Generalization analysis of an unfolding network for analysis-based Compressed Sensing

• URL: http://arxiv.org/abs/2303.05582v2
• Date: Thu, 06 Feb 2025 14:22:03 GMT
• Title: Generalization analysis of an unfolding network for analysis-based Compressed Sensing
• Authors: Vicky Kouni, Yannis Panagakis,
• Abstract summary: Unfolding networks have shown promising results in the Compressed Sensing (CS) field. We perform a generalization analysis of a state-of-the-art ADMM-based unfolding network. Our proposed framework complies with our theoretical findings and outperforms the baseline.
• Score: 17.814125871206077
• License:
• 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.

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