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Abstract PurposeTo introduce a novel deep model‐based architecture (DMBA), SPICER, that uses pairs of noisy and undersampled k‐space measurements of the same object to jointly train a model for MRI reconstruction and automatic coil sensitivity estimation. MethodsSPICER consists of two modules to simultaneously reconstructs accurate MR images and estimates high‐quality coil sensitivity maps (CSMs). The first module, CSM estimation module, uses a convolutional neural network (CNN) to estimate CSMs from the raw measurements. The second module, DMBA‐based MRI reconstruction module, forms reconstructed images from the input measurements and the estimated CSMs using both the physical measurement model and learned CNN prior. With the benefit of our self‐supervised learning strategy, SPICER can be efficiently trained without any fully sampled reference data. ResultsWe validate SPICER on both open‐access datasets and experimentally collected data, showing that it can achieve state‐of‐the‐art performance in highly accelerated data acquisition settings (up to ). Our results also highlight the importance of different modules of SPICER—including the DMBA, the CSM estimation, and the SPICER training loss—on the final performance of the method. Moreover, SPICER can estimate better CSMs than pre‐estimation methods especially when the ACS data is limited. ConclusionDespite being trained on noisy undersampled data, SPICER can reconstruct high‐quality images and CSMs in highly undersampled settings, which outperforms other self‐supervised learning methods and matches the performance of the well‐known E2E‐VarNet trained on fully sampled ground‐truth data. 

Abstract The purpose of the current study was to introduce a Deep learning‐based Accelerated and Noise‐Suppressed Estimation (DANSE) method for reconstructing quantitative maps of biological tissue cellular‐specific,R2t*, and hemodynamic‐specific,R2’, metrics of quantitative gradient‐recalled echo (qGRE) MRI. The DANSE method adapts a supervised learning paradigm to train a convolutional neural network for robust estimation ofR2t*andR2’maps with significantly reduced sensitivity to noise and the adverse effects of macroscopic (B₀) magnetic field inhomogeneities directly from the gradient‐recalled echo (GRE) magnitude images. TheR2t*andR2’maps for training were generated by means of a voxel‐by‐voxel fitting of a previously developed biophysical quantitative qGRE model accounting for tissue, hemodynamic, and B₀‐inhomogeneities contributions to multigradient‐echo GRE signal using a nonlinear least squares (NLLS) algorithm. We show that the DANSE model efficiently estimates the aforementioned qGRE maps and preserves all the features of the NLLS approach with significant improvements including noise suppression and computation speed (from many hours to seconds). The noise‐suppression feature of DANSE is especially prominent for data with low signal‐to‐noise ratio (SNR ~ 50–100), where DANSE‐generatedR2t*andR2’maps had up to three times smaller errors than that of the NLLS method. The DANSE method enables fast reconstruction of qGRE maps with significantly reduced sensitivity to noise and magnetic field inhomogeneities. The DANSE method does not require any information about field inhomogeneities during application. It exploits spatial and gradient echo time‐dependent patterns in the GRE data and previously gained knowledge from the biophysical model, thus producing high quality qGRE maps, even in environments with high noise levels. These features along with fast computational speed can lead to broad qGRE clinical and research applications. 

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized. 

Deformable image registration (DIR) is an active research topic in biomedical imaging. There is a growing interest in developing DIR methods based on deep learning (DL). A traditional DL approach to DIR is based on training a convolutional neural network (CNN) to estimate the registration field between two input images. While conceptually simple, this approach comes with a limitation that it exclusively relies on a pre-trained CNN without explicitly enforcing fidelity between the registered image and the reference. We present plug-and-play image registration network (PIRATE) as a new DIR method that addresses this issue by integrating an explicit data-fidelity penalty and a CNN prior. PIRATE pre-trains a CNN denoiser on the registration field and "plugs" it into an iterative method as a regularizer. We additionally present PIRATE+ that fine-tunes the CNN prior in PIRATE using deep equilibrium models (DEQ). PIRATE+ interprets the fixed-point iteration of PIRATE as a network with effectively infinite layers and then trains the resulting network end-to-end, enabling it to learn more task-specific information and boosting its performance. Our numerical results on OASIS and CANDI datasets show that our methods achieve state-of-the-art performance on DIR. 

Regularization by Denoising (RED) is a well-known method for solving image restoration problems by using learned image denoisers as priors. Since the regularization parameter in the traditional RED does not have any physical interpretation, it does not provide an approach for automatic parameter selection. This letter addresses this issue by introducing the Constrained Regularization by Denoising (CRED) method that reformulates RED as a constrained optimization problem where the regularization parameter corresponds directly to the amount of noise in the measurements. The solution to the constrained problem is solved by designing an efficient method based on alternating direction method of multipliers (ADMM). Our experiments show that CRED outperforms the competing methods in terms of stability and robustness, while also achieving competitive performances in terms of image quality.