Using a deep learning prior for accelerating hyperpolarized 13C MRSI on synthetic cancer datasets.

PURPOSE: We aimed to incorporate a deep learning prior with k-space data fidelity for accelerating hyperpolarized carbon-13 MRSI, demonstrated on synthetic cancer datasets. METHODS: A two-site exchange model, derived from the Bloch equation of MR signal evolution, was firstly used in simulating training and testing data, that is, synthetic phantom datasets. Five singular maps generated from each simulated dataset were used to train a deep learning prior, which was then employed with the fidelity term to reconstruct the undersampled MRI k-space data. The proposed method was assessed on synthetic human brain tumor images (N = 33), prostate cancer images (N = 72), and mouse tumor images (N = 58) for three undersampling factors and 2.5% additive Gaussian noise. Furthermore, varied levels of Gaussian noise with SDs of 2.5%, 5%, and 10% were added on synthetic prostate cancer data, and corresponding reconstruction results were evaluated. RESULTS: For quantitative evaluation, peak SNRs were approximately 32 dB, and the accuracy was generally improved for 5 to 8 dB compared with those from compressed sensing with L1-norm regularization or total variation regularization. Reasonable normalized RMS error were obtained. Our method also worked robustly against noise, even on a data with noise SD of 10%. CONCLUSION: The proposed singular value decomposition + iterative deep learning model could be considered as a general framework that extended the application of deep learning MRI reconstruction to metabolic imaging. The morphology of tumors and metabolic images could be measured robustly in six times acceleration using our method.

Bayesian MRI reconstruction with joint uncertainty estimation using diffusion models.

PURPOSE: We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. METHOD: Samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method, different from conventional deep learning-based MRI reconstruction techniques. In addition to the maximum a posteriori estimate for the image, which can be obtained by maximizing the log-likelihood indirectly or directly, the minimum mean square error estimate and uncertainty maps can also be computed from those drawn samples. The data-driven Markov chains are constructed with the score-based generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement. RESULTS: We numerically investigate the framework from these perspectives: (1) the interpretation of the uncertainty of the image reconstructed from undersampled k-space; (2) the effect of the number of noise scales used to train the generative models; (3) using a burn-in phase in MCMC sampling to reduce computation; (4) the comparison to conventional ℓ 1 $$ {\ell}_1 $$ -wavelet regularized reconstruction; (5) the transferability of learned information; and (6) the comparison to fastMRI challenge. CONCLUSION: A framework is described that connects the diffusion process and advanced generative models with Markov chains. We demonstrate its flexibility in terms of contrasts and sampling patterns using advanced generative priors and the benefits of also quantifying the uncertainty for every pixel.

Deep, deep learning with BART.

PURPOSE: To develop a deep-learning-based image reconstruction framework for reproducible research in MRI. METHODS: The BART toolbox offers a rich set of implementations of calibration and reconstruction algorithms for parallel imaging and compressed sensing. In this work, BART was extended by a nonlinear operator framework that provides automatic differentiation to allow computation of gradients. Existing MRI-specific operators of BART, such as the nonuniform fast Fourier transform, are directly integrated into this framework and are complemented by common building blocks used in neural networks. To evaluate the use of the framework for advanced deep-learning-based reconstruction, two state-of-the-art unrolled reconstruction networks, namely the Variational Network and MoDL, were implemented. RESULTS: State-of-the-art deep image-reconstruction networks can be constructed and trained using BART's gradient-based optimization algorithms. The BART implementation achieves a similar performance in terms of training time and reconstruction quality compared to the original implementations based on TensorFlow. CONCLUSION: By integrating nonlinear operators and neural networks into BART, we provide a general framework for deep-learning-based reconstruction in MRI.

MRI reconstruction using deep Bayesian estimation.

PURPOSE: To develop a deep learning-based Bayesian estimation for MRI reconstruction. METHODS: We modeled the MRI reconstruction problem with Bayes's theorem, following the recently proposed PixelCNN++ method. The image reconstruction from incomplete k-space measurement was obtained by maximizing the posterior possibility. A generative network was utilized as the image prior, which was computationally tractable, and the k-space data fidelity was enforced by using an equality constraint. The stochastic backpropagation was utilized to calculate the descent gradient in the process of maximum a posterior, and a projected subgradient method was used to impose the equality constraint. In contrast to the other deep learning reconstruction methods, the proposed one used the likelihood of prior as the training loss and the objective function in reconstruction to improve the image quality. RESULTS: The proposed method showed an improved performance in preserving image details and reducing aliasing artifacts, compared with GRAPPA, ℓ1 -ESPRiT, model-based deep learning architecture for inverse problems (MODL), and variational network (VN), last two were state-of-the-art deep learning reconstruction methods. The proposed method generally achieved more than 3 dB peak signal-to-noise ratio improvement for compressed sensing and parallel imaging reconstructions compared with the other methods. CONCLUSIONS: The Bayesian estimation significantly improved the reconstruction performance, compared with the conventional ℓ1 -sparsity prior in compressed sensing reconstruction tasks. More importantly, the proposed reconstruction framework can be generalized for most MRI reconstruction scenarios.