Abstract
Deep networks have achieved remarkable success in image compressed sensing (CS) task, namely reconstructing a high-fidelity image from its compressed measurement. However, existing works are deficient inincoherent compressed measurement at sensing phase and implicit measurement representations at reconstruction phase, limiting the overall performance. In this work, we answer two questions: 1) how to improve the measurement incoherence for decreasing the ill-posedness; 2) how to learn informative representations from measurements. To this end, we propose a novel asymmetric Kronecker CS (AKCS) model and theoretically present its better incoherence than previous Kronecker CS with minimal complexity increase. Moreover, we reveal that the unfolding networks' superiority over non-unfolding ones result from sufficient gradient descents, called explicit measurement representations. We propose a measurement-aware cross attention (MACA) mechanism to learn implicit measurement representations. We integrate AKCS and MACA into widely-used unfolding architecture to get a measurement-enhanced unfolding network (MEUNet). Extensive experiences demonstrate that our MEUNet achieves state-of-the-art performance in reconstruction accuracy and inference speed.
Abstract (translated)
深度网络在图像压缩感知（CS）任务中取得了显著的成功，即从其压缩测量值重构出高质量的图像。然而，现有的研究工作在传感阶段缺乏不相干的压缩测量，在重建阶段也未能明确表示测量结果，这限制了整体性能的表现。本文旨在回答两个问题：1）如何改进测量的不相关性以减少不适定性；2）如何从测量数据中学习出具有信息量的表示。 为此，我们提出了一个新颖的非对称克罗内克压缩感知（AKCS）模型，并从理论上证明了其比之前的克罗内克压缩感知方法在复杂度最小增加的情况下具备更好的不相关性。此外，我们揭示了解折叠网络优于非解折叠网络的原因在于充分的梯度下降过程，即显式的测量表示。 为了学习隐含的测量表示，我们提出了一个基于测量的认知交叉注意力（MACA）机制。我们将AKCS和MACA整合到广泛使用的解折叠架构中，得到了一种增强测量信息的解折叠网络（MEUNet）。大量的实验经验表明，我们的MEUNet在重建精度和推理速度方面达到了最先进的性能水平。
URL
https://arxiv.org/abs/2508.09528
