Reaching the sparse-sampling limit for reconstructing a single peak in a 2D NMR spectrum using iterated maps.

Many of the ubiquitous experiments of biomolecular NMR, including [Formula: see text], [Formula: see text], and CEST, involve acquiring repeated 2D spectra under slightly different conditions. Such experiments are amenable to acceleration using non-uniform sampling spectral reconstruction methods that take advantage of prior information. We previously developed one such technique, an iterated maps method (DiffMap) that we successfully applied to 2D NMR spectra, including [Formula: see text] relaxation dispersion data. In that prior work, we took a top-down approach to reconstructing the 2D spectrum with a minimal number of sparse samples, reaching an undersampling fraction that appeared to leave some room for improvement. In this study, we develop an in-depth understanding of the action of the DiffMap algorithm, identifying the factors that cause reconstruction errors for different undersampling fractions. This improved understanding allows us to formulate a bottom-up approach to finding the lowest number of sparse samples required to accurately reconstruct individual spectral features with DiffMap. We also discuss the difficulty of extending this method to reconstructing many peaks at once, and suggest a way forward.

Accelerating 2D NMR relaxation dispersion experiments using iterated maps.

NMR relaxation dispersion experiments play a central role in exploring molecular motion over an important range of timescales, and are an example of a broader class of multidimensional NMR experiments that probe important biomolecules. However, resolving the spectral features of these experiments using the Fourier transform requires sampling the full Nyquist grid of data, making these experiments very costly in time. Practitioners often reduce the experiment time by omitting 1D experiments in the indirectly observed dimensions, and reconstructing the spectra using one of a variety of post-processing algorithms. In prior work, we described a fast, Fourier-based reconstruction method using iterated maps according to the Difference Map algorithm of Veit Elser (DiffMap). Here we describe coDiffMap, a new reconstruction method that is based on DiffMap, but which exploits the strong correlations between 2D data slices in a pseudo-3D experiment. We apply coDiffMap to reconstruct dispersion curves from an [Formula: see text] relaxation dispersion experiment, and demonstrate that the method provides fast reconstructions and accurate relaxation curves down to very low numbers of sparsely-sampled data points.

Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System.

A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsic lifetime of the DTC.

Accelerating multidimensional NMR and MRI experiments using iterated maps.

Techniques that accelerate data acquisition without sacrificing the advantages of fast Fourier transform (FFT) reconstruction could benefit a wide variety of magnetic resonance experiments. Here we discuss an approach for reconstructing multidimensional nuclear magnetic resonance (NMR) spectra and MR images from sparsely-sampled time domain data, by way of iterated maps. This method exploits the computational speed of the FFT algorithm and is done in a deterministic way, by reformulating any a priori knowledge or constraints into projections, and then iterating. In this paper we explain the motivation behind this approach, the formulation of the specific projections, the benefits of using a 'QUasi-Even Sampling, plus jiTter' (QUEST) sampling schedule, and various methods for handling noise. Applying the iterated maps method to real 2D NMR and 3D MRI of solids data, we show that it is flexible and robust enough to handle large data sets with significant noise and artifacts.

Phosphorus-31 MRI of hard and soft solids using quadratic echo line-narrowing.

Magnetic resonance imaging (MRI) of solids is rarely attempted. One of the main reasons is that the broader MR linewidths, compared to the narrow resonance of the hydrogen ((1)H) in free water, limit both the attainable spatial resolution and the signal-to-noise ratio. Basic physics research, stimulated by the quest to build a quantum computer, gave rise to a unique MR pulse sequence that offers a solution to this long-standing problem. The "quadratic echo" significantly narrows the broad MR spectrum of solids. Applying field gradients in sync with this line-narrowing sequence offers a fresh approach to carry out MRI of hard and soft solids with high spatial resolution and with a wide range of potential uses. Here we demonstrate that this method can be used to carry out three-dimensional MRI of the phosphorus ((31)P) in ex vivo bone and soft tissue samples.