PE-CSNet：一种具有可学习基于块的稀疏表示的等变网络架构
PE-CSNet: An equivariant network architecture with learnable patch-based sparse representation
- The Hong Kong Polytechnic University（香港理工大学）
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
- University of Chinese Academy of Sciences（中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对压缩感知中稀疏变换与优化设计的难题，提出PE-CSNet等变深度展开架构，结合可学习稀疏性与随机等变训练，在CS-MRI等任务上性能优于传统及现有深度展开方法
AI中文摘要：
压缩感知（Compressive sensing, CS）能够从稀疏测量中实现精确的信号重建，广泛应用于医学成像、遥感和图像压缩领域。然而，为高质量CS设计有效的、针对特定任务的稀疏变换及对应的优化过程仍然具有挑战性，该过程通常需要专业领域知识和繁琐的参数调整。为解决这一问题，我们提出了一种基于块的等变深度展开架构，命名为PE-CSNet，用于精确的CS重建。传统CS方法通常使用预定义的基于块的变换稀疏性，我们通过引入可学习的变换稀疏性来推广这一思路，该稀疏性通过优化驱动过程适配特定的CS任务。具体而言，我们首先建立了一个通用的基于块的CS模型，通过块坐标下降（Block coordinate descent, BCD）算法求解；随后将BCD求解器展开为深度神经网络，其中CS模型和求解器的所有参数均通过端到端训练学习得到。为提高数据效率，我们引入了随机等变训练策略，该策略利用网络的块级结构，使PE-CSNet即使在有限数据下也能有效学习。我们还提供了PE-CSNet的更简单的参数共享版本，并简要讨论其作为迭代求解器的收敛性。对于实际应用，该网络使用特定阶段（非共享）参数以增强其表达能力，进而提升性能。在CS磁共振成像（CS-MRI）和CS编码衍射图样（CS-CDP）任务上，PE-CSNet达到了最先进的精度，且计算速度快，优于传统方法和现有深度展开方法。
英文摘要：
Compressive sensing (CS) enables accurate signal reconstruction from sparse measurements and is widely applied in medical imaging, remote sensing, and image compression. However, designing an effective, task-specific sparse transform and the corresponding optimization procedure for high-quality CS remains challenging. This process typically requires expert domain knowledge and laborious parameter tuning. To address this issue, we present a Patch-based Equivariant deep unrolling architecture, termed PE-CSNet, for accurate CS recovery. While traditional CS methods generally use predefined patch-based transform sparsity, we generalize this idea by incorporating learnable transform sparsity that adapts to the specific CS task through an optimization-driven process. Specifically, we first establish a generalized patch-based CS model, which we solve via a block coordinate descent (BCD) algorithm. The BCD solver is then unrolled into a deep neural network, where all parameters of both the CS model and solver are learned through end-to-end training. To improve data efficiency, we introduce a stochastic equivariant training strategy that exploits the patch-wise structure of the network, enabling PE-CSNet to learn effectively even from limited data. We further provide a simpler, parameter-shared version of PE-CSNet and briefly discuss its convergence as an iterative solver. For practical applications, the network uses stage-specific (non-shared) parameters to enhance its expressive power and thereby improve its performance. On the tasks of CS magnetic resonance imaging (CS-MRI) and CS coded diffraction patterns (CS-CDP), PE-CSNet achieves state-of-the-art accuracy with fast computational speed, outperforming traditional methods and existing deep unrolling methods.
