Physics-Driven Compressed Sensing for Imaging

Historically, imaging quality was limited by hardware-intensive data collection. Compressed sensing has shifted this burden to software, using optimization to reconstruct images from sparse, incoherent measurements. While modalities such as MRI, CT, and array imaging rely on linear models, physical constraints often result in highly underdetermined systems that defy traditional reconstruction. This work moves beyond ”black-box” optimization by treating the model matrix !!!x1D49C; as a rigorous encoding of wave propagation and sensor geometry. We show that mathematical properties like mutual coherence are direct manifestations of physical laws, and that exploiting this structure through sparsity-promoting regularization is essential for reliable recovery. By analyzing hardware-specific constraints and non-periodic sensor placement, we bridge the gap between abstract mathematical theory and the fundamental physical bounds of imaging.