Deep Unfolding With Weighted ℓ₂ Minimization for Compressive Sensing

Compressive sensing (CS) aims to accurately reconstruct high-dimensional signals from a small number of measurements by exploiting signal sparsity and structural priors. However, signal priors utilized in existing CS reconstruction algorithms rely mainly on hand-crafted design, which often cannot offer the best sparsity-undersampling tradeoff because high-order structural priors of signals are hard to be captured in this manner. In this article, a new recovery guarantee of the unified CS reconstruction model-weighted $\ell _{1}$ minimization (WL1M) is derived, which indicates universal priors could hardly lead to the optimal selection of the weights. Motivated by the analysis, we propose a deep unfolding network for the general WL1M model. The proposed deep unfolding-based WL1M (D-WL1M) integrates universal priors with learning capability so that all of the parameters, including the crucial weights, can be learned from training data. We demonstrate the proposed D-WL1M outperforms several state-of-the-art CS-based methods and deep learning-based methods by a large margin via the experiments on the Caltech-256 image data set.