Theoretical Validation of the Latent Optimally Partitioned-$\ell_2/\ell_1$ Penalty with Application to Angular Power Spectrum Estimation
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913168951869440 |
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| author | Kuroda, Hiroki Cavalcante, Renato Luis Garrido Yukawa, Masahiro |
| author_facet | Kuroda, Hiroki Cavalcante, Renato Luis Garrido Yukawa, Masahiro |
| contents | This paper demonstrates that, in both theory and practice, the latent optimally partitioned (LOP)-$\ell_2/\ell_1$ penalty is effective for exploiting block-sparsity without knowledge of the concrete block structure. More precisely, we first present a novel theoretical result showing that the optimized block partition in the LOP-$\ell_2/\ell_1$ penalty satisfies a condition required for accurate recovery of block-sparse signals. Motivated by this result, we present a new application of the LOP-$\ell_2/\ell_1$ penalty to estimation of angular power spectrum, which is block-sparse with unknown block partition, in MIMO communication systems. Numerical simulations show that the proposed use of block-sparsity with the LOP-$\ell_2/\ell_1$ penalty significantly improves the estimation accuracy of the angular power spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theoretical Validation of the Latent Optimally Partitioned-$\ell_2/\ell_1$ Penalty with Application to Angular Power Spectrum Estimation Kuroda, Hiroki Cavalcante, Renato Luis Garrido Yukawa, Masahiro Signal Processing This paper demonstrates that, in both theory and practice, the latent optimally partitioned (LOP)-$\ell_2/\ell_1$ penalty is effective for exploiting block-sparsity without knowledge of the concrete block structure. More precisely, we first present a novel theoretical result showing that the optimized block partition in the LOP-$\ell_2/\ell_1$ penalty satisfies a condition required for accurate recovery of block-sparse signals. Motivated by this result, we present a new application of the LOP-$\ell_2/\ell_1$ penalty to estimation of angular power spectrum, which is block-sparse with unknown block partition, in MIMO communication systems. Numerical simulations show that the proposed use of block-sparsity with the LOP-$\ell_2/\ell_1$ penalty significantly improves the estimation accuracy of the angular power spectrum. |
| title | Theoretical Validation of the Latent Optimally Partitioned-$\ell_2/\ell_1$ Penalty with Application to Angular Power Spectrum Estimation |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2509.13745 |