An Over Complete Deep Learning Method for Inverse Problems
This work addresses limitations in existing machine learning methods for inverse problems, which are important in science and engineering, but it appears incremental as it builds on prior over-complete dictionary approaches.
The paper tackles challenges in solving inverse problems by proposing a method that jointly learns an embedding into higher dimensions and a regularizer, demonstrating its effectiveness on several common inverse problems.
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.