# Deep Convolutional Neural Network for Inverse Problems in Imaging

arXiv: https://arxiv.org/abs/1611.03679 · HTML: https://mlsanity.com/paper/1611.03679/

## Key facts

- Cited by 433 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2016.

## Built on by (most cited first, 30 of 433)

- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Transformers in Medical Imaging: A Survey](https://mlsanity.com/paper/2201.09873/) (2022)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models](https://mlsanity.com/paper/2211.10655/) (2022)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [Direct Diffusion Bridge using Data Consistency for Inverse Problems](https://mlsanity.com/paper/2305.19809/) (2023)
- [What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theory](https://mlsanity.com/paper/2105.03361/) (2021)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem](https://mlsanity.com/paper/2101.08286/) (2021)
- [Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Models](https://mlsanity.com/paper/2303.08440/) (2023)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Learned reconstruction methods with convergence guarantees](https://mlsanity.com/paper/2206.05431/) (2022)
- [Multi-Modal Transformer for Accelerated MR Imaging](https://mlsanity.com/paper/2106.14248/) (2021)
- [Plug-and-Play Algorithms for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2101.04822/) (2021)
- [Learning Deep Intensity Field for Extremely Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2303.06681/) (2023)
- [A Neural-Network-Based Convex Regularizer for Inverse Problems](https://mlsanity.com/paper/2211.12461/) (2022)
- [3D MedDiffusion: A 3D Medical Latent Diffusion Model for Controllable and High-quality Medical Image Generation](https://mlsanity.com/paper/2412.13059/) (2024)
- [On Measuring and Controlling the Spectral Bias of the Deep Image Prior](https://mlsanity.com/paper/2107.01125/) (2021)
- [Imaging with Equivariant Deep Learning](https://mlsanity.com/paper/2209.01725/) (2022)
- [End-to-end reconstruction meets data-driven regularization for inverse problems](https://mlsanity.com/paper/2106.03538/) (2021)
- [Self-Supervised Coordinate Projection Network for Sparse-View Computed Tomography](https://mlsanity.com/paper/2209.05483/) (2022)
- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
- [Sensing Theorems for Unsupervised Learning in Linear Inverse Problems](https://mlsanity.com/paper/2203.12513/) (2022)
- [Generative Modeling in Sinogram Domain for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2211.13926/) (2022)
- [Equivariant plug-and-play image reconstruction](https://mlsanity.com/paper/2312.01831/) (2023)

## Abstract (arXiv)

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyper parameter selection. The starting point of our work is the observation that unrolled iterative methods have the form of a CNN (filtering followed by point-wise non-linearity) when the normal operator (H*H, the adjoint of H times H) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill-posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 x 512 image on GPU.