由X射线数据重建分段常数函数
Reconstruction of piecewise constant functions from X-ray data
摘要：
证明了在具有严格凸边界的二维紧致非陷波黎曼流形上，分段常数函数可以由它在测地线上的积分恢复出来。我们适应的注入证明，它使用通过测地线的变化，以恢复功能，我们改善了这一结果时，流形是简单的，功能是恒定的瓷砖测地线的边缘，显示这些变化的雅可比字段是足够的。我们也给出了明确的公式的值附近的边界。最后研究了重建方法的稳定性。
英文摘要：
We show that on a two-dimensional compact nontrapping Riemannian manifold with strictly convex boundary, a piecewise constant function can be recovered from its integrals over geodesics. We adapt the injectivity proof which uses variations through geodesics to recover the function and we improve this result when the manifold is simple and the function is constant on tiles with geodesic edges, showing that the Jacobi fields of these variations are sufficient. We give also explicit formulas for the values near the boundary. We finally study the stability of the reconstruction method.
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