A Radon-type transform arising in photoacoustic tomography with circular detectors: spherical geometry

Figures & data

Figure 1. The great circle on the sphere $\mathit{\partial }B(0,r_{det})$ of radius $r_{det}$ in the plane perpendicular to $\widehat{\mathit{\theta }}$.

Figure 2. Reconstructions of a sharp phantom with centres $(0,-0.6,0.4)$, $(0,0,0.5)$, $(0,0.55,0.5)$, and $(0,0.55,0.15)$, radii 0.2, 0.3, 0.15, and 0.1 and values 0.6, 1, 1.1, and 0.8, respectively. (a) Cross section of the phantom in the $x_2{x}_3$-plane, (b) Cross section of the reconstruction in the $x_2{x}_3$-plane, (c) Slice of the reconstruction and phantom along the $x_3$-axis and (d) Slice of the reconstruction and phantom along the line $x_1=0,x_3=0.5$.

Figure 3. Reconstructions of a smooth phantom with centres $(0,-0.6,0.4)$, $(0,0,0.5)$, $(0,0.55,0.5)$ and $(0,0.55,0.15)$, outer radii 0.2, 0.3, 0.15 and 0.1, inner radii 0.1, 0.15, 0.075 and 0.05 and central values 0.6, 1, 1.1 and 0.8, respectively. (a) Cross section of the phantom in the $x_2{x}_3$-plane, (b) Cross section of the reconstruction in the $x_2{x}_3$-plane from exact data, (c) Cross section of the reconstruction in the $x_2{x}_3$-plane from data with 20% uniform random noise, (d) Slice of the reconstruction and phantom along the $x_3$-axis from exact data, (e) Slice of the reconstruction and phantom along the $x_3$-axis from data with 20% uniform random noise, (f) Slice of the reconstruction and phantom along the line $x_1=0,x_3=0.5$ from exact data, (g) Slice of the reconstruction and phantom along the line $x_1=0,x_3=0.5$ from data with 20% uniform random noise.