Matrix-based imaging through dynamic scattering

Noninvasive optical imaging through complex scattering media presents a major challenge across multiple fields. State-of-the-art techniques, such as reflection matrix decomposition and neural networks, rely on multiple measurements with varying illumination within the sample decorrelation time, making their application challenging in rapidly varying dynamic media. Here, we show that due to commutativity property of the convolution operation, dynamic scattering in isoplanatic imaging is mathematically analogous to varying illumination in static media. This insight allows leveraging matrix-based approaches developed for static scattering to rapidly varying dynamic media. Specifically, we show that the covariance matrix of a set of scattered light camera frames captured through a dynamic scattering sample has the same mathematical form as the reflection matrix of a static medium, with the target object playing the scattering medium's role. We demonstrate this concept by high-resolution diffraction-limited imaging through dynamic scattering across multiple modalities, from incoherent fluorescence microscopy to coherence-gated holographic reflection imaging.