Total Variation Regularization in Electrical Impedance Tomography
Total Variation Regularization in Electrical Impedance Tomography
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发表时间：
2007-06
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通讯作者：
A. Borsic;B. Graham;A. Adler;W. Lionheart
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作者：
A. Borsic;B. Graham;A. Adler;W. Lionheart
本文评价了用原始对偶方法有效地正则化总变分(TV)泛函的电阻抗层析成像(EIT)问题。全变差泛函在反问题的正则化中扮演着重要的角色，这要归功于它在重建轮廓中保持间断的能力。这一特性在EIT成像的许多应用领域中是理想的，例如医学和工业，其中器官间边界(在第一种情况下)和相间边界(在后一种情况下)呈现难以用传统正则化方法重建的电属性的阶跃变化，因为它们倾向于平滑重建的图像。虽然TV泛函是可取的，但它将反问题表示为不可微函数的最小化，而用牛顿法等传统优化技术不能有效地解决这一问题。在本文中，我们演示了使用原始对偶内点方法(PD-IPM)作为电视正则化反演的框架。
This paper presents an evaluation of the use of Primal Dual Methods for efficiently regularizing the electric impedance tomography (EIT) problem with the Total Variation (TV) functional. The Total Variation functional is assuming an important role in the regularization of inverse problems thanks to its ability to preserve dis- continuities in reconstructed profiles. This property is desirable in many fields of application of EIT imaging, such as the medical and the industrial, where inter-organ boundaries, in the first case, and inter-phase boundaries, in the latter case, present step changes in electrical properties which are difficult to be reconstructed with traditional regularization methods, as they tend to smooth the reconstructed image. Though desirable, the TV functional leads to the formulation of the inverse problem as a minimization of a non-differentiable function whichcannot be efficiently solved with traditional optimization techniques such as the Newton Method. In this paper we demonstrate the use of Primal Dual - Interior Point Methods (PD-IPM) as a framework for TV regularized inversion.