Diffusion models are the current state-of-the-art for solving inverse problems in imaging. Their impressive generative capability allows them to approximate sampling from a prior distribution, which alongside a known likelihood function permits posterior sampling without retraining the model. While recent methods have made strides in advancing the accuracy of posterior sampling, the majority focuses on single-image inverse problems. However, for modalities such as magnetic resonance imaging (MRI), it is common to acquire multiple complementary measurements, each low-resolution along a different axis. In this work, we generalize common diffusion-based inverse single-image problem solvers for multi-image super-resolution (MISR) MRI. We show that the DPS likelihood correction allows an exactly-separable gradient decomposition across independently acquired measurements, enabling MISR without constructing a joint operator, modifying the diffusion model, or increasing network function evaluations. We derive MISR versions of DPS, DMAP, DPPS, and diffusion-based PnP/ADMM, and demonstrate substantial gains over SISR across $4\times/8\times/16\times$ anisotropic degradations. Our results achieve state-of-the-art super-resolution of anisotropic MRI volumes and, critically, enable reconstruction of near-isotropic anatomy from routine 2D multi-slice acquisitions, which are otherwise highly degraded in orthogonal views.

翻译：扩散模型是目前解决成像逆问题的最先进方法。其卓越的生成能力使其能够近似从先验分布中采样，结合已知的似然函数，便可在无需重新训练模型的情况下进行后验采样。尽管近期方法在后验采样精度方面取得了显著进展，但大多数研究集中于单图像逆问题。然而，对于磁共振成像等模态，通常需要获取多个互补的测量值，每个测量值沿不同轴方向均为低分辨率。在本研究中，我们将常见的基于扩散的单图像逆问题求解器推广至多图像超分辨率磁共振成像。我们证明，DPS似然校正允许在独立获取的测量值之间实现精确可分离的梯度分解，从而无需构建联合算子、修改扩散模型或增加网络函数评估次数即可实现多图像超分辨率。我们推导了DPS、DMAP、DPPS以及基于扩散的PnP/ADMM的多图像超分辨率版本，并在$4\times/8\times/16\times$各向异性退化条件下展示了相对于单图像超分辨率的显著提升。我们的结果实现了各向异性磁共振成像体数据的最先进超分辨率，并且关键地，能够从常规的二维多层采集数据中重建近乎各向同性的解剖结构，而这些数据在其他正交视图中通常存在严重退化。