Deep Equilibrium Architectures for Inverse Problems in Imaging
This addresses the limitation of fixed-iteration deep networks in imaging reconstruction, offering a more adaptable solution for researchers and practitioners in medical or scientific imaging.
The paper tackles the problem of solving inverse problems in imaging by proposing a deep equilibrium architecture that allows for an infinite number of iterations, leading to consistent improvements in reconstruction accuracy over state-of-the-art methods and enabling flexible trade-offs between accuracy and computation at test time.
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 infinite number of iterations, yielding a consistent 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.