Feature reconstruction in inverse problems
Feature reconstruction in inverse problems
复制标题
反问题中的特征重构
DOI：
10.1088/0266-5611/27/6/065010
复制
发表时间：
2011
期刊：
影响因子：
2.1
通讯作者：
A. Louis
中科院分区：
文献类型：
--
作者：
A. Louis
提出了一种快速、准确和稳定的算法，将重构和特征提取步骤结合起来，用一种方法求解线性不适定问题。针对这两种任务的组合，使用优化参数的特殊重构核进行预计算，可以快速实现，并且比单独实现效果更好。将序最优性的概念推广到特征重构和Banach空间的求解中，以找到选择合适柔化子的准则。从不同层析模式和扫描几何的真实数据中得到的结果是直接计算导数，如在Canny边缘检测器中，以及在许多分割算法中使用的解的拉普拉斯算子。该方法也适用于搜索解不平滑或数据噪声较大的情况。这显示了该方法的多功能性。
A strategy for the derivation of fast, accurate and stable algorithms for combining the reconstruction and the feature extraction step for solving linear ill-posed problems in just one method is presented. The precomputation of special reconstruction kernels with optimized parameters for the combination of the two tasks allows for fast implementations and better results than separate realizations. The concept of order optimality is generalized to the solution of feature reconstruction and to Banach spaces in order to find criteria for the selection of suitable mollifiers. Results from real data in different tomographic modalities and scanning geometries are presented with the direct calculation of derivatives, as in Canny edge detectors, and the Laplacian of the solution used in many segmentation algorithms. The method works also when the searched-for solution is not smooth or when the data are very noisy. This shows the versatility of the approach.