# Theoretical Validation of the Latent Optimally Partitioned-ℓ2/ℓ1 Penalty with Application to Angular Power Spectrum Estimation

arXiv: https://arxiv.org/abs/2509.13745 · HTML: https://mlsanity.com/paper/2509.13745/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2025.

## Built on by (most cited first, 2 of 2)

- [Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties](https://mlsanity.com/paper/2603.01304/) (2026)
- [Deep Unfolded Latent Optimally Partitioned-l2/l1 Networks for Data-driven Block-Sparse Recovery](https://mlsanity.com/paper/2606.12740/) (2026)

## Abstract (arXiv)

This paper demonstrates that, in both theory and practice, the latent optimally partitioned (LOP)-ℓ2/ℓ1 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-ℓ2/ℓ1 penalty satisfies a condition required for accurate recovery of block-sparse signals. Motivated by this result, we present a new application of the LOP-ℓ2/ℓ1 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-ℓ2/ℓ1 penalty significantly improves the estimation accuracy of the angular power spectrum.