Scalable deep learning reconstruction for accelerated multidimensional nuclear magnetic resonance spectroscopy of proteins

High-dimensional nuclear magnetic resonance (NMR) spectroscopy can assist in determining protein structure, but it requires time-consuming acquisition. Deep learning enables ultrafast reconstruction but is limited to spectra of up to three dimensions and cannot provide faithful reconstruction under unseen acceleration factors. Extending deep learning to handle higher-dimensional spectra and varying acceleration factors is desirable. However, scalability requires complex networks and more data, seriously hindering applications. To address this, we designed a network to learn data in one dimension (1D). First, time-domain signals were modeled as the outer product of 1D exponentials. Then, each 1D exponential was approximated with a rank-one Hankel matrix. Last, reconstruction error was corrected with a neural network. Here, we demonstrate robust 3D NMR reconstruction across acceleration factors (2 to 33) using one trained network. In addition, we find that reconstruction of 4D NMR is possible with artificial intelligence. This work opens an avenue for accelerating arbitrarily high-dimensional NMR.