EmNeF: Neural Fields for Embedded Variational Problems in Imaging

We propose a model-driven neural fields approach for solving variational problems. The approach can be applied to a variety of problems with convex, 1-homogeneous regularizer and arbitrary, possibly non-convex, data term. Our strategy is to embed the non-convex energy into a higher-dimensional space, reaching a convex primal-dual formulation. Instead of using classical gradient-descent based optimization algorithms, we propose training multiple fields representing the primal and dual variables in order to solve the problem.