  Recent efforts on solving inverse problems in imaging via deep neural
networks use architectures inspired by a fixed number of iterations of an
optimization method. The number of iterations is typically quite small due to
difficulties in training networks corresponding to more iterations; the
resulting solvers cannot be run for more iterations at test time without
incurring significant errors. This paper describes an alternative approach
corresponding to an {\em infinite} number of iterations, yielding up to a 4dB
PSNR improvement in reconstruction accuracy above state-of-the-art alternatives
and where the computational budget can be selected at test time to optimize
context-dependent trade-offs between accuracy and computation. The proposed
approach leverages ideas from Deep Equilibrium Models, where the fixed-point
iteration is constructed to incorporate a known forward model and insights from
classical optimization-based reconstruction methods.
