An inversion formula for the horizontal conical Radon transform

Analysis of the weighted conical Radon transform

“…Next, let's recall the result for the nonattenuated v-line Radon transform, i.e., in the equation (10), the attenuated parameter U(r) equals 1.…”

“…Specifically, in the two-dimensional space, the cone is reduced to a V-line, and various inversion formulas have been developed (e.g., [3][4][5]). In the three-dimensional space, several inversion formulas have been proposed (see, for example, [6][7][8][9][10][11][12][13]). In the more general case of an n-dimensional space, the inversion formula for the conical transform was presented in the paper [14][15][16][17].…”

“…Similar occurrences arise when Compton cameras are applied in domestic security, industrial imaging, and gamma-ray astronomy. In [10,21], the weighted parameter is equal to some power of the distance to the vertex. In [22,23], the weight has the form e − μ r where the attenuation parameter μ 0 is a known constant and r is the distance of propagating of photons.…”

Analysis of the weighted conical Radon transform

“…Specifically, in the two-dimensional space, the cone is simplified to a V-line, and various inversion formulas have been developed (e.g., [3,24,32]). In the three-dimensional space, several inversion formulas have been proposed (see, for example, [4,6,20,22,23,25,26,33]). In the more general case of an n-dimensional space, the inversion formula for the conical transform was presented in the paper [9,[29][30][31].…”