A new plug-and-play approach based on the Tseng algorithm: PNP-TSENG and super resolution application

Image restoration problems such as super-resolution, deblurring, compressed sensing, and tomography are typically formulated as optimization problems. Proximal algorithms such as ISTA and ADMM, along with Plug-and-Play (PnP) approaches, are widely used in modern image restoration problems. However, existing PnP methods have potential for improvement in terms of convergence speed and computational cost. In this thesis, a novel algorithm called PnP-Tseng has been developed as an alternative to existing PnP methods, based on Tseng's forward-backward-forward algorithm. It has been theoretically proven that the sequence generated by this algorithm, defined for averaged operators, converges to the fixed point of the operator, and the existence of the objective function minimized by the algorithm has been demonstrated. The performance of the PnP-Tseng algorithm has been evaluated comparatively with PnP-ISTA and PnP-ADMM algorithms on the super-resolution problem. Experimental results reveal that the proposed PnP-Tseng algorithm exhibits competitive performance in terms of image quality and convergence properties. This study provides theoretical and practical contributions to the image restoration literature by realizing the first-time integration of Tseng's algorithm into the PnP framework.