Accelerated NMR Spectroscopy with Low-Rank Reconstruction

Accelerated MRI Reconstruction With Separable and Enhanced Low-Rank Hankel Regularization

Magnetic resonance imaging serves as an essential tool for clinical diagnosis, however, suffers from a long acquisition time. Sparse sampling effectively saves this time but images need to be faithfully reconstructed from undersampled data. Among the existing reconstruction methods, the structured low-rank methods have advantages in robustness to the sampling patterns and lower error. However, the structured low-rank methods use the 2D or higher dimension k-space data to build a huge block Hankel matrix, leading to considerable time and memory consumption. To reduce the size of the Hankel matrix, we proposed to separably construct multiple small Hankel matrices from rows and columns of the k-space and then constrain the low-rankness on these small matrices. This separable model can significantly reduce the computational time but ignores the correlation existed in inter- and intra-row or column, resulting in increased reconstruction error. To improve the reconstructed image without obviously increasing the computation, we further introduced the self-consistency of k-space and virtual coil prior. Besides, the proposed separable model can be extended into other imaging scenarios which hold exponential characteristics in the parameter dimension. The in vivo experimental results demonstrated that the proposed method permits the lowest reconstruction error with a fast reconstruction. The proposed approach requires only 4% of the state-of-the-art STDLR-SPIRiT runtime for parallel imaging reconstruction, and achieves the fastest computational speed in parameter imaging reconstruction.

Temperature as an Extra Dimension in Multidimensional Protein NMR Spectroscopy

NMR spectroscopy is a particularly informative method for studying protein structures and dynamics in solution; however, it is also one of the most time-consuming. Modern approaches to biomolecular NMR spectroscopy are based on lengthy multidimensional experiments, the duration of which grows exponentially with the number of dimensions. The experimental time may even be several days in the case of 3D and 4D spectra. Moreover, the experiment often has to be repeated under several different conditions, for example, to measure the temperature-dependent effects in a spectrum (temperature coefficients (TCs)). Herein, a new approach that involves joint sampling of indirect evolution times and temperature is proposed. This allows TCs to be measured through 3D spectra in even less time than that needed to acquire a single spectrum by using the conventional approach. Two signal processing methods that are complementary, in terms of sensitivity and resolution, 1) dividing data into overlapping subsets followed by compressed sensing reconstruction, and 2) treating the complete data set with a variant of the Radon transform, are proposed. The temperature-swept 3D HNCO spectra of two intrinsically disordered proteins, osteopontin and CD44 cytoplasmic tail, show that this new approach makes it possible to determine TCs and their non-linearities effectively. Non-linearities, which indicate the presence of a compact state, are particularly interesting. The complete package of data acquisition and processing software for this new approach are provided.

Accelerated Nuclear Magnetic Resonance Spectroscopy with Deep Learning

Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental times. We present a proof-of-concept of the application of deep learning and neural networks for high-quality, reliable, and very fast NMR spectra reconstruction from limited experimental data. We show that the neural network training can be achieved using solely synthetic NMR signals, which lifts the prohibiting demand for a large volume of realistic training data usually required for a deep learning approach.

Predicting Carbon Spectrum in Heteronuclear Single Quantum Coherence Spectroscopy for Online Feedback During Surgery

¹H High-Resolution Magic Angle Spinning (HRMAS) Nuclear Magnetic Resonance (NMR) is a reliable technology used for detecting metabolites in solid tissues. Fast response time enables guiding surgeons in real time, for detecting tumor cells that are left over in the excision cavity. However, severe overlap of spectral resonances in 1D signal often render distinguishing metabolites impossible. In that case, Heteronuclear Single Quantum Coherence Spectroscopy (HSQC) NMR is applied which can distinguish metabolites by generating 2D spectra ( ¹H- ¹³C). Unfortunately, this analysis requires much longer time and prohibits real time analysis. Thus, obtaining 2D spectrum fast has major implications in medicine. In this study, we show that using multiple multivariate regression and statistical total correlation spectroscopy, we can learn the relation between the ¹H and ¹³C dimensions. Learning is possible with small sample sizes and without the need for performing the HSQC analysis, we can predict the ¹³C dimension by just performing ¹H HRMAS NMR experiment. We show on a rat model of central nervous system tissues (80 samples, 5 tissues) that our methods achieve 0.971 and 0.957 mean R² values, respectively. Our tests on 15 human brain tumor samples show that we can predict 104 groups of 39 metabolites with 97 percent accuracy. Finally, we show that we can predict the presence of a drug resistant tumor biomarker (creatine) despite obstructed signal in ¹H dimension. In practice, this information can provide valuable feedback to the surgeon to further resect the cavity to avoid potential recurrence.

Manifold recovery using kernel low-rank regularization: application to dynamic imaging

We introduce a novel kernel low-rank algorithm to recover free-breathing and ungated dynamic MRI data from highly undersampled measurements. The image frames in the free breathing and ungated dataset are assumed to be points on a bandlimited manifold. We show that the non-linear features of these images satisfy annihilation conditions, which implies that the kernel matrix derived from the dataset is low-rank. We penalize the nuclear norm of the feature matrix to recover the images from highly undersampled measurements. The regularized optimization problem is solved using an iterative reweighted least squares (IRLS) algorithm, which alternates between the update of the Laplacian matrix of the manifold and the recovery of the signals from the noisy measurements. To improve computational efficiency, we use a two step algorithm using navigator measurements. Specifically, the Laplacian matrix is estimated from the navigators using the IRLS scheme, followed by the recovery of the images using a quadratic optimization. We show the relation of this two step algorithm with our recent SToRM approach, thus reconciling SToRM and manifold regularization methods with algorithms that rely on explicit lifting of data to a high dimensional space. The IRLS based estimation of the Laplacian matrix is a systematic and noise-robust alternative to current heuristic strategies based on exponential maps. We also approximate the Laplacian matrix using a few eigen vectors, which results in a fast and memory efficient algorithm. The proposed scheme is demonstrated on several patients with different breathing patterns and cardiac rates.

XLSY: Extra-Large NMR Spectroscopy

NMR studies of intrinsically disordered proteins and other complex biomolecular systems require spectra with the highest resolution and dimensionality. An efficient approach, extra‐large NMR spectroscopy, is presented for experimental data collection, reconstruction, and handling of very large NMR spectra by a combination of the radial and non‐uniform sampling, a new processing algorithm, and rigorous statistical validation. We demonstrate the first high‐quality reconstruction of a full seven‐dimensional HNCOCACONH and two five‐dimensional HACACONH and HN(CA)CONH experiments for a representative intrinsically disordered protein α‐synuclein. XLSY will significantly enhance the NMR toolbox in challenging biomolecular studies.

ADAPT-NMR 3.0: utilization of BEST-type triple-resonance NMR experiments to accelerate the process of data collection and assignment

ADAPT-NMR (Assignment-directed Data collection Algorithm utilizing a Probabilistic Toolkit in NMR) is a software package whose Bayesian core uses on-the-fly chemical shift assignments to guide data acquisition by non-uniform sampling from a panel of through-bond NMR experiments. The new version of ADAPT-NMR (ADAPT-NMR v3.0) has the option of utilizing 2D tilted-plane versions of 3D fast spectral acquisition with BEST-type pulse sequences, while also retaining the capability of acquiring and processing data from tilted-plane versions of conventional sensitivity-enhanced experiments. The use of BEST experiments significantly reduces data collection times and leads to enhanced performance by ADAPT-NMR.