JOSR-Net: A jointly optimized sampling and reconstruction deep learning network for accelerated NMR spectroscopy

The acquisition of high-quality multi-dimensional nuclear magnetic resonance (NMR) spectra can be accelerated through the implementation of non-uniform sampling (NUS) and the employment of reconstruction method. However, the optimization of the NUS scheme and the reconstruction method have been performed independently up to now. This results in a weakened relationship between the NUS scheme and the reconstruction method and thus suboptimal reconstructed spectra, leading to shortcomings such as lost peaks and artifacts. Here, a deep learning network for jointly optimized sampling and reconstruction, referred to as JOSR-Net, is proposed. It integrates the sampling sub-network and the reconstruction sub-network into a unified end-to-end framework, aiming to simultaneously optimize both the sampling scheme and the reconstruction of undersampled data during the training process. This enables the optimal co-adaptation between the NUS scheme and the reconstruction algorithm, ultimately achieving high quality spectral reconstruction. And the results on protein spectra demonstrate that the proposed method effectively learns optimal sampling schemes and achieves superior reconstruction performance, compared to both traditional reconstruction methods and current deep learning reconstruction methods.