Communication Dans Un Congrès Année : 2025

Revisiting CHAMPAGNE: Sparse Bayesian Learning as Reweighted Sparse Coding

Résumé

This paper revisits the CHAMPAGNE algorithm within the Sparse Bayesian Learning (SBL) framework and establishes its connection to reweighted sparse coding. We demonstrate that the SBL objective can be reformulated as a reweighted ℓ21-minimization problem, providing a more straightforward interpretation of the sparsity mechanism and enabling the design of an efficient iterative algorithm. Additionally, we analyze the behavior of this reformulation in the low signal-to-noise ratio (SNR) regime, showing that it simplifies to a weighted ℓ21-regularized least squares problem. Numerical experiments validate the proposed approach, highlighting its improved computational efficiency and ability to produce exact sparse solutions, particularly in simulated MEG source localization tasks.

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Dates et versions

hal-05130740 , version 1 (26-06-2025)

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Dylan Sechet, Matthieu Kowalski, Samy Mokhtari, Bruno Torrésani. Revisiting CHAMPAGNE: Sparse Bayesian Learning as Reweighted Sparse Coding. SampTA 2025 - International Conference on Sampling Theory and Applications, Jul 2025, Vienna, Austria. ⟨10.1109/SampTA64769.2025.11133512⟩. ⟨hal-05130740⟩
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