Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as diffusion posterior sampling 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 Methods: In 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 on fastMRI data and tested on retrospectively undersampled brain data of a healthy volunteer. Results: For posterior sampling in Cartesian and non-Cartesian accelerated MRI the new approach outperforms annealed sampling in terms of reconstruction speed and sample quality. Conclusion: The proposed exact likelihood with preconditioning enables rapid and reliable posterior sampling across various MRI reconstruction tasks without the need for parameter tuning.

Magnetic resonance imaging (MRI) is a widely used non-invasive imaging modality. However, a persistent challenge lies in balancing image quality with imaging speed.

Magnetic resonance imaging (MRI) is a widely used non-invasive imaging modality. However, a persistent challenge lies in balancing image quality with imaging speed.

Diffusion-based inverse problem solvers (DIS) have recently shown outstanding performance in compressed-sensing parallel MRI reconstruction by combining diffusion priors with physical measurement models. However, they typically rely on pre-calibrated coil sensitivity maps (CSMs) and ground truth images, making them often impractical: CSMs are difficult to estimate accurately under heavy undersampling and ground-truth images are often unavailable. We propose Calibration-free Measurement Score-based diffusion Model (C-MSM), a new method that eliminates these dependencies by jointly performing automatic CSM estimation and self-supervised learning of measurement scores directly from k-space data. C-MSM reconstructs images by approximating the full posterior distribution through stochastic sampling over partial measurement posterior scores, while simultaneously estimating CSMs. Experiments on the multi-coil brain fastMRI dataset show that C-MSM achieves reconstruction performance close to DIS with clean diffusion priors -- even without access to clean training data and pre-calibrated CSMs.

Magnetic Resonance Imaging (MRI) offers unparalleled soft-tissue contrast but is fundamentally limited by long acquisition times. While deep learning-based accelerated MRI can dramatically shorten scan times, the reconstruction from undersampled data introduces ambiguity resulting from an ill-posed problem with infinitely many possible solutions that propagates to downstream clinical tasks. This uncertainty is usually ignored during the acquisition process as acceleration factors are often fixed a priori, resulting in scans that are either unnecessarily long or of insufficient quality for a given clinical endpoint. This work introduces a dynamic, uncertainty-aware acquisition framework that adjusts scan time on a per-subject basis. Our method leverages a probabilistic reconstruction model to estimate image uncertainty, which is then propagated through a full analysis pipeline to a quantitative metric of interest (e.g., patellar cartilage volume or cardiac ejection fraction). We use conformal prediction to transform this uncertainty into a rigorous, calibrated confidence interval for the metric. During acquisition, the system iteratively samples k-space, updates the reconstruction, and evaluates the confidence interval. The scan terminates automatically once the uncertainty meets a user-predefined precision target. We validate our framework on both knee and cardiac MRI datasets. Our results demonstrate that this adaptive approach reduces scan times compared to fixed protocols while providing formal statistical guarantees on the precision of the final image. This framework moves beyond fixed acceleration factors, enabling patient-specific acquisitions that balance scan efficiency with diagnostic confidence, a critical step towards personalized and resource-efficient MRI.

--Quantitative magnetic resonance imaging (qMRI) provides tissue-specific parameters vital for clinical diagnosis. Although simultaneous multi-parametric qMRI (MP-qMRI) technologies enhance imaging efficiency, robustly reconstructing qMRI from highly undersampled, high-dimensional measurements remains a significant challenge. This difficulty arises primarily because current reconstruction methods that rely solely on a single prior or physics-informed model to solve the highly ill-posed inverse problem, which often leads to suboptimal results. T o overcome this limitation, we propose LoREIN, a novel unsupervised and dual-prior-integrated framework for accelerated 3D MP-qMRI reconstruction. T echnically, LoREIN incorporates both low-rank prior and continuity prior via low-rank representation (LRR) and implicit neural representation (INR), respectively, to enhance reconstruction fidelity. The powerful continuous representation of INR enables the estimation of optimal spatial bases within the low-rank subspace, facilitating high-fidelity reconstruction of weighted images. Simultaneously, the predicted multi-contrast weighted images provide essential structural and quantitative guidance, further enhancing the reconstruction accuracy of quantitative parameter maps. Furthermore, our work introduces a zero-shot learning paradigm with broad potential in complex spatiotemporal and high-dimensional image reconstruction tasks, further advancing the field of medical imaging.

