论文标题
在光学扩散断层扫描中鉴定分段恒定系数按级别集
On the identification of piecewise constant coefficients in optical diffusion tomography by level set
论文作者
论文摘要
在本文中，我们提出了一种水平集正规化方法，并结合了一种拆分策略，以同时识别从有限的光学断层扫描数据集（Neumann to-Dirichlet数据）中的分段恒定扩散和吸收系数。这个问题是一个高非线性反问题，将扩散和吸收系数的指数性和轻度差异结合在一起。我们证明，参数到测量图满足了足够的条件（$ l^1 $拓扑中的连续性），以保证所提出的级别设置方法的正则化属性。另一方面，考虑不同配置的数值测试带来了有关如何同时识别系数的融合拆分策略的新想法。通过一些数值示例说明了所提出的数值策略的行为和性能。
In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coefficients from a finite set of optical tomography data (Neumann-to-Dirichlet data). This problem is a high nonlinear inverse problem combining together the exponential and mildly ill-posedness of diffusion and absorption coefficients, respectively. We prove that the parameter-to-measurement map satisfies sufficient conditions (continuity in the $L^1$ topology) to guarantee regularization properties of the proposed level set approach. On the other hand, numerical tests considering different configurations bring new ideas on how to propose a convergent split strategy for the simultaneous identification of the coefficients. The behavior and performance of the proposed numerical strategy is illustrated with some numerical examples.
