Universal back-projection algorithm for photoacoustic computed tomography

We report results of a reconstruction algorithm for three-dimensional photoacoustic computed tomography. A universal back-projection formula is presented for three types of imaging geometries: planar, spherical, and cylindrical surfaces. A solid-angle weighting factor is introduced in the back-projection formula to compensate for the variations of detection views. A method for implementing this algorithm is described. Numerical simulation is used to demonstrate the performance of the algorithm.

Figure 1

(a) In the measurement, an ultrasonic detector at position ${\mathbf{r}}_0$ on a surface $S_0$ receives PA signals emitted from source $p_0\left({\mathbf{r}}^{\prime }\right)$. In the reconstruction, a quantity related to the measurement at position ${\mathbf{r}}_0$ projects backward on a spherical surface with respect to position ${\mathbf{r}}_0$. (b) In the planar geometry, assume there is another surface $S_0^{\prime }$ at infinity and that the combination of $S_0$ and $S_0^{\prime }$ encloses the source inside.

Figure 2

Diagram of the solid angle $d{\Omega }_0$ for a detection element $d{S}_0$ with respect to a point $P$ at $\mathbf{r}$.

Figure 3

Diagram of planar measurement geometry. See the text for detail.

Figure 4

Reconstruction without noise. (a) Gray scale image of the reconstructed pressure distribution in the $z=15\mathrm{mm}$ plane. Comparison between the original (dashed line) and reconstructed (solid line) distributions: (b) along $y=0\mathrm{mm}$ and (c) along $x=0\mathrm{mm}$.

Figure 5

Reconstruction with noise. (a) Gray scale image of the reconstructed pressure distribution in the $z=15\mathrm{mm}$ plane. Comparison between the original (dashed line) and reconstructed (solid line) distributions: (b) along $y=0\mathrm{mm}$ and (c) along $x=0\mathrm{mm}$.