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Block compressive sensing is a well-known signal acquisition and reconstruction paradigm with widespread application prospects in science, engineering and cybernetic systems. However, state-of-the-art block-based image compressive sensing (BCS) methods generally suffer from two issues. The sparsifying domain and the sensing matrices widely used for image acquisition are not data-driven, and thus both the features of the image and the relationships among subblock images are ignored. Moreover, doing so requires addressing high-dimensional optimization problems with extensive computational complexity for image reconstruction. In this paper, we provide a deep learning strategy for BCS, called AutoBCS, which takes the prior knowledge of images into account in the acquisition step and establishes a subsequent reconstruction model for performing fast image reconstruction with a low computational cost. More precisely, we present a learning-based sensing matrix (LSM) derived from training data to accomplish image acquisition, thereby capturing and preserving more image characteristics than those captured by existing methods. In particular, the generated LSM is proven to satisfy the theoretical requirements of compressive sensing, such as the so-called restricted isometry property. Additionally, we build a noniterative reconstruction network, which provides an end-to-end BCS reconstruction framework to eliminate blocking artifacts and maximize image reconstruction accuracy, in our AutoBCS architecture. Furthermore, we investigate comprehensive comparison studies with both traditional BCS approaches and newly developed deep learning methods. Compared with these approaches, our AutoBCS framework can not only provide superior performance in terms of image quality metrics (SSIM and PSNR) and visual perception, but also automatically benefit reconstruction speed.