Plug-and-play (PnP) methods solve imaging inverse problems by replacing the proximal step of a classical optimization algorithm with an off-the-shelf or learned denoiser. The idea is simple and empirically powerful, but it leaves open what the resulting iterations actually compute. In this talk I will survey the theory that has emerged over the past decade around four questions: do PnP iterations converge, is the limit a minimizer of an explicit energy, how fast can we get there, and does the method behave as a convergent regularization when the measurement noise vanishes? Along the way I will highlight the key theoretical results and proof techniques, from averaged-operator arguments to sufficient-decrease arguments, and the denoiser structures they require. I will then present two of our contributions. The first is a quasi-Newton PnP method that uses the forward-backward envelope of a gradient-step denoiser to accelerate convergence while retaining convergence to critical points of a weakly convex functional. The second shows that spectral filtering of a learned linear denoiser turns PnP into a provably convergent regularization method. I will close with open problems for nonlinear denoisers and diffusion-based samplers.
Subhadip Mukherjee is an Assistant Professor in the Department of Electronics and Electrical Communication Engineering at IIT Kharagpur. He received a B.E. from Jadavpur University, followed by an M.E. in Signal Processing and a Ph.D. from the Indian Institute of Science, Bangalore. Before joining IIT Kharagpur in 2023, he was a postdoctoral researcher at KTH Stockholm and at the University of Cambridge, and a Lecturer in Machine Learning and AI at the University of Bath. His work combines model-based and data-driven approaches to inverse problems in imaging, with a focus on efficient algorithms with provable convergence guarantees.