  Conventional compressed sensing (CS) algorithms typically apply a uniform
sampling rate to different image blocks. A more strategic approach could be to
allocate the number of measurements adaptively, based on each image block's
complexity. In this paper, we propose a Measurement-Bounds-based Rate-Adaptive
Image Compressed Sensing Network (MB-RACS) framework, which aims to adaptively
determine the sampling rate for each image block in accordance with traditional
measurement bounds theory. Moreover, since in real-world scenarios statistical
information about the original image cannot be directly obtained, we suggest a
multi-stage rate-adaptive sampling strategy. This strategy sequentially adjusts
the sampling ratio allocation based on the information gathered from previous
samplings. We formulate the multi-stage rate-adaptive sampling as a convex
optimization problem and address it using a combination of Newton's method and
binary search techniques. Additionally, we enhance our decoding process by
incorporating skip connections between successive iterations to facilitate a
richer transmission of feature information across iterations. Our experiments
demonstrate that the proposed MB-RACS method surpasses current leading methods,
with experimental evidence also underscoring the effectiveness of each module
within our proposed framework.
