Adaptive stochastic Gauss–Newton method with optical Monte Carlo for quantitative photoacoustic tomography

Significance: The image reconstruction problem in quantitative photoacoustic tomography (QPAT) is an ill-posed inverse problem. Monte Carlo method for light transport can be utilized in solving this image reconstruction problem. Aim: The aim was to develop an adaptive image reconstruction method where the number of photon packets in Monte Carlo simulation is varied to achieve a sufficient accuracy with reduced computational burden. Approach: The image reconstruction problem was formulated as a minimization problem. An adaptive stochastic Gauss–Newton (A-SGN) method combined with Monte Carlo method for light transport was developed. In the algorithm, the number of photon packets used on Gauss–Newton (GN) iteration was varied utilizing a so-called norm test. Results: The approach was evaluated with numerical simulations. With the proposed approach, the number of photon packets needed for solving the inverse problem was significantly smaller than in a conventional approach where the number of photon packets was fixed for each GN iteration. Conclusions: The A-SGN method with a norm test can be utilized in QPAT to provide accurate and computationally efficient solutions.