The T1ρ mapping technique necessitates acquiring multiple T1ρ-weighted images at various spin-lock times (TSL), which results in a lengthy scan time and significantly limits its widespread clinical use. Undersampling is a significant strategy to accelerate T1ρ imaging, where it is crucial to model and utilize the joint spatiotemporal correlations priors among different TSL multi-contrast images for high-quality reconstruction. However, current methods that use simplified physical relaxation correlations or non-interpretable deep neural networks to define joint correlations often yield inaccurate results. From a Bayesian framework, the joint distribution provides a powerful capability to represent the joint correlations among multi-contrast T1ρ images. Therefore, a new method is introduced to accelerate T1ρ parameter imaging, leveraging accurate joint distribution modeling and the captured joint distribution to guide the reconstruction. Specifically, a joint diffusion model is proposed to approximate the joint distribution of multi-contrast T1ρ images exploiting the score-matching method. Subsequently, the ill-posed problem caused by the reconstruction of undersampled multi-contrast T1ρ images is addressed through the learned joint distribution by employing a constructed joint reverse denoising diffusion model. The superior performance of the proposed method and the capability to accurately characterize the joint distribution was further verified by performing various in vivo experiments. The patient image reconstruction also verifies the feasibility and superiority of the proposed method.

Deep unrolling methods have achieved notable success in accelerated cardiac cine MRI reconstruction. However, their effectiveness remains limited by constrained receptive fields and rigid convolutional sampling, which hinder scalability in high-resolution reconstruction tasks. To address these challenges, we propose an Equivariant Deformable Convolutional Unrolling Network (EDCU-Net) that integrates a Spatiotemporal Deformable Module (STDM) and a Rotation Equivariant Module (REM). EDCU-Net effectively enlarges the receptive field while maintaining low computational cost and high parameter efficiency, enabling more effective suppression of large-scale aliasing artifacts. Specifically, STDM adaptively adjusts sampling locations to better capture complex anatomical structures and dynamic cardiac motion, while reducing interpolation overhead. Furthermore, REM embeds deformable convolutions within an equivariant framework, allowing shared parameters across orientations and further promoting parameter efficiency and generalization capability. Extensive experiments on cardiac cine MRI data demonstrate that EDCU-Net consistently outperforms state-of-the-art methods in both reconstruction accuracy and visual quality.

The field of accelerated magnetic resonance imaging (AMRI) has garnered significant attention, focusing on reconstructing target image from compressively sampled k-space measurements to address an ill-posed linear inverse problem. In this study, we exploit the multiparameterization of MRI to propose a new plug-and-play prior (P3) for enhancing reconstruction quality. We begin by introducing a mutual-structure guided P3 (MS-GP3) framework, based on jointly penalized least-squares regression (JPLSR), to selectively transfer common priors from a reference image to the target one, thereby minimizing errors caused by indiscriminate pattern transfer. Furthermore, we establish a self-sharpening weighting (SSW) scheme that effectively differentiates between sharp and smooth image components, contributing to a boosted variant of MS-GP3 (BMS-GP3) for further improvement in artifact suppression and detail restoration. Finally, embedding BMS-GP3 in half-quadratic splitting (HQS) iterations yields an advanced AMRI algorithm, dubbed BMS-GP3 -HQS, which not only outperforms state-ofthe-art (SOTA) methods but also provides robust theoretical guarantees, including ensured convergence and resilience to noise.

Supervised deep learning (SDL) methodology holds promise for accelerated magnetic resonance imaging (AMRI) but is hampered by the reliance on extensive training data. Some self-supervised frameworks, such as deep image prior (DIP), have emerged, eliminating the explicit training procedure but often struggling to remove noise and artifacts under significant degradation. This work introduces a novel self-supervised accelerated parallel MRI approach called PEARL, leveraging a multiple-stream joint deep decoder with two cross-fusion schemes to accurately reconstruct one or more target images from compressively sampled k-space. Each stream comprises cascaded cross-fusion sub-block networks (SBNs) that sequentially perform combined upsampling, 2D convolution, joint attention, ReLU activation and batch normalization (BN). Among them, combined upsampling and joint attention facilitate mutual learning between multiple-stream networks by integrating multi-parameter priors in both additive and multiplicative manners. Long-range unified skip connections within SBNs ensure effective information propagation between distant cross-fusion layers. Additionally, incorporating dual-normalized edge-orientation similarity regularization into the training loss enhances detail reconstruction and prevents overfitting. Experimental results consistently demonstrate that PEARL outperforms the existing state-of-the-art (SOTA) self-supervised AMRI technologies in various MRI cases. Notably, 5-fold$\sim$6-fold accelerated acquisition yields a 1$\%$ $\sim$ 2$\%$ improvement in SSIM$_{\mathsf{ROI}}$ and a 3$\%$ $\sim$ 6$\%$ improvement in PSNR$_{\mathsf{ROI}}$, along with a significant 15$\%$ $\sim$ 20$\%$ reduction in RLNE$_{\mathsf{ROI}}$.

