Our goal is to solve the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. The proposed modified time reversal algorithm recovers the source term up to an infinitely smooth error term. Similarly to (Eller M et al 2020 Inverse Problems 36 085012), numerical simulations show that the error term is quite small in practical terms. Unlike the latter method, the present technique is applicable in the presence of a known variable speed of sound. It is also significantly more efficient from a computational standpoint. It can be implemented using either standard finite difference techniques or through methods based on separation of variables, that for special geometries yield extremely fast image reconstruction. We illustrate our results with numerical simulations in 2 and 3 spatial dimensions.

我们的目标是解决热和光声层析成像的逆源问题，将数据记录在部分围绕声波源的开放表面上。所提出的改进的时间反转算法将源项恢复到无限平滑的误差项。与（Eller M et al 2020 Inverse Problems 36085012），数值模拟表明，误差项实际上很小。与后一种方法不同，本技术适用于已知的可变声速。从计算的角度来看，它的效率也大大提高。它可以使用标准的有限差分技术或基于变量分离的方法来实现，对于特殊的几何形状，它可以实现极快的图像重建。我们通过在2和3空间维度上的数值模拟来说明我们的结果。