# Projection-Based Correction for Enhancing Deep Inverse Networks

arXiv: https://arxiv.org/abs/2505.15777 · HTML: https://mlsanity.com/paper/2505.15777/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 13 references that are in the map.
- First posted on arXiv 21 May 2025.

## Builds on (most cited first, 8 of 8)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees](https://mlsanity.com/paper/1802.08406/) (2018)
- [Deep Gaussian Scale Mixture Prior for Spectral Compressive Imaging](https://mlsanity.com/paper/2103.07152/) (2021)
- [Deep Decomposition Learning for Inverse Imaging Problems](https://mlsanity.com/paper/1911.11028/) (2019)

## Built on by (most cited first, 2 of 2)

- [Scale Equivariance Regularization and Feature Lifting in High Dynamic Range Modulo Imaging](https://mlsanity.com/paper/2601.23037/) (2026)
- [A Gradient-Regularized Deep Learning Method for Restoring Image in Myopic Vision](https://mlsanity.com/paper/2610.19218/) (2026)

## Abstract (arXiv)

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.