PE-CSNet achieves SOTA compressed sensing MRI with learnable sparse transforms

Compressive sensing (CS) enables signal reconstruction from sparse measurements, powering applications like medical imaging and remote sensing. But designing task-specific sparse transforms typically requires expert knowledge and heavy tuning. In the paper arXiv:2608.14708, Kai Li and colleagues introduce PE-CSNet, a patch-based equivariant deep unrolling architecture that automates this process. The authors generalize traditional patch-based transform sparsity by incorporating learnable transforms adapted to the CS task through an optimization-driven approach. They first establish a generalized patch-based CS model solved via a block coordinate descent (BCD) algorithm, then unroll that solver into a deep neural network. All model and solver parameters are trained end-to-end, removing the need for manual parameter tuning.

To boost data efficiency, the team introduces a stochastic equivariant training strategy that exploits the network's patch-wise structure, allowing PE-CSNet to learn effectively from limited data. They also provide a simpler parameter-shared variant and discuss convergence, while the full model uses stage-specific parameters to enhance expressive power. Benchmarked on CS-MRI (magnetic resonance imaging) and CS-CDP (coded diffraction patterns), PE-CSNet reaches state-of-the-art accuracy with fast computational speed, beating both classical CS algorithms and existing deep unrolling approaches. The paper includes 35 pages and 10 figures, and is currently under review. This work could accelerate MRI reconstruction times and improve image compression in real-world systems.