  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.
