Learning to Optimally Sample in MRI for Denoising-Driven Regularization

The reconstruction quality in compressed sensing MRI can be significantly improved by optimizing the k-space sampling. While previous works have mainly focused on total variation and other traditional regularizers, more recent denoising-driven regularizers have not been fully explored. We address this gap by developing a computational framework to learn the optimal sampling for Plug-and-Play (PnP) regularization. A technical challenge here is the computation of the gradient of the training loss with respect to the reconstruction variable, which is used within the learning algorithm to optimize the sampling. A notable finding in this direction is that the gradient can be computed analytically for a kernel denoiser such as the nonlocal means. Moreover, the superior regularization offered by PnP helps discover sampling patterns that significantly improve the reconstruction. We demonstrate the effectiveness of our proposal for different anatomical datasets.