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Hyperspectral imaging plays a pivotal role in a wide range of applications, like remote sensing, medicine, and cytology. By acquiring 3D hyperspectral images (HSIs) via 2D sensors, the coded aperture snapshot spectral imaging (CASSI) has achieved great success due to its hardware-friendly implementation and fast imaging speed. However, for some less spectrally sparse scenes, single snapshot and unreasonable coded aperture design tend to make HSI recovery more ill-posed and yield poor spatial and spectral fidelity. In this paper, we propose a novel Progressive Content-Aware CASSI framework, dubbed PCA-CASSI, which captures HSIs with multiple optimized content-aware coded apertures and fuses all the snapshots for reconstruction progressively. Simultaneously, by mapping the Range-Null space Decomposition (RND) into a deep network with several phases, an RND-HRNet is proposed for HSI recovery. Each recovery phase can fully exploit the hidden physical information in the coded apertures via explicit decomposition and explore the spatial-spectral correlation by dual transformer blocks. Our method is validated to surpass other state-of-the-art methods on both multiple- and single-shot HSI imaging tasks by large margins.