Plug-and-play (PnP) methods can reconstruct images by employing iterative algorithms that leverage the knowledge of the forward model and a sophisticated denoiser. The performance of PnP can be improved by utilizing an application-specific denoiser. However, training such denoisers may not be feasible for many MRI applications. Here, we describe a PnP-inspired 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. For validation, ReSiDe is applied to T1-weighted brain and myocardial first-pass perfusion data.