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Forward–backward splitting method for quantitative photoacoustic tomography

Quantitative photoacoustic tomography (PAT) reconstructs optical maps using ultrasonic measurements, with improved resolution from conventional optical imaging due to significantly smaller acoustic scattering than optical scattering for detecting signals in depth. In this work, formulating quantitative PAT as a nonlinear least-squares problem with l1-norm sparsity regularization, we develop an efficient gradient-based reconstruction algorithm using a forward–backward splitting method, and prove its convergence for such a nonconvex problem.