Photoacoustic tomography with time-dependent damping: Theoretical and a convolutional neural network-guided numerical inversion procedure
This addresses image distortion in PAT for biomedical applications, offering a theoretical and computational framework for handling attenuation, but it appears incremental as it builds on existing PAT models with specific damping considerations.
The paper tackles the problem of image reconstruction in photoacoustic tomography (PAT) under acoustic attenuation by modeling it with a damped wave equation and proving uniqueness of the initial pressure from boundary measurements. It develops a gradient-free numerical method based on Pontryagin's maximum principle for robust reconstruction in attenuating media.
In photoacoustic tomography (PAT), a hybrid imaging modality that is based on the acoustic detection of optical absorption from biological tissue exposed to a pulsed laser, a short pulse laser generates an initial pressure proportional to the absorbed optical energy, which then propagates acoustically and is measured on the boundary. To account for the significant signal distortion caused by acoustic attenuation in biological tissue, we model PAT in heterogeneous media using a damped wave equation featuring spatially varying sound speed and a time-dependent damping term. Under natural assumptions, we show that the initial pressure is uniquely determined by the boundary measurements using a harmonic extension of the boundary data with energy decay. For constant damping, an expansion in Dirichlet eigenfunctions of $-c^2(\xx)Î$ leads to an explicit series reconstruction formula for the initial pressure. Finally, we develop a gradient free numerical method based on the Pontryagin's maximum principle to provide a robust and computationally viable approach to image reconstruction in attenuating PAT.