Spatio-Temporal Simulation of Laser Speckles Using Stochastic Differential Equations

Laser speckle imaging modalities are receiving considerable attention for applications in both superficial and deep tissue imaging. This growing interest arises from their straightforward and cost-effective instrumentation, as well as the ease of computational implementation. Recent developments in this field require the calibration of devices, which often necessitates the simulation of dynamic laser speckles in tissue. Previous simulation models have predominantly relied on statistical tools such as copulas or Fourier transform methods based on diffraction theory. In our recent work, we introduced the use of Stochastic Differential Equations (SDEs) to model the temporal evolution of speckles, utilizing a predetermined probability density function and temporal autocorrelation. We further extended this simulation to create a calibrating phantom by inputting the stochastic time series data generated by SDEs into a piezo actuator. In the previous studies, the time evolution of each pixel was modeled independently using multiple SDEs. In the current work, we introduce a method for generating spatio-temporal dynamics of speckles characterized by predefined spatial and temporal correlation structures. This approach integrates SDE with Cholesky decomposition and inverse sampling method to achieve the desired spatial correlation profiles. The simulation results are obtained for practically feasible experimental parameters, effectively generating speckles that closely approximate the values observed in experimental settings.