SL0-Net: Fractal Dimension-Guided Adaptive Compressed Sensing via Deep Unfolding With Measurement-Injection Cross Attention

Deep unfolding networks (DUNs), which integrate the interpretability of traditional optimization solvers with the representation learning capabilities of deep neural networks, have shown remarkable potential in compressed sensing (CS). However, existing DUNs treat all image regions uniformly, ignoring structural variations and limiting reconstruction fidelity. Many also require heavy parameters and iterations, while still over-looking fine-grained features and inter-stage dependencies. To address these challenges, this paper proposes the Smoothed ℓ0Norm Unfolding Network (SL0-Net), a novel adaptive deep CS framework inspired by the traditional smoothed ℓ0norm optimization algorithm for sparse signal recovery. Specifically, we introduce the fractal dimension as a quantitative metric to precisely characterize the texture complexity of local regions. This design enables SL0-Net to adaptively allocate a significantly higher number of measurements to structurally intricate regions, while assigning fewer measurements to low-complexity regions. Secondly, to mitigate the issue of feature loss and enhance inter-stage information flow, we further design the SL0-inspired Measurement-Injected Cross-Attention (SMICA) module, which effectively captures inter-dependencies between feature maps from different unfolding stages and also explicitly incorporates physical CS measurements into the attention computation pipeline. This design facilitates robust information interaction between high-level abstract feature representations and low-level measurement signals, thereby substantially improving the reconstruction fidelity of fine-grained image details. Extensive experiments were conducted on widely used benchmark datasets to validate the effectiveness of the proposed network. The results demonstrate that the proposed SL0-Net outperforms existing methods in terms of image reconstruction quality, while maintaining a more favorable trade-off between performance and model complexity.