Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given the measurements, such that the model can be readily used for solving inverse problems in imaging, especially for accelerated MRI. In short, we train a continuous time-dependent score function with denoising score matching. Then, at the inference stage, we iterate between numerical SDE solver and data consistency projection step to achieve reconstruction. Our model requires magnitude images only for training, and yet is able to reconstruct complex-valued data, and even extends to parallel imaging. The proposed method is agnostic to sub-sampling patterns, and can be used with any sampling schemes. Also, due to its generative nature, our approach can quantify uncertainty, which is not possible with standard regression settings. On top of all the advantages, our method also has very strong performance, even beating the models trained with full supervision. With extensive experiments, we verify the superiority of our method in terms of quality and practicality.
翻译:基于分数的传播模型为利用数据分布梯度来模拟图像提供了强大的方法。 将所学得的分数函数作为先期利用, 在此我们引入了一种方法, 从测量条件下的有条件分布中取样数据, 这样模型可以很容易地用于解决成像中的反向问题, 特别是加速的磁共振。 简言之, 我们用分数匹配来训练一个持续的时间依赖的得分函数。 然后, 在推论阶段, 我们将数字SDE解码器和数据一致性预测步骤进行循环, 以实现重建。 我们的模型需要数量级图像, 仅用于培训, 并且能够重建复杂价值的数据, 甚至可以扩展到平行的成像。 所提议的方法对于次抽样模式来说是不可知的, 并且可以用于任何取样计划。 此外, 由于其具有基因化的性质, 我们的方法可以量化不确定性, 而在标准的回归设置上是不可能的。 在所有的优点上, 我们的方法也有非常强的性能, 甚至击败经过全面监督的模型。 通过广泛的实验, 我们核查了我们的方法在质量和实用性方面的优势。