well as from analytical models, to compare the accuracy and consistency of the results obtained from RVFL and ELM. Furthermore, we discuss how RVFL is more suitable for embedded hardware due to its lower computational complexity than ELM and CNN for training and inference.