On the reconstruction of the absorption coefficient for the 2D acoustic system

We consider the coefficient inverse problem for the 2D system of acoustics. Our goal is to recover the coefficient of acoustic attenuation by using the additional information of the wave-field in the number of receivers. We obtain the gradient of the cost functional and implement the numerical algorithm for solving the inverse problem, based on a optimization approach. We provide the numerical results of recovering the absorption coefficient and study its influence on the efficiency of reconstructing other parameters of the system. By taking into account the absorption of the sounding wave we aim to bring the mathematical model closer to the applications, related to the ultrasound tomography of the human tissue.