Block Coordinate Plug-and-Play Algorithms for Image Restoration

Simone Rebegoldi (Università di Modena e Reggio Emilia)

Abstract: Plug-and-Play (PnP) algorithms represent a powerful and innovative paradigm for solving inverse problems in computational imaging. These methods replace the usual explicit regularization step with an implicit step, implemented by means of a denoising algorithm. In the last decade, PnP methods have achieved state-of-the-art results in several image restoration tasks, often outperforming traditional regularization techniques. In [1] a new denoising operator has been proposed, defined explicitly as the gradient step of a potential function parametrized by a convolutional neural network. Such denoisers allow for a clearer variational interpretation of PnP methods; however, they are high-memory consuming, as their implementation requires storing large computational graphs.

We propose a novel class of block coordinate PnP methods to address imaging inverse problems [2]. The block coordinate strategy is designed to reduce the high memory consumption arising in PnP methods that rely on Gradient Step denoisers. The proposed methods are based on a block coordinate forward backward framework for solving nonconvex and nonseparable composite optimization problems. Under mild assumptions on the objective function, we establish a sublinear convergence rate and the stationarity of the limit points. Moreover, convergence of the entire sequence of the iterates is guaranteed under a Kurdyka-Łojasiewicz assumption. Numerical experiments on ill-posed imaging problems, including deblurring and super-resolution, demonstrate that the proposed PnP approach achieves state-of-the-art reconstruction quality while substantially reducing GPU memory requirements.

[1] S. Hurault, A. Leclaire, and N. Papadakis, Gradient step denoiser for convergent Plug-and-Play, in International Conference on Learning Representations (ICLR), 2022.

[2] F. Porta, S. Rebegoldi, A. Sebastiani, Block-coordinate Plug-And-Play Methods with Armijo-like line-search for Image Restoration, arXiv:2603.01734, 2026.