The X-ray transform is a mathematical operation used in various fields, particularly in imaging and tomography, to reconstruct images from projection data. The concept is analogous to how X-ray machines work in medical imaging, where X-rays penetrate through the body and produce projections of the internal structures onto a detector.
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The X-ray transform records integrals of a function or tensor evaluation over a specified family of curves. The curve family, parametrization and any weights are part of the definition. Straight lines, geodesics and magnetic flows give different versions; their injectivity and unavoidable potential kernels depend on that geometry.