Total Variation Sparse Bayesian Learning for Block Sparsity via Majorization-Minimization
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910011667513344 |
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| author | He, Yanbin Joseph, Geethu |
| author_facet | He, Yanbin Joseph, Geethu |
| contents | Block sparsity is a widely exploited structure in sparse recovery, offering significant gains when signal blocks are known. Yet, practical signals often exhibit unknown block boundaries and isolated non-zero entries, which challenge traditional approaches. A promising method to handle such complex sparsity patterns is the difference-of-logs total variation (DoL-TV) regularized sparse Bayesian learning (SBL). However, due to the complex form of DoL-TV term, the resulting optimization problem is hard to solve. This paper develops a new optimization framework for the DoL-TV SBL cost function. By introducing an exponential reparameterization of the SBL hyperparameters, we reveal a novel structure that admits a majorization-minimization formulation and naturally extends to unknown noise variance estimation. Sparse recovery results on both synthetic data and extended source direction-of-arrival estimation demonstrate improved accuracy and runtime performance compared to benchmark methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04623 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Total Variation Sparse Bayesian Learning for Block Sparsity via Majorization-Minimization He, Yanbin Joseph, Geethu Signal Processing Block sparsity is a widely exploited structure in sparse recovery, offering significant gains when signal blocks are known. Yet, practical signals often exhibit unknown block boundaries and isolated non-zero entries, which challenge traditional approaches. A promising method to handle such complex sparsity patterns is the difference-of-logs total variation (DoL-TV) regularized sparse Bayesian learning (SBL). However, due to the complex form of DoL-TV term, the resulting optimization problem is hard to solve. This paper develops a new optimization framework for the DoL-TV SBL cost function. By introducing an exponential reparameterization of the SBL hyperparameters, we reveal a novel structure that admits a majorization-minimization formulation and naturally extends to unknown noise variance estimation. Sparse recovery results on both synthetic data and extended source direction-of-arrival estimation demonstrate improved accuracy and runtime performance compared to benchmark methods. |
| title | Total Variation Sparse Bayesian Learning for Block Sparsity via Majorization-Minimization |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2602.04623 |