Deep learning is emerging as a new paradigm for solving inverse imaging
problems. However, the deep learning methods often lack the assurance of
traditional physics-based methods due to the lack of physical information
considerations in neural network training and deploying. The appropriate
supervision and explicit calibration by the information of the physic model can
enhance the neural network learning and its practical performance. In this
paper, inspired by the geometry that data can be decomposed by two components
from the null-space of the forward operator and the range space of its
pseudo-inverse, we train neural networks to learn the two components and
therefore learn the decomposition, i.e. we explicitly reformulate the neural
network layers as learning range-nullspace decomposition functions with
reference to the layer inputs, instead of learning unreferenced functions. We
empirically show that the proposed framework demonstrates superior performance
over recent deep residual learning, unrolled learning and nullspace learning on
tasks including compressive sensing medical imaging and natural image
super-resolution. Our code is available at
this https URL

本文提出一种通过 Range-Nullspace 分解的深度学习框架，为解决逆成像问题提供了一种新的范式。通过对数据空间进行分解，模型获得了更多的物理信息，可以有效提高神经网络的学习性能和实际表现。实验结果表明，该框架在压缩感知医学成像和自然图像超分辨率等任务中均具有优异的性能表现。