Solving inverse problems with deep neural networks driven by sparse signal decomposition in a physics-based dictionary
Solving inverse problems with deep neural networks driven by sparse signal decomposition in a physics-based dictionary
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发表时间：
2021-07
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通讯作者：
Gaëtan Rensonnet;Louise Adam;B. Macq
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作者：
Gaëtan Rensonnet;Louise Adam;B. Macq
深度神经网络（DNN）具有反转非常复杂模型的令人印象深刻的能力，即从模型的输出中学习生成参数。一旦经过训练，深度神经网络的正向传递通常比用于解决逆问题的传统的基于优化的方法快得多。然而，这样做的代价是较低的可解释性，这是大多数医学应用的基本限制。我们提出了一种将深度神经网络的效率与传统解析方法的可解释性相结合的求解一般逆问题的方法。测量结果首先被投射到一个密集的基于模型的响应字典中。然后将得到的稀疏表示馈送到具有由问题物理驱动的架构的深度神经网络中，以实现快速参数学习。我们的方法可以处理生成前向模型，这些模型的评估成本很高，并且在准确性和计算时间上表现出与完全学习的深度神经网络相似的性能，同时保持高可解释性并且更容易训练。以磁共振成像（MRI）为例，给出了基于模型的脑参数估计的具体结果。
Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional, optimization-based methods used to solve inverse problems. This is however done at the cost of lower interpretability, a fundamental limitation in most medical applications. We propose an approach for solving general inverse problems which combines the efficiency of DNN and the interpretability of traditional analytical methods. The measurements are first projected onto a dense dictionary of model-based responses. The resulting sparse representation is then fed to a DNN with an architecture driven by the problem's physics for fast parameter learning. Our method can handle generative forward models that are costly to evaluate and exhibits similar performance in accuracy and computation time as a fully-learned DNN, while maintaining high interpretability and being easier to train. Concrete results are shown on an example of model-based brain parameter estimation from magnetic resonance imaging (MRI).