Abstract
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.
Abstract (translated)
扩散模型目前是解决成像逆问题的最先进方法。它们令人印象深刻的生成能力允许从先验分布中近似采样，结合已知的概率函数可以无需重新训练模型就能进行后验采样。尽管最近的方法在提高后验采样的准确性方面取得了进展，但大多数研究都集中在单一图像的逆向问题上。然而，在诸如磁共振成像（MRI）等模式下，通常会获取多个互补测量值，每个测量值沿不同轴低分辨率。 在这项工作中，我们将常见的基于扩散模型解决单张图像逆向问题的方法推广到了多图超分辨率（MISR）MRI。我们展示了DPS概率修正使得在独立获取的测量之间可以精确分离梯度分解，从而能够实现无需构建联合算子、修改扩散模型或增加网络函数评估次数的情况下进行MISR。 我们推导了适用于MISR的DPS、DMAP、DPPS和基于扩散的PnP/ADMM方法，并展示了它们在$4\times/8\times/16\times$各向异性退化情况下的显著性能提升。我们的结果实现了各向异性MRI体素的超分辨率的新纪录，更重要的是，这些结果能够从常规2D多切片获取中重建近似等方向解剖结构，在正交视图下这些获取通常会严重退化。 总的来说，这项研究展示了如何通过利用扩散模型和精确的概率修正技术来解决复杂的多图像逆问题，并且在MRI超分辨率领域取得了重要的进展。
URL
https://arxiv.org/abs/2601.14030
