diffusion-based k-space reconstruction

This work addresses the significant degradation in k-space reconstruction quality of magnetic resonance imaging (MRI) under undersampled and high-noise conditions by proposing a unified high-dimensional k-space reconstruction framework. The method enhances the representational capacity of the data space through the incorporation of high-dimensional embedding priors, enabling existing diffusion-based inverse problem solvers to operate more robustly in an enriched k-space without altering the underlying diffusion model architecture or optimization procedure. As a model-agnostic enhancement mechanism, the proposed framework consistently improves reconstruction performance across multiple public and internal datasets, with the most pronounced gains observed in high-noise scenarios.

To address severe aliasing artifacts and temporal inconsistency arising from k-space undersampling in accelerated dynamic MRI reconstruction, this paper proposes the first autoregressive diffusion model specifically designed for dynamic MRI sequences. Methodologically, we embed an autoregressive mechanism into the image-domain diffusion process to explicitly model inter-frame temporal dependencies, while jointly enforcing consistency with k-space measurements and image priors. Evaluated on the fastMRI dataset, our model significantly suppresses hallucination artifacts inherent in standard diffusion models, achieving superior structural fidelity and enhanced temporal coherence. Quantitative metrics—including PSNR and SSIM—as well as expert radiologist assessments consistently outperform existing diffusion-based baselines, with strong robustness across diverse undersampling patterns. The core contribution lies in the first explicit autoregressive modeling of inter-frame dependencies within a diffusion generative framework, establishing a novel paradigm for high-fidelity reconstruction of dynamic medical imaging.

To address the high computational cost and excessive GPU memory consumption of full-image diffusion models in MRI inverse problem solving, this work systematically validates and implements patch-based diffusion prior modeling for the first time. We propose a lightweight adaptation mechanism and an overlapping patch fusion strategy to effectively suppress blocking artifacts. The diffusion prior is seamlessly integrated into the Plug-and-Play (PnP) optimization framework, enabling joint evaluation across multiple tasks (e.g., super-resolution, reconstruction) and diverse datasets. Experiments demonstrate that our approach achieves reconstruction quality comparable to full-image inference while reducing GPU memory usage by 62% and accelerating inference by 2.3×. Moreover, it exhibits cross-PnP algorithm compatibility—i.e., plug-and-play capability without retraining. This work establishes a new paradigm for efficient and scalable generative prior modeling in medical imaging.

Diffusion models for accelerating inverse problem reconstruction (e.g., MRI) suffer from poor generalization—especially under fast sampling and few-step denoising—due to heavy reliance on manually tuned data fidelity weights. To address this, we propose Zero-shot Adaptive Denoising Sampling (ZADS), the first method enabling *test-time automatic fidelity weight optimization without retraining the diffusion prior*. Built upon an unrolled sampler architecture, ZADS jointly optimizes fidelity weights and the denoising trajectory in a self-supervised manner, using only undersampled measurements. It supports arbitrary numbers of sampling steps and non-uniform time schedules. Evaluated on the fastMRI knee dataset, ZADS significantly outperforms compressed sensing and state-of-the-art diffusion-based methods, achieving both high reconstruction fidelity and robustness across diverse imaging conditions—thereby overcoming the fundamental limitations of fixed or heuristic weight schemes.

To address clinical bottlenecks in low-field (<1.5 T) neonatal MRI in the NICU—including prolonged scan times, severe motion artifacts, scarce training data, and low signal-to-noise ratio (SNR)—this work introduces the first acquisition-agnostic diffusion generative model as a universal image prior. We pioneer the adaptation of diffusion models to real-world NICU neonatal MRI by proposing: (i) an adaptive noise scheduling scheme tailored for low-SNR and few-shot regimes; (ii) low-rank k-space modeling; (iii) physics-driven embedding of the forward operator; and (iv) unsupervised motion artifact modeling. Without fine-tuning, the model jointly solves three inverse problems—accelerated reconstruction, motion correction, and super-resolution—achieving 2–4× acceleration (PSNR gain +3.2 dB), marked suppression of head motion artifacts, and 2× super-resolution while preserving fine anatomical details—all with zero task-specific retraining on real clinical data.

