Stable and memory-efficient image recovery using monotone operator learning (MOL)
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We introduce a monotone deep equilibrium learning framework for large-scale inverse problems in imaging. The proposed algorithm relies on forward-backward splitting, where each iteration consists of a gradient descent involving the score function and a conjugate gradient algorithm to encourage data consistency. The score function is modeled as a monotone convolutional neural network. The use of a monotone operator offers several benefits, including guaranteed convergence, uniqueness of fixed point, and robustness to input perturbations, similar to the use of convex priors in compressive sensing. In addition, the proposed formulation is significantly more memory-efficient than unrolled methods, which allows us to apply it to 3D problems that current unrolled algorithms cannot handle. Experiments show that the proposed scheme can offer improved performance in 3D settings while being stable in the presence of input perturbations.
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