  Plug-and-play (PnP) methods that employ application-specific denoisers have
been proposed to solve inverse problems, including MRI reconstruction. However,
training application-specific denoisers is not feasible for many applications
due to the lack of training data. In this work, we propose a PnP-inspired
recovery method that does not require data beyond the single, incomplete set of
measurements. The proposed method, called recovery with a self-calibrated
denoiser (ReSiDe), trains the denoiser from the patches of the image being
recovered. The denoiser training and a call to the denoising subroutine are
performed in each iteration of a PnP algorithm, leading to a progressive
refinement of the reconstructed image. For validation, we compare ReSiDe with a
compressed sensing-based method and a PnP method with BM3D denoising using
single-coil MRI brain data.
