High-order Total Variation Regularization Approach for Axially Symmetric Object Tomography from a Single Radiograph
نویسندگان
چکیده
In this paper, we consider tomographic reconstruction for axially symmetric objects from a single radiograph formed by fan-beam X-rays. All contemporary methods are based on the assumption that the density is piecewise constant or linear. From a practical viewpoint, this is quite a restrictive approximation. The method we propose is based on high-order total variation regularization. Its main advantage is to reduce the staircase effect while keeping sharp edges and enable the recovery of smoothly varying regions. The optimization problem is solved using the augmented Lagrangian method which has been recently applied in image processing. Furthermore, we use a one-dimensional (1D) technique for fan-beam X-rays to approximate 2D tomographic reconstruction for cone-beam X-rays. For the 2D problem, we treat the cone beam as fan beam located at parallel planes perpendicular to the symmetric axis. Then the density of the whole object is recovered layer by layer. Numerical results in 1D show that the proposed method has improved the preservation of edge location and the accuracy of the density level when compared with several other contemporary methods. The 2D numerical tests show that cylindrical symmetric objects can be recovered rather accurately by our high-order regularization model.
منابع مشابه
Special Topics in Test Methodology: Tomographic Reconstruction of Axially Symmetric Objects from a Single Dynamic Radiograph
I' is possible to reconstruct the cross section of a three-dimensional, axially symmetric object from a single radiograph, as depicted in Fig. 1. This method of analysis has been applied to many problems in many different fields in the past, including several recent applications to static and dynamic testing at Los Alam~s . ' -~ In industrial radiography, where many objects have nearly circular...
متن کاملAxially Symmetric Vibrations of a Liquid-Filled Poroelastic Thin Cylinder Saturated with Two Immiscible Liquids Surrounded by a Liquid
This paper studies axially symmetric vibrations of a liquid-filled poroelastic thin cylinder saturated with two immiscible liquids of infinite extent that is surrounded by an inviscid elastic liquid. By considering the stress free boundaries, the frequency equation is obtained. Particular case, namely, liquid-filled poroelastic cylinder saturated with single liquid is discussed. When the waven...
متن کاملImage Reconstruction Method with the Exploitation of the Spatial Correlation for Electrical Capacitance Tomography
Electrical capacitance tomography (ECT) is considered to be a competitive measurement method. The imaging objects in ECT measurements are often in a time-varying process, and exploiting the prior information related to the dynamic nature is important for reconstructing high-quality images. Different from existing reconstruction models, in this paper a new model that incorporates the spatial cor...
متن کاملReconstruction of high-resolution fluorescence microscopy images based on axial tomography
For a reliable understanding of cellular processes, high resolution 3D images of the investigated cells are necessary. Unfortunately, the ability of fluorescence microscopes to image a cell in 3D is limited since the resolution along the optical axis is by a factor of two to three worse than the transversal resolution. Standard microscopy image deblurring algorithms like the Total Variation reg...
متن کامل