Untrained CNN and coefficient-space regularization for joint reconstruction in photoacoustic tomography

The joint reconstruction of the initial pressure and spatially varying sound speed in photoacoustic tomography from boundary measurements is considered. A regularized data-driven framework is proposed in which the unknown fields are represented in finite-dimensional wavelet spaces and fixed nonlinear features generated by an untrained convolutional neural network (CNN) are used to reconstruct the initial-pressure coefficients through Tikhonov-regularized least squares. A learned coefficient-space prior is subsequently used to infer the squared sound-speed coefficients. Numerical experiments demonstrate accurate reconstruction on held-out data and strong generalization to previously unseen phantom geometries. The frozen reconstruction map also remains stable under measurement noise not represented during training, with only minor changes in reconstruction accuracy for noise levels up to $10\%$. In comparison with the supervised trained-CNN approach considered in this work, the untrained representation yields substantially smaller reconstruction errors while requiring approximately one-sixth of the computational time. These results demonstrate that fixed random convolutional features combined with regularized coefficient-space learning provide an efficient and robust approach to joint reconstruction in photoacoustic tomography.