Projection-Based Correction for Enhancing Deep Inverse Networks

TL;DR

This paper proposes a projection-based correction method to improve the physical consistency and accuracy of deep inverse networks in solving ill-posed inverse problems.

Contribution

It introduces a novel projection step that enforces measurement constraints, enhancing deep inverse network reconstructions with theoretical guarantees.

Findings

Improved reconstruction accuracy across various inverse problems

Theoretical proof of the correction's effect on well-trained models

Validated effectiveness through extensive simulations and experiments

Abstract

Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a projection-based correction method to enhance the inference of deep inverse networks by ensuring consistency with the forward model. Specifically, given an initial estimate from a learned reconstruction network, we apply a projection step that constrains the solution to lie within the valid solution space of the inverse problem. We theoretically demonstrate that if the recovery model is a well-trained deep inverse network, the solution can be decomposed into range-space and null-space components, where the projection-based correction reduces to an identity transformation. Extensive simulations and experiments validate the proposed method, demonstrating improved reconstruction accuracy across diverse inverse problems and deep network architectures.