This work addresses the limitations of existing diffusion-based MRI reconstruction methods, which rely on large networks, opaque time-conditioning mechanisms, and offline-estimated coil sensitivity maps, leading to poor interpretability and limited adaptability across acquisition protocols. To overcome these issues, the authors propose a novel paradigm that jointly reconstructs both the image and coil sensitivities within an end-to-end framework. Central to this approach is a parameter-efficient Gaussian mixture product diffusion model serving as an interpretable image prior, complemented by a smoothness prior on coil sensitivities. The resulting method enables k-space trajectory-adaptive reconstruction, achieving rapid convergence and strong robustness under shifts in contrast and anatomical distribution as well as varying sampling trajectories, thereby significantly enhancing denoising and reconstruction performance.

This work addresses the challenge of effectively leveraging score-based diffusion models as priors within the Plug-and-Play (PnP) framework. The authors propose a stochastic generative PnP method that establishes, for the first time, a theoretical connection between PnP and diffusion models from a score-matching perspective—without relying on reverse diffusion sampling. By incorporating a noise injection mechanism, the approach is equivalent to optimizing a Gaussian-smoothed objective, which enhances robustness in severely ill-posed inverse problems and facilitates escape from strict saddle points. Experimental results demonstrate that the proposed method significantly outperforms conventional PnP approaches in multi-coil MRI reconstruction and large-mask image inpainting, achieving performance comparable to state-of-the-art diffusion-based solvers.

Existing parallel MRI reconstruction methods are confined to discrete k-space grids and struggle to explicitly model continuous signals, limiting reconstruction accuracy. This work proposes k-space Gaussian Representation (KGR), the first approach to establish an explicit continuous signal model directly in the native k-space domain. KGR parameterizes the continuous spectrum using Gabor-Gaussian primitives that share spatial geometry, integrating low-rank manifold projection, frequency-adaptive fitting, and multi-coil phase smoothness constraints. By design, the method inherently preserves inter-coil correlations. Extensive experiments across multiple datasets and sampling patterns demonstrate that KGR consistently achieves superior quantitative metrics and visual quality compared to current baselines, validating the efficacy of combining continuous modeling with structured priors.

Medical images are frequently compromised by artifacts, missing regions, or pathological alterations, which can undermine diagnostic reliability. This work presents a systematic review of diffusion model–based approaches for medical image inpainting and introduces the first taxonomy specifically tailored to this domain. The proposed framework encompasses prevailing architectures—such as Denoising Diffusion Probabilistic Models (DDPM) and Latent Diffusion Models (LDM)—alongside key clinical applications (e.g., MRI and CT), benchmark datasets, and evaluation protocols. Empirical analysis demonstrates that diffusion models excel at generating anatomically plausible reconstructions, yet critical challenges persist, notably the absence of standardized benchmarks and limited data diversity. By synthesizing current advances and identifying open problems, this study offers a structured foundation to guide future research in medical image restoration.

Diffusion-based image generators are promising priors for ill-posed inverse problems like sparse-view X-ray Computed Tomography (CT). As most studies consider synthetic data, it is not clear whether training data mismatch (``domain shift'') or forward model mismatch complicate their successful application to experimental data. We measured CT data from a physical phantom resembling the synthetic Shepp-Logan phantom and trained diffusion priors on synthetic image data sets with different degrees of domain shift towards it. Then, we employed the priors in a Decomposed Diffusion Sampling scheme on sparse-view CT data sets with increasing difficulty leading to the experimental data. Our results reveal that domain shift plays a nuanced role: while severe mismatch causes model collapse and hallucinations, diverse priors outperform well-matched but narrow priors. Forward model mismatch pulls the image samples away from the prior manifold, which causes artifacts but can be mitigated with annealed likelihood schedules that also increase computational efficiency. Overall, we demonstrate that performance gains do not immediately translate from synthetic to experimental data, and future development must validate against real-world benchmarks.