Multilevel wavelet-based hierarchical networks for image compressed sensing

Recently, deep learning-based compressed sensing (CS) algorithms have been reported, which remarkably achieve pleasing reconstruction quality with low computational complexity. However, the sampling process of the common deep learning-based CS methods and the conventional ones cannot sufficiently exploit the structured sparsity within image sequences, especially in preserving finer texture details. In this paper, we propose a novel multilevel wavelet-based hierarchical networks for image compressed sensing (dubbed MWHCS-Net). In particular, MWHCS-Net consists of three modules: a sampling module based on a multilevel wavelet transform, a hierarchical initial reconstruction module and a lightweight deep reconstruction module. Motivated by the fact that a sparser signal is easier to reconstruct accurately, we present the sampling module based on multilevel wavelet transform with hierarchical subspace learning for progressive acquisition of measurements to further optimize sampling efficiency and stability. To enhance the finer texture details, the hierarchical initial reconstruction module is designed as a basic initial reconstruction network plus an enhanced initial reconstruction network, which corresponding to the dominant structure component and the texture detail component of the reconstructed image, respectively. At the same time, we also further explore the impact of the hierarchical initial reconstruction module and prove that the texture detail component branch plays an important role in improving the reconstruction quality. Experimental results demonstrate that the proposed MWHCS-Net achieves the state-of-the-art performance while maintaining an efficient running speed. Furthermore, MWHCS-Net outperforms the existing image CS methods based on deep learning in terms of anti-noise performance in most cases.