(untitled) (Journal of Computational Mathematics, 2021)
A practical image reconstruction method for multi-source quantitative photoacoustic tomography (QPAT) is proposed in this work with the consideration of detector response function and limited-view scanning. First, the correct detector response function, i.e., spatial impulse response (SIR) and acousto-electric impulse response (EIR), is considered for the ultrasonic transducer to accurately model the acoustic measurement; second, acoustic data is only measured near optical sources with meaningful signal-to-noise ratio (SNR), i.e., the limited-view scanning, which also reduces the data acquisition time for point transducer. However, due to the incomplete limited-view data, a two-step image reconstruction method (i.e., to first reconstruct initial acoustic pressure and then reconstruct optical coefficients) no longer applies, since it is neither possible nor necessary to robustly reconstruct initial acoustic pressure with limited-view data. Therefore, here we propose a direct image reconstruction method that incorporates SIR, EIR and limited-view scanning in a coupled opto-acoustic forward model, regularizes the nonlinear QPAT data fidelity with tensor framelet sparsity, and then solves the QPAT problem with Quasi-Newton method based alternating direction method of multipliers.