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To eliminate the computationally prohibitive inner-loop solvers required when data-fitting proximal maps lack analytic solutions, the authors introduce the deep Pseudo-Proximal Map (PPM), which reformulates proximal evaluation as a minimum mean square error estimation problem. This self-supervised neural operator requires zero ground-truth training data, learning the data-fidelity step for any linear forward model using only evaluations of the forward operator and its adjoint on synthetic Gaussian noise. Integrated into iterative reconstruction pipelines for deblurring, super-resolution, and computed tomography, the approach matches reference reconstructions within 1% NRMSE while accelerating CT inner-loop solves by 18x via a single forward pass.
Expensive inner-loop solvers in model-based inverse reconstruction can be entirely replaced by a neural network trained on pure Gaussian noise, delivering an 18x speedup without sacrificing analytic precision.
Iterative algorithms for inverse imaging problems split reconstruction into alternating subproblems, one of which requires evaluating the data-fitting proximal map. In many practical cases, this proximal map has no analytic solution and so must be approximated by an inner loop solver at every iteration, compounding the cost of the outer reconstruction loop. To address this, we propose the pseudo-proximal map (PPM), a reformulation of the data-fitting proximal map as the minimum mean square error estimate of a synthetic probabilistic model. We implement the deep PPM as a self-supervised neural network trained only on sampled Gaussian noise, requiring no ground-truth training images. The deep PPM can be trained for any operator for which the forward model $A$ and its transpose $A^T$ can be evaluated, with provable equivalence to the proximal map when $A$ is linear. We validate the deep PPM on Gaussian deblurring and 4x super-resolution, where the proximal map has an analytic solution, and on X-ray computed tomography (XCT), where no analytic solution exists. Used as the data-fitting agent within an iterative reconstruction method, the deep PPM reproduces the reference reconstruction to within 1% NRMSE for all three operators, and for XCT, it replaces the inner conjugate-gradient loop with a single network evaluation that is 18x faster.
