The optimally designed autoencoder network for compressed sensing

Compressed sensing (CS) is a signal processing framework, which reconstructs a signal from a small set of random measurements obtained by measurement matrices. Due to the strong randomness of measurement matrices, the reconstruction performance is unstable. Additionally, current reconstruction algorithms are relatively independent of the compressed sampling process and have high time complexity. To this end, a deep learning based stacked sparse denoising autoencoder compressed sensing (SSDAE_CS) model, which mainly consists of an encoder sub-network and a decoder sub-network, is proposed and analyzed in this paper. Instead of traditional linear measurements, a multiple nonlinear measurements encoder sub-network is trained to obtain measurements. Meanwhile, a trained decoder sub-network solves the CS recovery problem by learning the structure features within the training data. Specifically, the two sub-networks are integrated into SSDAE_CS model through end-to-end training for strengthening the connection between the two processes, and their parameters are jointly trained to improve the overall performance of CS. Finally, experimental results demonstrate that the proposed method significantly outperforms state-of-the-art methods in terms of reconstruction performance, time cost, and denoising ability. Most importantly, the proposed model shows excellent reconstruction performance in the case of a few measurements.