Deep external and internal learning for noisy compressive sensing

Reconstructing natural image from its corresponding compressive sensing (CS) measurements is an ill-posed problem. Learning accurate prior of desirable image is essential to solve this inverse problem in high quality, especially for CS reconstruction from noisy measurements. The existing learning-based methods cannot effectively simulate whole potential noise in the testing data during external learning, and cannot effectively exploit the information from internal testing data. In this paper, we present an effective convolutional neural network (CNN) based method for CS reconstruction from noisy measurements, which learns the deep prior from an external dataset and internal noisy testing data with Stein's unbiased risk estimator (SURE). Specifically, we first pre-train an arbitrary CNN for CS reconstruction with an external dataset to learn a common prior. Then, we utilize meta learning to find a generic initial parameter that is suitable for fast internal learning and adaption to various noisy measurements. Finally, we customize the learned network to learn a specific prior for each internal testing data under Gaussian noise or more general mixed Poisson-Gaussian noise. Experimental results show that the proposed method outperforms the state-of-the-art methods under both comprehensively quantitative metrics and perceptive quality.