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.

翻译：求解逆问题以获得有意义的解一直是科学与工程领域诸多应用中的重大挑战。近年来基于近端方法和扩散方法的机器学习技术展现出可喜成果。然而，正如本研究所示，这些方法在应用于若干典型问题时仍面临挑战。我们证明，类似于先前关于超完备字典的研究，通过将解嵌入到更高维度空间中可以克服这些缺陷。本文的创新之处在于，我们联合设计并学习嵌入过程以及嵌入向量的正则化项。我们通过几个典型且常见的逆问题实例验证了该方法的优越性。