# A Projectional Ansatz to Reconstruction

arXiv: https://arxiv.org/abs/1907.04675 · HTML: https://mlsanity.com/paper/1907.04675/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [DIPLI: Deep Image Prior Lucky Imaging for Blind Astronomical Image Restoration](https://mlsanity.com/paper/2503.15984/) (2025)
- [Data-Consistent Learning of Inverse Problems](https://mlsanity.com/paper/2601.12831/) (2026)

## Abstract (arXiv)

Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the incorporation of these priors, while still guaranteeing data consistency. We implement this projectional method (PM) on the one hand via very general Plug-and-Play priors and on the other hand, via an end-to-end training approach. To this end, we introduce a novel alternating neural architecture, allowing for the incorporation of highly customized priors from data in a principled manner. We also show how the recent success of Regularization by Denoising (RED) can, at least to some extent, be explained as an approximation of the PM. Furthermore, we demonstrate how the idea can be applied to stop the degradation of Deep Image Prior (DIP) reconstructions over time.