Abstract

Plug-and-Play Forward-Backward Splitting (PnP-FBS) leverages one off-theshelf denoiser for image reconstruction in an iterative fashion. With this paradigm, the same denoiser can be employed for various reconstruction tasks without requiring any modification. Due to the simplicity and effectiveness, PnP-FBS has attracted widespread attention in imaging community. As the iteration style in implementation, its stability analysis has become a fundamental topic. However, this issue is particularly hallenging, especially for powerful deep convolutional neural network (DCNN) denoisers, since they usually lack closed-form expressions. Recently, opening a new path different from DCNNs, researchers have proposed a novel fixed deep denoiser by unfolding FBS. Encouragingly, for PnP-FBS with this denoiser, the outputs of iterations converge to a high-quality reconstruction, thereby ensuring the stability. Notably, it is well known that, benefiting from flexibility, replacing a fixed denoiser with its adaptive version generally yields superior performance in practice. Motivated by this viewpoint and the unfolding FBS strategy in existing work, in this paper, we propose a method for constructing adaptive deep denoisers. For the constructed denoisers, it is theoretically proven that, under a mild assumption, there exists an upper bound on the distance between the outputs of the PnP-FBS iterations and the ground-truth image. That is, the stability of PnP-FBS is guaranteed. To validate the theoretical results, we develop a specific instance of the denoisers following the proposed construction method and plug it into PnP-FBS for image reconstruction. Experimental results demonstrate the stability of the iterations. Additionally, as expected, with the developed adaptive instance, the PnP-FBS achieves more accurate reconstructions than the one with the fixed version.
 
　

Paper

Q. Guo^#, Z. Sun*. Designing Adaptive Deep Denoisers for Plug-and-Play FBS with Stable Iterations. Neurocomputing (Elsevier), vol. 631, 129710, 2025.  [pdf | code]

Architecture

Visualization Results

Theories