Inverse Problems and Reconstruction Algorithms for Photoacoustic, Ultrasound, and Radar Imaging
This community develops the mathematical and computational methods required to reconstruct images from indirect measurements, specifically applying inverse problem theory to photoacoustic, ultrasound, and radar data to enable target detection and system characterization.
The work centers on solving inverse problems where direct observation is impossible, relying heavily on the Radon transform, Fourier analysis, and compressed sensing to recover source distributions from boundary data. Recurring methods include total variation regularization, synthetic aperture processing, and coherent integration, applied to modalities such as photoacoustic tomography, ultrasound imaging, and inverse synthetic aperture radar (ISAR). A significant portion of the research involves deep learning and neural networks for image reconstruction and target detection, particularly for moving or maneuvering targets in radar and seismic contexts. The community also addresses parameter estimation and shear wave analysis, bridging pure mathematical analysis with engineering applications in medical imaging and remote sensing.
The largest share of the community's output is found in radon research, accounting for 9.9% of all radon-related papers tracked, with 4,781 papers in this group. Silver and titanium research also appear, though with negligible shares of their respective element totals.
The community comprises 22,523 papers, publishing most frequently in arXiv (Cornell University), Ultrasonic Imaging, and Inverse Problems.
Recent work continues to focus on photoacoustic microscopy probes, non-line-of-sight imaging, and robust ISAR imaging for geostationary targets, alongside advances in stochastic optimization for deep learning models and mathematical analysis of maximal functions.