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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. 

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. 

Deep learning-based methods deliver state-of-the-art performance for solving inverse problems that arise in computational imaging. These methods can be broadly divided into two groups: (1) learn a network to map measurements to the signal estimate, which is known to be fragile; (2) learn a prior for the signal to use in an optimization-based recovery. Despite the impressive results from the latter approach, many of these methods also lack robustness to shifts in data distribution, measurements, and noise levels. Such domain shifts result in a performance gap and in some cases introduce undesired artifacts in the estimated signal. In this paper, we explore the qualitative and quantitative effects of various domain shifts and propose a flexible and parameter efficient framework that adapts pretrained networks to such shifts. We demonstrate the effectiveness of our method for a number of reconstruction tasks that involve natural image, MRI, and CT imaging domains under distribution, measurement model, and noise level shifts. Our experiments demonstrate that our method achieves competitive performance compared to independently fully trained networks, while requiring significantly fewer additional parameters, and outperforms several domain adaptation techniques.