论文标题
热声断层扫描的逆源问题的微隔离溶液
Microlocally accurate solution of the inverse source problem of thermoacoustic tomography
论文作者
论文摘要
我们考虑了热声断层扫描和光声断层扫描的逆源问题，数据在围绕声波来源的开放表面上注册。在恒定速度的假设下，我们开发了一个明确的非著作重建程序，该过程恢复了所寻求的源的ra换灯，直至无限平滑的加性误差项。然后可以通过反转ra换变换来找到源。 我们的分析本质上是微局部性的，并且无法对SO获得的图像中的误差提供规范估计。但是，数值模拟表明，实际上，此错误很小。我们还为在2D中的圆形电弧上给出数据的情况下，渐近地实施了此过程。
We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an explicit non-iterative reconstruction procedure that recovers the Radon transform of the sought source, up to an infinitely smooth additive error term. The source then can be found by inverting the Radon transform. Our analysis is microlocal in nature and does not provide a norm estimate on the error in the so obtained image. However, numerical simulations show that this error is quite small in practical terms. We also present an asymptotically fast implementation of this procedure for the case when the data are given on a circular arc in 2D.
