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。

使用迭代深度神经网络解决不适定的反问题

Solving ill-posed inverse problems using iterative deep neural networks

A client-server architecture to simultaneously solve multiple learning tasks
from distributed datasets is described. In such architecture, each client is
associated with an individual learning task and the associated dataset of
examples. The goal of the architecture is to perform information fusion from
multiple datasets while preserving privacy of individual data. The role of the
server is to collect data in real-time from the clients and codify the
information in a common database. The information coded in this database can be
used by all the clients to solve their individual learning task, so that each
client can exploit the informative content of all the datasets without actually
having access to private data of others. The proposed algorithmic framework,
based on regularization theory and kernel methods, uses a suitable class of
mixed effect kernels. The new method is illustrated through a simulated music
recommendation system.

描述了一个客户端 - 服务器体系结构，该体系结构可以同时处理分布式数据集中的多个学习任务。该体系结构的目标是从多个数据集进行信息融合，同时保护个体数据的隐私。所提出的算法框架基于正则化理论和核方法，并使用适当的混合效应内核。该方法通过模拟音乐推荐系统进行了说明。