A multimodal adjoint-state formulation of Quantitative Photoacoustic Tomography with external acoustic sources
TL;DR
This work presents a fully coupled, one-step QPAT reconstruction method for the simultaneous recovery of optical absorption, density, and compressibility directly from measurement data, with speed of sound obtained as a derived property.
Abstract
Quantitative Photoacoustic Tomography (QPAT) aims to recover spatially varying optical and acoustic tissue parameters by utilizing the photoacoustic effect. The associated inverse problem is highly ill-conditioned due to strong coupling between optical absorption, optical scattering, density, and speed of sound. To alleviate the ill-conditioned nature of this problem, an externally generated ultrasonic wavefield is incorporated in addition to photoacoustic sources, resulting in a multimodal formulation of QPAT. We present a fully coupled, one-step QPAT reconstruction method for the simultaneous recovery of optical absorption, density, and compressibility directly from measurement data, with speed of sound obtained as a derived property. Conventional QPAT and multimodal QPAT arise as special cases within the proposed method. The approach is formulated as a PDE-constrained optimization problem, and the Fréchet derivative of the complete forward model is derived using an optimize-then-discretize adjoint state method. Two-dimensional numerical simulations demonstrate accurate reconstruction of optical absorption, density, and compressibility.