Label-Free, Physics-Constrained Learning for Multi-Exposure Speckle Imaging Parameter Estimation

Multi-exposure speckle imaging (MESI) estimates flow-related parameters by fitting a physics-based speckle contrast model to measurements acquired over multiple exposure times. In standard pipelines, parameters are recovered via nonlinear least-squares fitting at each pixel, which is computationally expensive and can yield spatially inconsistent maps when uncertainty in the estimated speckle contrast variance [Formula] (from camera noise and finite spatial/temporal sampling used to compute speckle contrast) is amplified by independent pixel wise inversion. This work reframes MESI parameter estimation as identification of a globally shared inverse operator of the analytical forward model, exploiting the fact that a single physical mapping governs all pixels while noise drives large variance in independent pixel wise inversion. Rather than solving millions of iterative optimizations, a single parameterized inverse mapping is learned directly from a single acquired MESI dataset. Physics consistency is enforced by embedding the fixed MESI forward model as an analysis-by-synthesis layer that re-synthesizes speckle contrast curves from the predicted parameters. Training is self-supervised: the inverse mapping is optimized by minimizing a reconstruction loss between measured and re-synthesized speckle contrast curves, which constrains estimates to the set of physically admissible MESI curves without requiring ground truth parameter labels. Experiments on a numerical MESI phantom with known ground truth and on in vivo mouse cortex data show that the proposed method produces more stable inverse correlation time (ICT) maps (1/{tau}c) and improved spatial coherence relative to conventional per-pixel fitting, while substantially reducing inference time by replacing iterative optimization with a single feed-forward evaluation.