论文标题

部分可观测时空混沌系统的无模型预测

Scale-Equivariant Unrolled Neural Networks for Data-Efficient Accelerated MRI Reconstruction

论文作者

Gunel, Beliz, Sahiner, Arda, Desai, Arjun D., Chaudhari, Akshay S., Vasanawala, Shreyas, Pilanci, Mert, Pauly, John

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

Unrolled neural networks have enabled state-of-the-art reconstruction performance and fast inference times for the accelerated magnetic resonance imaging (MRI) reconstruction task. However, these approaches depend on fully-sampled scans as ground truth data which is either costly or not possible to acquire in many clinical medical imaging applications; hence, reducing dependence on data is desirable. In this work, we propose modeling the proximal operators of unrolled neural networks with scale-equivariant convolutional neural networks in order to improve the data-efficiency and robustness to drifts in scale of the images that might stem from the variability of patient anatomies or change in field-of-view across different MRI scanners. Our approach demonstrates strong improvements over the state-of-the-art unrolled neural networks under the same memory constraints both with and without data augmentations on both in-distribution and out-of-distribution scaled images without significantly increasing the train or inference time.

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