Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders
We consider the problem of recovering complex-valued block sparse signals with unknown borders. Such signals arise naturally in numerous applications. Several algorithms have been developed to solve the problem of unknown block partitions. In pattern-coupled sparse Bayesian learning (PCSBL), each co...
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| Format: | Article |
| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Open Journal of Signal Processing |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10417118/ |
| _version_ | 1797302649990676480 |
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| author | Didem Dogan Geert Leus |
| author_facet | Didem Dogan Geert Leus |
| author_sort | Didem Dogan |
| collection | DOAJ |
| description | We consider the problem of recovering complex-valued block sparse signals with unknown borders. Such signals arise naturally in numerous applications. Several algorithms have been developed to solve the problem of unknown block partitions. In pattern-coupled sparse Bayesian learning (PCSBL), each coefficient involves its own hyperparameter and those of its immediate neighbors to exploit the block sparsity. Extended block sparse Bayesian learning (EBSBL) assumes the block sparse signal consists of correlated and overlapping blocks to enforce block correlations. We propose a simpler alternative to EBSBL and reveal the underlying relationship between the proposed method and a particular case of EBSBL. The proposed algorithm uses the fact that immediate neighboring sparse coefficients are correlated. The proposed model is similar to classical sparse Bayesian learning (SBL). However, unlike the diagonal correlation matrix in conventional SBL, the unknown correlation matrix has a tridiagonal structure to capture the correlation with neighbors. Due to the entanglement of the elements in the inverse tridiagonal matrix, instead of a direct closed-form solution, an approximate solution is proposed. The alternative algorithm avoids the high dictionary coherence in EBSBL, reduces the unknowns of EBSBL, and is computationally more efficient. The sparse reconstruction performance of the algorithm is evaluated with both correlated and uncorrelated block sparse coefficients. Simulation results demonstrate that the proposed algorithm outperforms PCSBL and correlation-based methods such as EBSBL in terms of reconstruction quality. The numerical results also show that the proposed correlated SBL algorithm can deal with isolated zeros and nonzeros as well as block sparse patterns. |
| first_indexed | 2024-03-07T23:41:23Z |
| format | Article |
| id | doaj.art-6b6f1fe609354dd89235e75f4a97075b |
| institution | Directory Open Access Journal |
| issn | 2644-1322 |
| language | English |
| last_indexed | 2024-03-07T23:41:23Z |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Signal Processing |
| spelling | doaj.art-6b6f1fe609354dd89235e75f4a97075b2024-02-20T00:01:33ZengIEEEIEEE Open Journal of Signal Processing2644-13222024-01-01542143510.1109/OJSP.2024.336091410417118Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown BordersDidem Dogan0https://orcid.org/0009-0004-0170-1332Geert Leus1https://orcid.org/0000-0001-8288-867XFaculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, The NetherlandsFaculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, The NetherlandsWe consider the problem of recovering complex-valued block sparse signals with unknown borders. Such signals arise naturally in numerous applications. Several algorithms have been developed to solve the problem of unknown block partitions. In pattern-coupled sparse Bayesian learning (PCSBL), each coefficient involves its own hyperparameter and those of its immediate neighbors to exploit the block sparsity. Extended block sparse Bayesian learning (EBSBL) assumes the block sparse signal consists of correlated and overlapping blocks to enforce block correlations. We propose a simpler alternative to EBSBL and reveal the underlying relationship between the proposed method and a particular case of EBSBL. The proposed algorithm uses the fact that immediate neighboring sparse coefficients are correlated. The proposed model is similar to classical sparse Bayesian learning (SBL). However, unlike the diagonal correlation matrix in conventional SBL, the unknown correlation matrix has a tridiagonal structure to capture the correlation with neighbors. Due to the entanglement of the elements in the inverse tridiagonal matrix, instead of a direct closed-form solution, an approximate solution is proposed. The alternative algorithm avoids the high dictionary coherence in EBSBL, reduces the unknowns of EBSBL, and is computationally more efficient. The sparse reconstruction performance of the algorithm is evaluated with both correlated and uncorrelated block sparse coefficients. Simulation results demonstrate that the proposed algorithm outperforms PCSBL and correlation-based methods such as EBSBL in terms of reconstruction quality. The numerical results also show that the proposed correlated SBL algorithm can deal with isolated zeros and nonzeros as well as block sparse patterns.https://ieeexplore.ieee.org/document/10417118/Block sparse signalscorrelated sparse Bayesian learningexpectation-maximization (EM) methodcompressive sensing |
| spellingShingle | Didem Dogan Geert Leus Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders IEEE Open Journal of Signal Processing Block sparse signals correlated sparse Bayesian learning expectation-maximization (EM) method compressive sensing |
| title | Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders |
| title_full | Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders |
| title_fullStr | Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders |
| title_full_unstemmed | Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders |
| title_short | Correlated Sparse Bayesian Learning for Recovery of Block Sparse Signals With Unknown Borders |
| title_sort | correlated sparse bayesian learning for recovery of block sparse signals with unknown borders |
| topic | Block sparse signals correlated sparse Bayesian learning expectation-maximization (EM) method compressive sensing |
| url | https://ieeexplore.ieee.org/document/10417118/ |
| work_keys_str_mv | AT didemdogan correlatedsparsebayesianlearningforrecoveryofblocksparsesignalswithunknownborders AT geertleus correlatedsparsebayesianlearningforrecoveryofblocksparsesignalswithunknownborders |