Bayesian Dictionary Learning via Approximate Message Passing

Junhua Chen

doi:10.1109/lwc.2026.3716633

Bayesian Dictionary Learning via Approximate Message Passing

2026-07-24

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DOI：10.1109/lwc.2026.3716633

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This letter proposes a Bayesian dictionary learning framework that integrates vector approximate message passing (VAMP) with variance-corrected Bayesian method of optimal direction (Bayes-MOD) updates under an expectation-maximization (EM) hyperparameter-learning scheme. Under a Bernoulli–Gaussian prior, VAMP estimates the posterior means, variances, and activity probabilities of the sparse coefficients, and passes these statistics to Bayes-MOD for variance-aware dictionary updates. The updated dictionary is then fed back to VAMP, forming a closed-loop inference-and-learning procedure. In addition, state evolution (SE) is employed as a lightweight diagnostic for convergence and stable inference, providing practical traceability for the dictionary learning process. Numerical results demonstrate the superiority of the proposed framework and show that well-conditioned dictionaries can be guaranteed.

Keywords:

Dictionary learning

compressive sensing

approximate message passing

state evolution

method of optimal direction

Bayesian Dictionary Learning via Approximate Message Passing

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