PE-CSNet: An equivariant network architecture with learnable patch-based sparse representation

• URL: http://arxiv.org/abs/2608.14708v1
• Date: Tue, 11 Aug 2026 04:11:27 GMT
• Title: PE-CSNet: An equivariant network architecture with learnable patch-based sparse representation
• Abstract summary: We present a Patch-based Equivariant deep unrolling architecture, termed PE-CSNet, for accurate CS recovery.<n>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.
• Score: 11.707157690423061
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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