Learning Deeply Aggregated Alternating Minimization for General Inverse Problems

Abstract

Regularization-based image restoration is one of the most powerful tools in image processing and computer vision thanks to its flexibility for handling various inverse problems. However, designing an optimal regularization function still remains unsolved since natural images and related scene types have a complex structure. In this paper, we present a general and principled framework, called deeply aggregated alternating minimization (DeepAM). We design a convolutional neural network (CNN) to implicitly parameterize the regularizer of the alternating minimization (AM) algorithm. Contrary to the conventional AM algorithm based on a point-wise proximal mapping, the DeepAM projects intermediate estimate into a set of natural images via deep aggregation. Since the CNN is fully integrated into the AM procedure, all parameters can be jointly optimized through end-to-end training. These properties enable the DeepAM to converge with a small number of iterations, while maintaining an algorithmic simplicity. We show that the DeepAM outperforms state-of-the-art methods, including nonlocal-based methods, Plug-and-Play regularization, and recent data-driven approaches. The effectiveness of our framework is demonstrated in a variety of image restoration tasks: Guassian denoising, deraining, deblurring, super-resolution, color-guided depth upsampling, and RGB/NIR restoration.