Magnetic Resonance Imaging (MRI) is an essential tool for the early detection, risk stratification, prognosis, treatment selection, and monitoring of many diseases, including cancer, cardiovascular disease, metabolic, musculoskeletal, and brain disorders, among many others. Its ability to produce multi-contrast and multi-parametric images of soft tissues, coupled with its non-invasive and radiation-free nature, makes it a highly valuable tool in clinical practice. Over the past five decades, the technology behind MRI has undergone significant advancements, especially in terms of the magnetic field strengths used for imaging. Early MRI systems operated at low field strengths (0.15 T to 0.35 T) [1-3], and while they offered important diagnostic insights, they were limited by low signal-to-noise ratio (SNR) and image resolution. Over time, several advancements led to the development of systems operating at higher field strengths, such as 1.5 T and 3 T, which are now considered the clinical standard due to their superior SNR and image quality [4, 5]. Recent developments have even pushed field strengths to ultra-high levels ( 3 T), including 5 T, 7 T and beyond, further enhancing the spatial and temporal resolution of MRI [4, 6, 7]. However, high-field MRI has its challenges [8].

In order to speed up the acquisition time, MRI instruments acquire sub-sampled k-space data, a technique where only a fraction of the total k-space data points are sampled during the imaging process. Several attempts have been proposed to develop two-dimensional (2D) and three-dimensional (3D) image reconstruction techniques for sub-sampled k-space, as discussed in [11, 13, 31]. Advancements in 3D MR imaging methods can address the challenges posed by complex anatomical structures of human organs and plant growths. Consequently, the demand for developing 3D MR image reconstruction methods has intensified. Currently, most works reconstruct a 3D volumetric image by stacking 2D reconstructions because MR images are acquired slice by slice. This method doesn't consider the inter-dependency between the slices, thus can lead to inconsistencies and artifacts, as discussed in [4, 8, 50]. This particularly affects datasets that have equally distributed information and structures with high continuity on all dimensions, such as roots and vessels [4, 38, 50]. Before the deep learning-based models, which learn the data-driven prior, the model-based iterative reconstruction method proved its effectiveness in the 3D MRI reconstruction problem [15, 54]. The problem is formulated as an optimization problem where a data consistency term is applied to ensure fidelity, and a regularisation term, such as the Total Variation (TV) penalty [24] is utilized to provide general prior knowledge of MRI data.

Diffusion model-based approaches recently achieved re-markable success in MRI reconstruction, but integration into clinical routine remains challenging due to its time-consuming convergence. This phenomenon is partic-ularly notable when directly apply conventional diffusion process to k-space data without considering the inherent properties of k-space sampling, limiting k-space learning efficiency and image reconstruction quality. To tackle these challenges, we introduce subspace diffusion model with orthogonal decomposition, a method (referred to as Sub-DM) that restrict the diffusion process via projections onto subspace as the k-space data distribution evolves toward noise. Particularly, the subspace diffusion model circumvents the inference challenges posed by the com-plex and high-dimensional characteristics of k-space data, so the highly compact subspace ensures that diffusion process requires only a few simple iterations to produce accurate prior information. Furthermore, the orthogonal decomposition strategy based on wavelet transform hin-ders the information loss during the migration of the vanilla diffusion process to the subspace. Considering the strate-gy is approximately reversible, such that the entire pro-cess can be reversed. As a result, it allows the diffusion processes in different spaces to refine models through a mutual feedback mechanism, enabling the learning of ac-curate prior even when dealing with complex k-space data. Comprehensive experiments on different datasets clearly demonstrate that the superiority of Sub-DM against state of-the-art methods in terms of reconstruction speed and quality.

Magnetic Resonance Imaging (MRI) has become essential in clinical diagnosis due to its high resolution and multiple contrast mechanisms. However, the relatively long acquisition time limits its broader application. To address this issue, this study presents an innovative conditional guided diffusion model, named as TC-KANRecon, which incorporates the Multi-Free U-KAN (MF-UKAN) module and a dynamic clipping strategy. TC-KANRecon model aims to accelerate the MRI reconstruction process through deep learning methods while maintaining the quality of the reconstructed images. The MF-UKAN module can effectively balance the tradeoff between image denoising and structure preservation. Specifically, it presents the multi-head attention mechanisms and scalar modulation factors, which significantly enhances the model's robustness and structure preservation capabilities in complex noise environments. Moreover, the dynamic clipping strategy in TC-KANRecon adjusts the cropping interval according to the sampling steps, thereby mitigating image detail loss typically caused by traditional cropping methods and enriching the visual features of the images. Furthermore, the MC-Model module incorporates full-sampling k-space information, realizing efficient fusion of conditional information, enhancing the model's ability to process complex data, and improving the realism and detail richness of reconstructed images. Experimental results demonstrate that the proposed method outperforms other MRI reconstruction methods in both qualitative and quantitative evaluations. Notably, TC-KANRecon method exhibits excellent reconstruction results when processing high-noise, low-sampling-rate MRI data. Our source code is available at https://github.com/lcbkmm/TC-KANRecon.