An Inverse Hyperbolic Problem with Application to Joint Photoacoustic Parameter Determination

2024/08/22 by Liu, Shitao, Uhlmann, Gunther, Yang, Yang
#35L05 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.12759

Abstract

We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated from applications in photoacoustic tomography when one seeks to recover both the wave speed and the initial ultrasound pressure from a single ultrasound signal. In particular, our result shows that the ratio of the initial ultrasound pressure and the wave speed squared uniquely determines both of them respectively.

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