demo.superres_pnp¶
Overview: A simple demo to demonstrate the solution of a PnP problem The forward model is a subsampling operation, and the prior agent is the bm3d denoiser.
First a clean image is subsampled, then white noise is added to produce noisy data. This is used to define a forward agent that updates to better fit the data.
In a classical Bayesian approach, this update has the form \(F(x) = x + c A^T (y - Ax)\), for a constant c. In some contexts, it’s useful to have a mismatched backprojector, which is equivalent to replacing \(A^T\) with an alternative matrix designed to promote better or faster reconstruction. As shown in a paper by Emma Reid, (in preparation) this is equivalent to using the standard back projector but changing the prior.
This demo provides the ability to explore mismatched backprojectors by changing the upsampling method used to define \(A^T\). It also provides the ability to change the relative weight of data-fitting and denoising by changing mu.
This demo uses the standard Plug and Play method, while superres_mace.py uses a parallel construction based on the MACE formulation and Mann iterations.
Functions
Illustrate Plug and Play ADMM reconstruction on an image superresolution problem. |