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ABSTRACT PurposeThe Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high qualityMRIreconstructions with uncertainty estimation from highly undersampled k‐space data. However, sampling methods such as diffusion posterior sampling (DPS) or likelihood annealing suffer from long reconstruction times and the need for parameter tuning. The purpose of this work is to develop a robust sampling algorithm with fast convergence. Theory and MethodsIn the reverse diffusion process used for sampling the posterior, the exact likelihood is multiplied with the diffused prior at all noise scales. To overcome the issue of slow convergence, preconditioning is used. The method is trained onfastMRIdata and tested on retrospectively undersampled brain data of a healthy volunteer. ResultsFor posterior sampling in Cartesian and non‐Cartesian acceleratedMRIthe new approach outperforms annealed sampling andDPSin terms of reconstruction speed and sample quality. ConclusionThe proposed exact likelihood with preconditioning enables rapid and reliable posterior sampling across variousMRIreconstruction tasks without the need for parameter tuning. 

Abstract PurposeTo examine the effect of incorporating self‐supervised denoising as a pre‐processing step for training deep learning (DL) based reconstruction methods on data corrupted by Gaussian noise. K‐space data employed for training are typically multi‐coil and inherently noisy. Although DL‐based reconstruction methods trained on fully sampled data can enable high reconstruction quality, obtaining large, noise‐free datasets is impractical. MethodsWe leverage Generalized Stein's Unbiased Risk Estimate (GSURE) for denoising. We evaluate two DL‐based reconstruction methods: Diffusion Probabilistic Models (DPMs) and Model‐Based Deep Learning (MoDL). We evaluate the impact of denoising on the performance of these DL‐based methods in solving accelerated multi‐coil magnetic resonance imaging (MRI) reconstruction. The experiments were carried out on T2‐weighted brain and fat‐suppressed proton‐density knee scans. ResultsWe observed that self‐supervised denoising enhances the quality and efficiency of MRI reconstructions across various scenarios. Specifically, employing denoised images rather than noisy counterparts when training DL networks results in lower normalized root mean squared error (NRMSE), higher structural similarity index measure (SSIM) and peak signal‐to‐noise ratio (PSNR) across different SNR levels, including 32, 22, and 12 dB for T2‐weighted brain data, and 24, 14, and 4 dB for fat‐suppressed knee data. ConclusionWe showed that denoising is an essential pre‐processing technique capable of improving the efficacy of DL‐based MRI reconstruction methods under diverse conditions. By refining the quality of input data, denoising enables training more effective DL networks, potentially bypassing the need for noise‐free reference MRI scans. 

Abstract PurposeThe aim of this work is to develop a method to solve the ill‐posed inverse problem of accelerated image reconstruction while correcting forward model imperfections in the context of subject motion during MRI examinations. MethodsThe proposed solution uses a Bayesian framework based on deep generative diffusion models to jointly estimate a motion‐free image and rigid motion estimates from subsampled and motion‐corrupt two‐dimensional (2D) k‐space data. ResultsWe demonstrate the ability to reconstruct motion‐free images from accelerated two‐dimensional (2D) Cartesian and non‐Cartesian scans without any external reference signal. We show that our method improves over existing correction techniques on both simulated and prospectively accelerated data. ConclusionWe propose a flexible framework for retrospective motion correction of accelerated MRI based on deep generative diffusion models, with potential application to other forward model corruptions. 

Abstract MRI acquisition and reconstruction research has transformed into a computation-driven field. As methods become more sophisticated, compute-heavy, and data-hungry, efforts to reproduce them become more difficult. While the computational MRI research community has made great leaps toward reproducible computational science, there are few tailored guidelines or standards for users to follow. In this review article, we develop a cookbook to facilitate reproducible research for MRI acquisition and reconstruction. Like any good cookbook, we list several recipes, each providing a basic standard on how to make computational MRI research reproducible. And like cooking, we show example flavours where reproducibility may fail due to under-specification. We structure the article, so that the cookbook itself serves as an example of reproducible research by providing sequence and reconstruction definitions as well as data to reproduce the experimental results in the figures. We also propose a community-driven effort to compile an evolving list of best practices for making computational MRI research reproducible. 

Diffusion models (DMs) are a powerful frame- work for image generation and restoration. How- ever, existing DMs are primarily trained in a su- pervised manner by using a large corpus of clean images. This poses fundamental challenges in many real-world scenarios, where acquiring noise- free data is hard or infeasible. While some meth- ods are capable of training DMs using noisy data, they are effective only when the amount of noise is very mild or when additional noise-free data is available. In addition, existing methods for training DMs from incomplete measurements re- quire access to multiple complementary acquisi- tion processes, a significant practical limitation. Here we introduce the first approach for learning DMs for image restoration using only noisy mea- surement data from a single operator. First, we show that DMs, and more broadly minimum mean squared error denoisers, exhibit a weak form of scale equivariance linking rescaling in signal am- plitude to changes in noise intensity. We then leverage this theoretical insight to develop a de- noising score-matching strategy that generalizes robustly to noise levels below the training data, thereby enabling the learning of DMs from noisy measurements. For problems involving measure- ments both noisy and incomplete, we integrate our method with equivariant imaging, a complemen- tary self-supervised learning framework that ex- ploits the inherent invariants of imaging problems. This allows training DMs for image restoration from single-operator noisy measurements. We validate the effectiveness of our approach through extensive experiments on image denoising, demo- saicing, inpainting, and MRI reconstruction along with comparisons with the state of the art. 

Quantitative MRI (qMRI) involves parameter estimation gov- erned by an explicit signal model. However, these models are often confounded and difficult to validate in vivo. A model is misspecified when the assumed signal model differs from the true data-generating process. Under misspecification, the variance of any unbiased estimator is lower-bounded by the misspecified Cram´ er–Rao bound (MCRB), and maximum- likelihood estimates (MLE) may exhibit bias and inconsis- tency. Based on these principles, we assess misspecification in qMRI using two tests: (i) examining whether empirical MCRB asymptotically approaches the CRB as repeated mea- surements increase; (ii) comparing MLE estimates from two equal-sized subsets and evaluating whether their empirical variance aligns with theoretical CRB predictions. We demon- strate the framework using arterial spin labeling (ASL) as an illustrative example. Our result shows the commonly used ASL signal model appears to be specified in the brain and moderately misspecified in the kidney. The proposed frame- work offers a general, theoretically grounded approach for assessing model validity in quantitative MRI. 

Magnetic Resonance Imaging (MRI) diagnoses and man- ages a wide range of diseases, yet long scan times drive high costs and limit accessibility. AI methods have demonstrated substantial potential for reducing scan times, but despite rapid progress, clinical translation of AI often fails. One particular failure mode, referred to as implicit data crimes, is a result of hidden biases introduced when MRI datasets incompletely model the MRI physics of the acquisition. Previous work identified data crimes resulting from algorithmic completion of k-space with parallel imaging and drew on simulation to demonstrate the resulting downstream biases. This work proposes a mathematical framework to re-characterize the problem as one of error reduction during interpolation between sets of evaluation coordinates. We establish a generalized matrix-based definition of the reconstruction error upper bound as a function of the input sampling pattern. Experiments on relevant sampling pattern struc- tures demonstrate the relevance of the framework and suggest future directions for analysis of data crimes.