In this paper, we investigate the relations between the Radon and weighted divergent beam and cone transforms. Novel inversion formulas are derived for the latter two. The weighted cone transform arises, for instance, in image reconstruction from the data obtained by Compton cameras, which have promising applications in various fields, including biomedical and homeland security imaging and gamma ray astronomy. The inversion formulas are applicable for a wide variety of detector geometries in any dimension. The results of numerical implementation of some of the formulas in dimensions two and three are also provided.
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Figure 3.
The density plot of
Figure 4.
The density plot of
Figure 5.
The density plot of
Figure 6.
The density plot of
Figure 8.
The 3D ball phantom with radius 0.5, center (0, 0, 0.25) and unit density (left), and
Figure 9.
Comparison of the
Figure 10.
The 3D ball phantom with radius 0.5, center (0, 0, 0.25) and unit density (left), and
Figure 11.
Comparison of the
Figure 12.
The 3D ball phantom with radius 0.5, center (0, 0, 0.25) and unit density (left), and
Figure 13.
Comparison of the
Figure 14.
The 3D ball phantom with radius 0.5, center (0, 0, 0.25) and unit density (left), and
Figure 15.
Comparison of the
Figure 16.
The 3D ball phantom with radius 0.5, center (0, 0, 0.25) and unit density (left), and
Figure 17.
Comparison of the
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