The last decade has shown a tremendous success in solving various computer
vision problems with the help of deep learning techniques. Lately, many works
have demonstrated that learning-based approaches with suitable network
architectures even exhibit superior performance for the solution of (ill-posed)
image reconstruction problems such as deblurring, super-resolution, or medical
image reconstruction. The drawback of purely learning-based methods, however,
is that they cannot provide provable guarantees for the trained network to
follow a given data formation process during inference. In this work we propose
energy dissipating networks that iteratively compute a descent direction with
respect to a given cost function or energy at the currently estimated
reconstruction. Therefore, an adaptive step size rule such as a line-search,
along with a suitable number of iterations can guarantee the reconstruction to
follow a given data formation model encoded in the energy to arbitrary
precision, and hence control the model's behavior even during test time. We
prove that under standard assumptions, descent using the direction predicted by
the network converges (linearly) to the global minimum of the energy. We
illustrate the effectiveness of the proposed approach in experiments on single
image super resolution and computed tomography (CT) reconstruction, and further
illustrate extensions to convex feasibility problems.

使用能量耗散网络在深度学习中提出了迭代计算下降方向以实现图像重构、特别是对噪声图像进行去模糊，超分辨率和医学图像中来实现。经实验证明，它可以控制网络在推断时遵循数据形成模型，并且它在单幅图像超分辨率和计算机成像重构上取得了良好效果，并进一步扩展到凸可行性问题。