Soft-Autoencoder and Its Wavelet Shrinkage Interpretation

Deep learning is a main focus of artificial intelligence and has greatly impacted other fields. However, deep learning is often criticized for its lack of interpretation. As a successful unsupervised model in deep learning, various autoencoders, especially convolutional autoencoders, are very popular and important. Since these autoencoders need improvements and insights, in this paper we shed light on the nonlinearity of a deep convolutional autoencoder in perspective of perfect signal recovery. In particular, we propose a new type of convolutional autoencoders, termed as Soft-Autoencoder (Soft-AE), in which the activations of encoding layers are implemented with adaptable soft-thresholding units while decoding layers are realized with linear units. Consequently, Soft-AE can be naturally interpreted as a learned cascaded wavelet shrinkage system. Our denoising numerical experiments on CIFAR-10, BSD-300 and Mayo Clinical Challenge Dataset demonstrate that Soft-AE gives a competitive performance relative to its counterparts.