Scene-aware Adaptive Compressive Sensing (ACS) has attracted significant interest due to its promising capability for efficient and high-fidelity acquisition of scene images. ACS typically prescribes adaptive sampling allocation (ASA) based on previous samples in the absence of ground truth. However, when confronting unknown scenes, existing ACS methods often lack accurate judgment and robust feedback mechanisms for ASA, thus limiting the high-fidelity sensing of the scene. In this paper, we introduce a Sampling Innovation-Based ACS (SIB-ACS) method that can effectively identify and allocate sampling to challenging image reconstruction areas, culminating in high-fidelity image reconstruction. An innovation criterion is proposed to judge ASA by predicting the decrease in image reconstruction error attributable to sampling increments, thereby directing more samples towards regions where the reconstruction error diminishes significantly. A sampling innovation-guided multi-stage adaptive sampling (AS) framework is proposed, which iteratively refines the ASA through a multistage feedback process. For image reconstruction, we propose a Principal Component Compressed Domain Network (PCCD-Net), which efficiently and faithfully reconstructs images under AS scenarios. Extensive experiments demonstrate that the proposed SIB-ACS method significantly outperforms the state-of-the-art methods in terms of image reconstruction fidelity and visual effects. Codes are available at https://github.com/giant-pandada/SIBACS_CVPR2025.