Cascade Deep Networks for Sparse Linear Inverse Problems

Sparse deep networks have been widely used in many linear inverse problems, such as image super-resolution and signal recovery. Its performance is as good as deep learning at the same time its parameters are much less than deep learning. However, when the linear inverse problems involve several linear transformations or the ratio of input dimension to output dimension is large, the performance of a single sparse deep network is poor. In this paper, we propose a cascade sparse deep network to address the above problem. In our model, we trained two cascade sparse networks based on Gregor and LeCun's "learned ISTA" and "learned CoD". The cascade structure can effectively improve the performance as compared to the non-cascade model. We use the proposed methods in image sparse code prediction and signal recovery. The experimental results show that both algorithms perform favorably against a single sparse network.