用投影修正提升深度反演网络的物理一致性
Projection-Based Correction for Enhancing Deep Inverse Networks
- 对网络输出进行投影，使其满足测量过程的物理约束
- 实验表明该方法在多种反问题中均提升重建精度
- 适合需要高物理可信度的医学成像与遥感应用
基于深度学习的模型在求解不适定反问题上表现优异，但许多方法未能严格遵守测量过程的物理约束。本文提出一种基于投影的修正方法，通过将学习到的重建网络输出投影到反问题的有效解空间，确保结果与前向模型一致。理论上证明，若恢复模型为训练良好的深度反演网络，其解可分解为范围空间与零空间分量，此时投影修正退化为恒等变换。大量仿真与实验验证了该方法的有效性，显著提升了多种反问题和网络架构下的重建准确率。
原文摘要 · Abstract (English)
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.
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