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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. 

Rhenium-catalyzed stereoselective transposition of allylic alcohols is reported. In the presence of 1 mol% of Re 2 O 7 , ( E )- or ( Z )-δ-hydroxymethyl- anti -homoallylic alcohols were converted into the acetals of 2-methyl-1,3- syn -diols with excellent diastereoselectivities. 1,3- syn -Diol acetals can also be synthesized from ( E )-δ-hydroxymethyl- syn -homoallylic alcohols. 

Plug-and-Play Priors (PnP) is a well-known class of methods for solving inverse problems in computational imaging. PnP methods combine physical forward models with learned prior models specified as image denoisers. A common issue with the learned models is that of a performance drop when there is a distribution shift between the training and testing data. Test-time training (TTT) was recently proposed as a general strategy for improving the performance of learned models when training and testing data come from different distributions. In this paper, we propose PnP-Ttt as a new method for overcoming distribution shifts in PnP. PnP-TTT uses deep equilibrium learning (DEQ) for optimizing a self-supervised loss at the fixed points of PnP iterations. PnP-TTT can be directly applied on a single test sample to improve the generalization of PnP. We show through simulations that given a sufficient number of measurements, PnP-TTT enables the use of image priors trained on natural images for image reconstruction in magnetic resonance imaging (MRI). 

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. 

Limited-Angle Computed Tomography (LACT) is a nondestructive 3D imaging technique used in a variety of applications ranging from security to medicine. The limited angle coverage in LACT is often a dominant source of severe artifacts in the reconstructed images, making it a challenging imaging inverse problem. Diffusion models are a recent class of deep generative models for synthesizing realistic images using image denoisers. In this work, we present DOLCE as the first framework for integrating conditionally-trained diffusion models and explicit physical measurement models for solving imaging inverse problems. DOLCE achieves the SOTA performance in highly ill-posed LACT by alternating between the data-fidelity and sampling updates of a diffusion model conditioned on the transformed sinogram. We show through extensive experimentation that unlike existing methods, DOLCE can synthesize high-quality and structurally coherent 3D volumes by using only 2D conditionally pre-trained diffusion models. We further show on several challenging real LACT datasets that the same pretrained DOLCE model achieves the SOTA performance on drastically different types of images. 

Three-dimensional fluorescence microscopy often suffers from anisotropy, where the resolution along the axial direction is lower than that within the lateral imaging plane. We address this issue by presenting Dual-Cycle, a new framework for joint deconvolution and fusion of dual-view fluorescence images. Inspired by the recent Neuroclear method, Dual-Cycle is designed as a cycle-consistent generative network trained in a self-supervised fashion by combining a dual-view generator and prior-guided degradation model. We validate Dual-Cycle on both synthetic and real data showing its state-of-the-art performance without any external training data.