Single-frame statistical gating in a speckle pattern generated by the dynamic scattering in disordered medium

The propagation of coherent light in a dynamic disordered medium generates dynamic speckle patterns. The dynamics intrinsic to the disordered medium result in a shorter decorrelation time for the multiple scattering component (τcM) relative to the single scattering component (τcS). In this study, we propose a single-frame statistical gating strategy for the single and multiple scattering components in reflective wide-field imaging when the exposure time T satisfies the condition τcM<T<τcS. The spatial matrix representation is modeled as the sum of a negative exponential matrix, which represents the single scattering component, and a Gaussian matrix, which represents the multiple scattering component. The Marchenko–Pastur distribution and the Tracy–Widom distribution are employed in conjunction to calculate the moments of the single and multiple scattering components. The single-frame statistical gating method is validated using an electric field Monte Carlo simulation and demonstrated in vivo in brain imaging. Based on rotational invariance, a rotational sampling strategy is proposed to significantly improve the imaging quality of the single-frame statistical gating method. The single-frame statistical gating method greatly facilitates future applications in scenarios such as clinical and complex natural environments.