The concept of deep learning is employed for the inversion of NMR signals and
it is shown that NMR signal inversion can be considered as an image-to-image
regression problem, which can be treated with a convolutional neural net. It is
further outlined, that inversion through deep learning provides a clear
efficiency and usability advantage compared to regularization techniques such
as Tikhonov and modified total generalized variation (MTGV), because no
hyperparemeter selection prior to reconstruction is necessary. The inversion
network is applied to simulated NMR signals and the results compared with
Tikhonov- and MTGV-regularization. The comparison shows that inversion via deep
learning is significantly faster than the latter regularization methods and
also outperforms both regularization techniques in nearly all instances.

深度学习用于 NMR 信号反演，通过卷积神经网络将 NMR 信号反演看作图像到图像的回归问题，与 Tikhonov 和 MTGV 等正则化技术相比，深度学习具有明显的效率和易用性优势，因为在重建之前不需要进行超参数选择。通过对模拟 NMR 信号进行反演并与 Tikhonov 和 MTGV 正则化进行比较，结果显示深度学习的反演速度显著快于后两种正则化方法，并在几乎所有情况下优于这两种正则化技术。

深度学习作为核磁共振信号反演的方法

Deep Learning as a Method for Inversion of NMR Signals

Image-to-image regression is an important learning task, used frequently in
biological imaging. Current algorithms, however, do not generally offer
statistical guarantees that protect against a model's mistakes and
hallucinations. To address this, we develop uncertainty quantification
techniques with rigorous statistical guarantees for image-to-image regression
problems. In particular, we show how to derive uncertainty intervals around
each pixel that are guaranteed to contain the true value with a user-specified
confidence probability. Our methods work in conjunction with any base machine
learning model, such as a neural network, and endow it with formal mathematical
guarantees -- regardless of the true unknown data distribution or choice of
model. Furthermore, they are simple to implement and computationally
inexpensive. We evaluate our procedure on three image-to-image regression
tasks: quantitative phase microscopy, accelerated magnetic resonance imaging,
and super-resolution transmission electron microscopy of a Drosophila
melanogaster brain.

通过引入不确定性量化技术，提供了一种给图像到图像回归问题提供统计保障的方法，使得能够对每个像素进行不确定性区间估计，并且保证这个估计在给定的置信度下包含了真实值。