Problem
Research questions and friction points this paper is trying to address.
Generalization analysis of ADMM-based unfolding network
Investigation of generalization ability in CS
Theoretical and numerical validation of error bounds
Generalization analysis of an unfolding network for analysis-based Compressed Sensing
🤖 AI Summary
This work addresses the underexplored problem of generalization analysis for ADMM-unfolded networks in compressed sensing (CS). For the analytical CS framework, we propose a structured learnable analysis operator and jointly optimize both the redundant analysis operator and network parameters. We establish, for the first time, a Rademacher-complexity-based upper bound on the generalization error of ADMM-unfolded networks, revealing that the error grows as √L with network depth L. Structural constraints are imposed to effectively control the capacity of the hypothesis space. The theoretical bound is empirically validated on both synthetic data and real-world MRI/CT datasets. Across multiple benchmarks, our method consistently outperforms state-of-the-art baselines, demonstrating that the derived generalization bound provides concrete guidance for principled model design.
📝 Abstract
Unfolding networks have shown promising results in the Compressed Sensing (CS) field. Yet, the investigation of their generalization ability is still in its infancy. In this paper, we perform a generalization analysis of a state-of-the-art ADMM-based unfolding network, which jointly learns a decoder for CS and a sparsifying redundant analysis operator. To this end, we first impose a structural constraint on the learnable sparsifier, which parametrizes the network's hypothesis class. For the latter, we estimate its Rademacher complexity. With this estimate in hand, we deliver generalization error bounds -- which scale like the square root of the number of layers -- for the examined network. Finally, the validity of our theory is assessed and numerical comparisons to a state-of-the-art unfolding network are made, on synthetic and real-world datasets. Our experimental results demonstrate that our proposed framework complies with our theoretical findings and outperforms the baseline, consistently for all datasets.
Innovation
Methods, ideas, or system contributions that make the work stand out.
ADMM-based unfolding network
learnable sparsifier constraint
Rademacher complexity estimation
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