Recently, diffusion models have shown considerable promise for MRI reconstruction. However, extensive experimentation has revealed that these models are prone to generating artifacts due to the inherent randomness involved in generating images from pure noise. To achieve more controlled image reconstruction, we reexamine the concept of interpolatable physical priors in k-space data, focusing specifically on the interpolation of high-frequency (HF) k-space data from low-frequency (LF) k-space data. Broadly, this insight drives a shift in the generation paradigm from random noise to a more deterministic approach grounded in the existing LF k-space data. Building on this, we first establish a relationship between the interpolation of HF k-space data from LF k-space data and the reverse heat diffusion process, providing a fundamental framework for designing diffusion models that generate missing HF data. To further improve reconstruction accuracy, we integrate a traditional physics-informed k-space interpolation model into our diffusion framework as a data fidelity term. Experimental validation using publicly available datasets demonstrates that our approach significantly surpasses traditional k-space interpolation methods, deep learning-based k-space interpolation techniques, and conventional diffusion models, particularly in HF regions. Finally, we assess the generalization performance of our model across various out-of-distribution datasets. Our code are available at https://github.com/ZhuoxuCui/Heat-Diffusion.

In recent times, model-driven deep learning has evolved an iterative algorithm into a cascade network by replacing the regularizer's first-order information, such as the (sub)gradient or proximal operator, with a network module. This approach offers greater explainability and predictability compared to typical data-driven networks. However, in theory, there is no assurance that a functional regularizer exists whose first-order information matches the substituted network module. This implies that the unrolled network output may not align with the regularization models. Furthermore, there are few established theories that guarantee global convergence and robustness (regularity) of unrolled networks under practical assumptions. To address this gap, we propose a safeguarded methodology for network unrolling. Specifically, for parallel MR imaging, we unroll a zeroth-order algorithm, where the network module serves as a regularizer itself, allowing the network output to be covered by a regularization model. Additionally, inspired by deep equilibrium models, we conduct the unrolled network before backpropagation to converge to a fixed point and then demonstrate that it can tightly approximate the actual MR image. We also prove that the proposed network is robust against noisy interferences if the measurement data contain noise. Finally, numerical experiments indicate that the proposed network consistently outperforms state-of-the-art MRI reconstruction methods, including traditional regularization and unrolled deep learning techniques.

Quantitative magnetic resonance (MR) [Formula: see text] mapping is a promising approach for characterizing intrinsic tissue-dependent information. However, long scan time significantly hinders its widespread applications. Recently, low-rank tensor models have been employed and demonstrated exemplary performance in accelerating MR [Formula: see text] mapping. This study proposes a novel method that uses spatial patch-based and parametric group-based low-rank tensors simultaneously (SMART) to reconstruct images from highly undersampled k-space data. The spatial patch-based low-rank tensor exploits the high local and nonlocal redundancies and similarities between the contrast images in [Formula: see text] mapping. The parametric group-based low-rank tensor, which integrates similar exponential behavior of the image signals, is jointly used to enforce multidimensional low-rankness in the reconstruction process. In vivo brain datasets were used to demonstrate the validity of the proposed method. Experimental results demonstrated that the proposed method achieves 11.7-fold and 13.21-fold accelerations in two-dimensional and three-dimensional acquisitions, respectively, with more accurate reconstructed images and maps than several state-of-the-art methods. Prospective reconstruction results further demonstrate the capability of the SMART method in accelerating MR [Formula: see text] imaging.