MB-RACS: Measurement-Bounds-based Rate-Adaptive Image Compressed Sensing Network

TL;DR

MB-RACS addresses adaptive image compressed sensing by grounding per-block sampling in traditional measurement bounds, enabling rate allocation that mirrors block sparsity. It introduces single-stage and multi-stage rate-adaptive sampling, with a convex-optimization-based distribution-ratio solver (Newton's method plus bisection) and a measurement-bounds predictor, complemented by decoder-side cross-iteration skip connections. The approach yields state-of-the-art PSNR/SSIM across seven datasets and demonstrates robustness to appearance changes, while ablations confirm the effectiveness of each module. The method has practical impact for efficient, high-quality image reconstruction in scenarios where original statistics are unavailable a priori.

Abstract

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.

Figures (14)

• Figure 1: The left figure presents an image named "baby" from the Set5 dataset BMVC.26.135, while the right illustrates the distribution of measurements across various blocks, following the measurement bounds proportions and with an overall sampling rate of 0.3. Notably, areas such as the baby's eyes and hat, rich in texture details, are allocated more measurements, whereas smoother regions, like the cheeks, receive fewer due to less detail.
• Figure 2: Empirical and logarithmically fitted trends for optimal $(s_\text{r}, p_\text{s})$ pairs in model performance.
• Figure 3: Illustration of single-stage measurement-bounds-based rate-adaptive sampling, comprising partitioning, DCT transformation, block-wise sparsity estimation, ratio and measurements allocation, and block-wise rate-adaptive sampling.
• Figure 4: Illustration of the multi-stage rate-adaptive sampling strategy: the first sampling stage employs rate-fixed sampling, with subsequent sampling stages involving measurement bounds prediction, optimization of allocation ratio, measurements allocation, and rate-adaptive sampling.
• Figure 5: A toy example of $r_i^t$, $q_i^t$, $\beta^t$, and $\alpha^t$.