ERAN TREISTER

Senior Academic

An over complete deep learning method for 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.

Publication language English
Pages 50-71
Journal Foundations of Data Science
Volume 7
Issue number 1
Publication status Published - 01.03.2025

Keywords

Convolutional neural networks
Inverse problems
Regularization

ASJC Scopus subject areas

Analysis
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics
Access to Document
10.3934/fods.2024036
Other files and links
Link to publication in Scopus