The ℓ₁-SVD Algorithm For Regularization Parameter Selection Basis On The BIC Criterion

The $\ell_{1}$-SVD algorithm is a compressive sensing algorithm based on $\ell_{1}$-norm constraints, but it can suffer from problems such as false targets and difficulties in selecting regularization parameters. Therefore, this paper proposes a spherical harmonic domain source localization algorithm based on the weighted $\ell_{1}$-SVD algorithm, abbreviated W-SHD-L1SVD. In this work, based on the orthogonality of the signal and noise subspaces, we construct a weighted coefficient vector to apply weighting to the $\ell_{1}$-norm constraint model. Additionally, an improved BIC criterion is used to automatically determine the regularization parameter to address the issue of regularization parameter selection. Through this weighting process and automatic regularization selection, the proposed algorithm enhances the sparsity of the recovered coefficient matrix and effectively suppresses false peaks, thereby achieving accurate direction of arrival (DOA) estimation. The simulation results prove that W-SHD-L1SVD is effective.