3F-PNP: Compressive Sensing Using Nonlocal Self-Similarity and Deep Learning Priors

We formalize compressed sensing image reconstruction as an optimization problem, incorporating penalization of the spectral representation of images. Leveraging the original formulation of the Alternating Direction Method of Multipliers (ADMM), we introduce the innovative 3F-PnP algorithm. This algorithm integrates three filters: two deep learning neural network-based filters and the spectral BM3D denoiser, implemented through plug-and-play modules. Additionally, we show that the partial solutions of the ADMM optimization correspond precisely to the analysis and synthesis stages of the BM3D filter. Through numerical comparative analysis against ten state-of-the-art methods, we demonstrate the superiority of our algorithm in terms of improved accuracy and faster convergence rates.