Deep Learning-Based Compressed Sensing: Methodologies, Theoretical Challenges and Future Directions

Compressed sensing (CS) recovers high-dimensional signals from low-dimensional measurements by exploiting structural priors such as sparsity. While conventional reconstruction mainly relies on iterative optimization, its practical use is often limited by computational overhead, sensitivity to hyperparameter tuning, and hardware-related artifacts. Deep learning (DL)-based methods have therefore been introduced to accelerate reconstruction and learn data-adaptive priors. This review surveys DL-based CS from the perspective of how signal priors are modeled and how the sensing process is incorporated into reconstruction. We organize methods into four families: optimization-inspired unfolding and plug-and-play (PnP) schemes, end-to-end (E2E) reconstruction networks, generative and untrained priors, and implicit neural representations (INRs). For each family, we summarize representative formulations, sensing-operator use, theoretical support, main limitations, and future directions.