We propose a partially learned approach for the solution of ill posed inverse
problems with not necessarily linear forward operators. The method builds on
ideas from classical regularization theory and recent advances in deep learning
to perform learning while making use of prior information about the inverse
problem encoded in the forward operator, noise model and a regularizing
functional. The method results in a gradient-like iterative scheme, where the
"gradient" component is learned using a convolutional network that includes the
gradients of the data discrepancy and regularizer as input in each iteration.
We present results of such a partially learned gradient scheme on a non-linear
tomographic inversion problem with simulated data from both the Sheep-Logan
phantom as well as a head CT. The outcome is compared against FBP and TV
reconstruction and the proposed method provides a 5.4 dB PSNR improvement over
the TV reconstruction while being significantly faster, giving reconstructions
of 512 x 512 volumes in about 0.4 seconds using a single GPU.

本文提出了一种部分学习方法，用于解决具有非线性正演算子的病态反问题。该方法利用经典正则化理论和深度学习的最新进展，通过对反问题的先验信息进行编码的正演算子、噪声模型和正则化函数来进行学习，其中包含每次迭代中的数据差异和正则化器的梯度做为卷积神经网络的输入。实验表明，与 FBP 和 TV 重建相比，所提出的方法在保证速度的同时，能够在 512 x 512 体积内产生 5.4dB 的 PSNR 提升。