# An Over Complete Deep Learning Method for Inverse Problems

arXiv: https://arxiv.org/abs/2402.04653 · HTML: https://mlsanity.com/paper/2402.04653/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 15 of 15)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [IMEXnet: A Forward Stable Deep Neural Network](https://mlsanity.com/paper/1903.02639/) (2019)
- [ANODEV2: A Coupled Neural ODE Evolution Framework](https://mlsanity.com/paper/1906.04596/) (2019)
- [Learning convex regularizers satisfying the variational source condition for inverse problems](https://mlsanity.com/paper/2110.12520/) (2021)
- [DRIP: Deep Regularizers for Inverse Problems](https://mlsanity.com/paper/2304.00015/) (2023)

## Built on by (most cited first, 3 of 3)

- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [Learning Regularization for Graph Inverse Problems](https://mlsanity.com/paper/2408.10436/) (2024)
- [DAWN-FM: Data-Aware and Noise-Informed Flow Matching for Solving Inverse Problems](https://mlsanity.com/paper/2412.04766/) (2024)

## Abstract (arXiv)

Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results. However, as we show in this work, they can also face challenges when applied to some exemplary problems. We show that similar to previous works on over-complete dictionaries, it is possible to overcome these shortcomings by embedding the solution into higher dimensions. The novelty of the work proposed is that we jointly design and learn the embedding and the regularizer for the embedding vector. We demonstrate the merit of this approach on several exemplary and common inverse problems.