  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.
