First, we review existing attenuation models and discuss their causality properties, which we believe to be essential for algorithms for inversion with attenuated data. Then, we survey causality properties of common attenuation models. We also derive integro-differential equations which the attenuated waves are satisfying. In addition we discuss the ill--conditionness of the inverse problem for calculating the unattenuated wave from the attenuated one.
- Pub Date:
- September 2010
- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- Mathematical Modeling in Biomedical Imaging II Lecture Notes in Mathematics, 2012, Volume 2035/2012, 85-130