Online Regularization by Denoising with Applications to Phase Retrieval
This work addresses the scalability issue of RED algorithms for large datasets in imaging, though it appears incremental as it adapts an existing framework to an online setting.
The paper tackles the limitation of iterative batch procedures in regularization by denoising (RED) for imaging inverse problems by introducing an online RED algorithm that processes data in small subsets, showing theoretical convergence in convex settings and empirical effectiveness in non-convex phase retrieval applications.
Regularization by denoising (RED) is a powerful framework for solving imaging inverse problems. Most RED algorithms are iterative batch procedures, which limits their applicability to very large datasets. In this paper, we address this limitation by introducing a novel online RED (On-RED) algorithm, which processes a small subset of the data at a time. We establish the theoretical convergence of On-RED in convex settings and empirically discuss its effectiveness in non-convex ones by illustrating its applicability to phase retrieval. Our results suggest that On-RED is an effective alternative to the traditional RED algorithms when dealing with large datasets.