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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. 

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. 

Plug-and-Play Alternating Direction Method of Multipliers (PnP-ADMM) is a widely-used algorithm for solving inverse problems by integrating physical measurement models and convolutional neural network (CNN) priors. PnP-ADMM has been theoretically proven to converge for convex data-fidelity terms and nonexpansive CNNs. It has however been observed that PnP-ADMM often empirically converges even for expansive CNNs. This paper presents a theoretical explanation for the observed stability of PnP-ADMM based on the interpretation of the CNN prior as a minimum mean-squared error (MMSE) denoiser. Our explanation parallels a similar argument recently made for the iterative shrinkage/thresholding algorithm variant of PnP (PnP-ISTA) and relies on the connection between MMSE denoisers and proximal operators. We also numerically evaluate the performance gap between PnP-ADMM using a nonexpan-sive DnCNN denoiser and expansive DRUNet denoiser, thus motivating the use of expansive CNNs. 

Plug-and-play (PnP) prior is a well-known class of methods for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image denoisers. While PnP methods have been extensively used for image recovery with known measurement operators, there is little work on PnP for solving blind inverse problems. We address this gap by presenting a new block-coordinate PnP (BC-PnP) method that efficiently solves this joint estimation problem by introducing learned denoisers as priors on both the unknown image and the unknown measurement operator. We present a new convergence theory for BC-PnP compatible with blind inverse problems by considering nonconvex data-fidelity terms and expansive denoisers. Our theory analyzes the convergence of BC-PnP to a stationary point of an implicit function associated with an approximate minimum mean-squared error (MMSE) denoiser. We numerically validate our method on two blind inverse problems: automatic coil sensitivity estimation in magnetic resonance imaging (MRI) and blind image deblurring. Our results show that BC-PnP provides an efficient and principled framework for using denoisers as PnP priors for jointly estimating measurement operators and images. 

Implicit neural representations (INR) have been recently proposed as deep learning (DL) based solutions for image compression. An image can be compressed by training an INR model with fewer weights than the number of image pixels to map the coordinates of the image to corresponding pixel values. While traditional training approaches for INRs are based on enforcing pixel-wise image consistency, we propose to further improve image quality by using a new structural regularizer. We present structural regularization for INR compression (SINCO) as a novel INR method for image compression. SINCO imposes structural consistency of the compressed images to the groundtruth by using a segmentation network to penalize the discrepancy of segmentation masks predicted from compressed images. We validate SINCO on brain MRI images by showing that it can achieve better performance than some recent INR methods.