Recently, deep learning becomes the main focus of machine learning research and has greatly impacted many important fields. However, deep learning is criticized for lack of interpretability. As a successful unsupervised model in deep learning, the autoencoder embraces a wide spectrum of applications, yet it suffers from the model opaqueness as well. In this paper, we propose a new type of convolutional autoencoders, termed as Soft Autoencoder (Soft-AE), in which the activation functions 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 experiments demonstrate that Soft-AE not only is interpretable but also offers a competitive performance relative to its counterparts. Furthermore, we propose a generalized linear unit (GenLU) to make an autoencoder more adaptive in nonlinearly filtering images and data, such as denoising and deblurring.