The convex Latent Optimal Partition (LOP)-l2/l1 approach enables block-sparse signal recovery with unknown partitions but relies on manual hyperparameter tuning. Additionally, numerical instability in differentiating its proximal operator prevents its automatic parameter tuning via Deep Unfolding (DU). To address these limitations, we propose two architectures: a stable framework utilizing implicit differentiation and a flexible variant leveraging Deep Weight Factorization (DWF). The DWF-based approach also supports nonconvex smooth data fidelity terms. Numerical experiments demonstrate that DU-LOP-l2/l1 yields competitive performance and high resilience against impulsive noise.

翻译：凸隐式最优化分块（LOP）-l2/l1方法能够实现未知分块下的块稀疏信号恢复，但依赖人工超参数调优。此外，其近端算子微分过程中的数值不稳定性阻碍了通过深度展开（DU）进行自动参数调优。为解决这些局限，我们提出两种架构：基于隐式微分的稳定框架和利用深度权重分解（DWF）的灵活变体。基于DWF的方法还支持非凸光滑数据保真项。数值实验表明，DU-LOP-l2/l1在对抗脉冲噪声时展现出具有竞争力的性能与高鲁棒性。