一维带噪声均值数据函数重构的二阶导数正则化方法

Second-order Derivative Regularization Method for the Function Reconstruction from Noisy Average Fluxes in One Dimension

针对一维带噪声均值数据的函数重构问题,构造了一个新型正则化方法.该方法正则化项由函数二阶导数导出.通过证明目标泛函严格凸证明了该方法的存在惟一性,再利用Banach空间的最优化理论和分部积分技巧的解可用4次样条函数表示,通过样条函数性质和插值函数构造给出近似解L2模意义下的误差估计及具体算法.

This paper proposed a second-order derivative regularization method to reconstruct functions from noisy average fluxes in one dimension. It proved the unique existence of the solution to this method, and the error analysis and algorithm implementation were also derived.