Inverse Problems, Image Reconstruction and Radar Signal Processing
This community develops the mathematical frameworks and algorithms required to reconstruct images from indirect measurements, detect targets in noisy environments, and solve complex differential equations.
The work centers on the Radon transform, inverse problems, and image reconstruction techniques. Recurring methods include neural networks, deep learning, and optimal transport applied to data analysis. Specific applications span photoacoustic imaging, computed tomography, and synthetic aperture radar for moving target detection. The mathematical foundations rely heavily on Banach spaces, boundary conditions, and stochastic differential equations. These tools are used to process seismic data, estimate parameters, and model reaction-diffusion systems. The research bridges abstract functional analysis with practical signal processing for radar and medical imaging.
The largest share of the community's output is found in radon research, accounting for 13.7% of all radon research, and 6,647 papers here.
The community comprises 41,952 papers, publishing most frequently in arXiv (Cornell University), the Pacific Journal of Mathematics, and the Transactions of the American Mathematical Society.
Recent work includes clinical ultrasound and photoacoustic image-guided microsurgery, GLRT-based detectors for mismatched signals, and convergence of non-symmetric forms with changing reference measures.