Reconstruction tasks in computer vision aim fundamentally to recover an
undetermined signal from a set of noisy measurements. Examples include
super-resolution, image denoising, and non-rigid structure from motion, all of
which have seen recent advancements through deep learning. However, earlier
work made extensive use of sparse signal reconstruction frameworks (e.g
convolutional sparse coding). While this work was ultimately surpassed by deep
learning, it rested on a much more developed theoretical framework. Recent work
by Papyan et. al provides a bridge between the two approaches by showing how a
convolutional neural network (CNN) can be viewed as an approximate solution to
a convolutional sparse coding (CSC) problem. In this work we argue that for
some types of inverse problems the CNN approximation breaks down leading to
poor performance. We argue that for these types of problems the CSC approach
should be used instead and validate this argument with empirical evidence.
Specifically we identify JPEG artifact reduction and non-rigid trajectory
reconstruction as challenging inverse problems for CNNs and demonstrate state
of the art performance on them using a CSC method. Furthermore, we offer some
practical improvements to this model and its application, and also show how
insights from the CSC model can be used to make CNNs effective in tasks where
their naive application fails.

本文介绍求解计算机视觉中的重构问题，阐述了使用卷积稀疏编码与卷积神经网络的优缺点，并提出了卷积稀疏编码可用于解决某些反问题的有效性，通过 JPEG 残留抑制和非刚性轨迹重建的操作，对使用 CSC 方法进行的应用进行了实证和验证，并指出如何将 CSC 模型的理论用于改进 CNN 模型的应用。