Magnetic resonance imaging (MRI) is a powerful noninvasive diagnostic imaging tool that provides unparalleled soft tissue contrast and anatomical detail. Noise contamination, especially in accelerated and/or low-field acquisitions, can significantly degrade image quality and diagnostic accuracy. Supervised learning based denoising approaches have achieved impressive performance but require high signal-to-noise ratio (SNR) labels, which are often unavailable. Self-supervised learning holds promise to address the label scarcity issue, but existing self-supervised denoising methods tend to oversmooth fine spatial features and often yield inferior performance than supervised methods. We introduce Corruption2Self (C2S), a novel score-based self-supervised framework for MRI denoising. At the core of C2S is a generalized denoising score matching (GDSM) loss, which extends denoising score matching to work directly with noisy observations by modeling the conditional expectation of higher-SNR images given further corrupted observations. This allows the model to effectively learn denoising across multiple noise levels directly from noisy data. Additionally, we incorporate a reparameterization of noise levels to stabilize training and enhance convergence, and introduce a detail refinement extension to balance noise reduction with the preservation of fine spatial features. Moreover, C2S can be extended to multi-contrast denoising by leveraging complementary information across different MRI contrasts. We demonstrate that our method achieves state-of-the-art performance among self-supervised methods and competitive results compared to supervised counterparts across varying noise conditions and MRI contrasts on the M4Raw and fastMRI dataset. The project website is available at: https://jiachentu.github.io/Corruption2Self-Self-Supervised-Denoising/.

We present a new method that integrates subspace modeling and a pre-learned spatiotemporal denoiser for reconstruction from highly noisy magnetic resonance spectroscopic imaging (MRSI) data. The subspace model imposes an explicit low-dimensional representation of the high-dimensional spatiospectral functions of interest for noise reduction, while the denoiser serves as a complementary spatiotemporal prior to constrain the subspace reconstruction. A self-supervised learning strategy was proposed to train a denoiser that can distinguish the spatiotemporally correlated signals from uncorrelated noise. An iterative reconstruction formalism was developed based on the Plug-and-Play (PnP)-ADMM framework to synergize the subspace constraint, plug-in denoiser and spatiospectral encoding model. We evaluated the proposed method using numerical simulations and in vivo data, demonstrating improved performance over state-of-the-art subspace-based methods. We also provided theoretical analysis on the utility of combining subspace projection and iterative denoising in terms of both algorithm convergence and performance. Our work demonstrated the potential of integrating self-supervised denoising priors and low-dimensional representations for high-dimensional imaging problems.

Short-echo-time (TE) proton magnetic resonance spectroscopic imaging (MRSI) allows for simultaneously mapping a number of molecules in the brain, and has been recognized as an important tool for studying in vivo biochemistry in various neuroscience and disease applications. However, separation of the metabolite and macromolecule (MM) signals present in the short-TE data with significant spectral overlaps remains a major technical challenge. This work introduces a new approach to solve this problem by integrating imaging physics and representation learning. Specifically, a mixed unsupervised and supervised learning-based strategy was developed to learn the metabolite and MM-specific low-dimensional representations using deep autoencoders. A constrained reconstruction formulation is proposed to integrate the MRSI spatiospectral encoding model and the learned representations as effective constraints for signal separation. An efficient algorithm was developed to solve the resulting optimization problem with provable convergence. Simulation and experimental results have been obtained to demonstrate the component-specific representation power of the learned models and the capability of the proposed method in separating metabolite and MM signals for practical short-TE [Formula: see text]-MRSI data.

Magnetic resonance spectroscopic imaging (MRSI) is a powerful molecular imaging modality but has very limited speed, resolution, and SNR tradeoffs. Construction of a low-dimensional model to effectively reduce the dimensionality of the imaging problem has recently shown great promise in improving these tradeoffs. This paper presents a new approach to model and reconstruct the spectroscopic signals by learning a nonlinear low-dimensional representation of the general MR spectra. Specifically, we trained a deep neural network to capture the low-dimensional manifold, where the high-dimensional spectroscopic signals reside. A regularization formulation is proposed to effectively integrate the learned model and physics-based data acquisition model for MRSI reconstruction with the capability to incorporate additional spatiospectral constraints. An efficient numerical algorithm was developed to solve the associated optimization problem involving back-propagating the trained network. Simulation and experimental results were obtained to demonstrate the representation power of the learned model and the ability of the proposed formulation in producing SNR-enhancing reconstruction from the practical MRSI data.

High-dimensional MR imaging often requires long data acquisition time, thereby limiting its practical applications. This paper presents a low-rank tensor based method for accelerated high-dimensional MR imaging using sparse sampling. This method represents high-dimensional images as low-rank tensors (or partially separable functions) and uses this mathematical structure for sparse sampling of the data space and for image reconstruction from highly undersampled data. More specifically, the proposed method acquires two datasets with complementary sampling patterns, one for subspace estimation and the other for image reconstruction; image reconstruction from highly undersampled data is accomplished by fitting the measured data with a sparsity constraint on the core tensor and a group sparsity constraint on the spatial coefficients jointly using the alternating direction method of multipliers. The usefulness of the proposed method is demonstrated in MRI applications; it may also have applications beyond MRI.

Magnetic resonance parameter mapping (e.g., T1 mapping, T2 mapping, T*2 mapping) is a valuable tool for tissue characterization. However, its practical utility has been limited due to long data acquisition time. This paper addresses this problem with a new model-based parameter mapping method. The proposed method utilizes a formulation that integrates the explicit signal model with sparsity constraints on the model parameters, enabling direct estimation of the parameters of interest from highly undersampled, noisy k-space data. An efficient greedy-pursuit algorithm is described to solve the resulting constrained parameter estimation problem. Estimation-theoretic bounds are also derived to analyze the benefits of incorporating sparsity constraints and benchmark the performance of the proposed method. The theoretical properties and empirical performance of the proposed method are illustrated in a T2 mapping application example using computer simulations.