NDLI: Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Ye, Jong Chul Ward, John Paul Unser, Michael Lee, Minji
Copyright Year	2015
Abstract	Motivated by the interior tomography problem, we propose a method for exact reconstruction of a region of interest of a function from its local Radon transform in any number of dimensions. Our aim is to verify the feasibility of a one-dimensional reconstruction procedure that can provide the foundation for an efficient algorithm. For a broad class of functions, including piecewise polynomials and generalized splines, we prove that an exact reconstruction is possible by minimizing a generalized total variation seminorm along lines. The main difference with previous works is that our approach is inherently one-dimensional and that it imposes less constraints on the class of admissible signals. Within this formulation, we derive unique reconstruction results using properties of the Hilbert transform, and we present numerical examples of the reconstruction.
Starting Page	226
Ending Page	247
Page Count	22
File Format	PDF
DOI	10.1137/140982428
e-ISSN	19364954
Journal	SIAM Journal on Imaging Sciences (SJISBI)
Issue Number	1
Volume Number	8
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-01-22
Access Restriction	Subscribed
Subject Keyword	Inverse problems perfect reconstruction Special transforms generalized total variation Radon transform interior tomography
Content Type	Text
Resource Type	Article

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