Projection-Based Correction for Enhancing Deep Inverse Networks

2025-05-21

AI Summary

To address the violation of physical measurement constraints by deep inverse networks when solving ill-posed inverse problems, this paper proposes a forward-model-based projection post-correction method that projects network outputs onto the feasible solution space consistent with the forward operator. Theoretically, for well-trained networks, this projection reduces to an identity mapping—enabling seamless integration of data-driven learning and physics-based constraints without retraining. The method is architecture-agnostic, compatible with mainstream backbones (e.g., U-Net, ResNet), and supports end-to-end joint optimization with differentiable forward operators (e.g., pseudo-inverse, conjugate gradient iterations). Evaluated on CT reconstruction, MRI reconstruction, and single-image super-resolution, it consistently improves PSNR and SSIM by 1.2–2.8 dB over baselines. The approach demonstrates strong generalization across modalities and significantly enhances inference reliability and physical consistency of reconstructed solutions.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Enforce physical constraints in deep inverse networks
• Improve reconstruction accuracy via projection-based correction
• Ensure solution consistency with forward model

Innovation

• Projection-based correction enhances deep inverse networks
• Ensures solution consistency with forward model constraints
• Decomposes solution into range-space and null-space components