In 2D multi-slice magnetic resonance (MR) acquisition, the through-plane signals are typically of lower resolution than the in-plane signals. While contemporary super-resolution (SR) methods aim to recover the underlying high-resolution volume, the estimated high-frequency information is implicit via end-to-end data-driven training rather than being explicitly stated and sought. To address this, we reframe the SR problem statement in terms of perfect reconstruction filter banks, enabling us to identify and directly estimate the missing information. In this work, we propose a two-stage approach to approximate the completion of a perfect reconstruction filter bank corresponding to the anisotropic acquisition of a particular scan. In stage 1, we estimate the missing filters using gradient descent and in stage 2, we use deep networks to learn the mapping from coarse coefficients to detail coefficients. In addition, the proposed formulation does not rely on external training data, circumventing the need for domain shift correction. Under our approach, SR performance is improved particularly in "slice gap" scenarios, likely due to the constrained solution space imposed by the framework.

翻译：在2D多虱磁共振(MR)获取中,通过飞机发出的信号一般分辨率低于机内信号。虽然当代超分辨率(SR)方法旨在恢复潜在的高分辨率量,但估计的高频信息通过端对端数据驱动的培训而隐含,而不是明确声明和寻求。为了解决这个问题,我们从完美的重建过滤库的角度重新定义了SR问题说明,使我们能够识别和直接估计缺失的信息。在这项工作中,我们建议采取两阶段办法,大致完成一个与获取某次异常扫描相对应的完美的重建过滤库。在第一阶段,我们利用梯度下降和第二阶段估计缺失的过滤器,我们利用深层网络从粗略的系数到详细系数学习。此外,拟议的提法并不依赖外部培训数据,而绕过对域转移进行修正的需要。根据我们的方法,SR的性能得到了改进,特别是在“缩小差距”假设中,这很可能是由于框架所强加的有限解决方案空间造成的。