Inversion of the Radon transform with incomplete data

摘要

AbstractThe Radon transformR(p, θ), θ∈Sn−1,p∈ℝ1, of a compactly supported functionf(x) with support in a ballBaof radius a centred at the origin is given for alldocumentclass{article}pagestyle{empty}begin{document}$ theta in mathop {S^{n - 1} }limits^tilde $end{document}, wheredocumentclass{article}pagestyle{empty}begin{document}$ mathop {S^{n - 1} }limits^tilde $end{document}is an open set onSn−1, and allp∈(− ∞, ∞),n≥2. An approximate formula is given to calculatef(x