RadonTransform
RadonTransform, named after Johann Radon, is an integral transform that assigns to a function defined on the plane its line integrals along all possible straight lines. In two dimensions, if f is a function on R^2, its Radon transform Rf is defined by Rf(θ, s) = ∫_{−∞}^{∞} f(s cos θ − t sin θ, s sin θ + t cos θ) dt, where θ ∈ [0, π) specifies the line orientation and s ∈ R is the signed distance of the line from the origin. Equivalently, Rf(θ, s) is the integral of f over the line x cos θ + y sin θ = s.
The transform is central to computed tomography, where projections Rf(θ, s) are measured for many angles and
The Radon transform satisfies the Fourier slice theorem: the two-dimensional Fourier transform of f is given
Beyond medical imaging, the Radon transform is used in geophysics, astronomy, and materials science, as a mathematical