Recovering jumps in X-ray tomography

被引：0

作者：

Romanov V.G. ^{[1
]}

机构：

[1] Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk

来源：

Journal of Applied and Industrial Mathematics | 2014年 / 8卷 / 04期

基金：

俄罗斯基础研究基金会;

关键词：

recovering lines of discontinuity; stability; tomography; uniqueness;

D O I：

10.1134/S1990478914040164

中图分类号：

TB [一般工业技术];

学科分类号：

摘要：

We consider the problem of finding the boundaries of discontinuities and jumps at these discontinuities of a piecewise smooth function for X-ray tomography. We give some algorithm for the reconstruction of the unknown values as well as formulas for their calculation. The original problem of X-ray tomography is reduced to a problem for a continuous piecewise differentiable function. © 2014, Pleiades Publishing, Ltd.

引用

页码：582 / 593

页数：11

共 9 条

[1]

Anikonov D.S., Integro-Differential Heterogeneity Indicator in Tomography Problem, J. Inverse Ill-Posed Probl., 7, 1, pp. 17-59, (1999)

[2]

Anikonov D.S., The Indicator of Contact Boundaries for an Integral Geometry Problem, Sibirsk. Mat. Zh., 49, 4, pp. 739-755, (2008)

[3]

Anikonov D.S., Konovalova D.S., The Integral Geometry Boundary Determination Problem for a Pencil of Straight Lines, Sibirsk. Mat. Zh., 52, 5, pp. 972-976, (2011)

[4]

Anikonov D.S., Balakina E.Y., A Polychromatic Inhomogeneity Indicator in an Unknown Medium for an X-Ray Tomography Problem, Sibirsk. Mat. Zh., 53, 4, pp. 721-740, (2012)

[5]

Vainberg E.N., Kazak I.A., Faingoiz M.L., X-Ray Computer Tomography by the Backprojection Method with Double Differentiation Filtering, Defektoskopiya No. 2, pp. 31-39, (1985)

[6]

Faridani A., Keinert F., Natterer F., Ritman T.L., Smith K.T., Local and Global Tomography, Signal Processing, 23, pp. 241-255, (1990)

[7]

Katsevich A.I., Ramm A.G., New Methods for Finding Values of the Jumps of a Function from Its Local Tomographic Data, Inverse Problems, 11, pp. 1005-1023, (1995)

[8]

Louis A.K., Maass P., Contour Reconstruction in 3-D X-Ray CT, IEEE Trans. Med. Imag., 12, 4, pp. 109-115, (1993)

[9]

Mukhometov R.G., The Problem of Recovery of a Two-Dimensional Riemannian Metric and Integral Geometry, Dokl. Akad. Nauk SSSR, 232, 1, pp. 32-35, (1977)

← 1 →