发表机构
Eindhoven University of Technology（埃因霍温理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出SR-TL1稀疏恢复框架，结合square-root LASSO与TL1范数，采用DCA和ADMM算法实现低复杂度，在高相干字典下的SMV DoA估计中，正则化超参数鲁棒性更好，恢复性能具竞争力。
AI 中文摘要
本文针对带有角相关阵列缺陷的高相干过完备字典下的单测量向量（SMV）波达方向（DoA）估计问题，提出了平方根变换L1范数（SR-TL1）稀疏恢复框架。该框架结合了对噪声方差具有鲁棒性的平方根最小绝对收缩与选择算子（square-root LASSO）框架，以及在高相干字典下比经典凸L1范数恢复性能更强的非凸惩罚项——变换L1范数（TL1范数）。我们采用凸差算法（DCA）与乘子交替方向法（ADMM）来获得简单的闭式更新规则，并利用字典格拉姆矩阵的低秩特性实现高效实现，使得每次迭代的计算复杂度最多为O(MN)，其中M为阵列尺寸，N为字典长度。我们还为SR-TL1的DCA迭代提供了收敛性保证。对该框架的实验验证表明，其正则化超参数对噪声方差水平的敏感性更低，且与最新基线相比具有竞争力的恢复性能。
英文摘要
This paper proposes a Square-Root Transformed $L_1$-norm ($SR\text{-}TL_{1}$) sparse recovery framework for single-measurement-vector (SMV) direction of arrival (DoA) estimation under highly-coherent overcomplete dictionaries with angular-dependent array imperfections. The proposed framework combines the square-root Least Absolute Shrinkage and Selection Operator (square-root LASSO) framework which is known to be robust against noise variance with the Transformed $L_1$-norm ($TL_1$-norm), a non-convex penalty that shows a stronger recovery performance than the classical convex $L_1$-norm under highly-coherent dictionaries. We use the Difference of Convex Algorithm (DCA) along with the Alternating Direction Method of Multipliers (ADMM) algorithm to obtain simple, closed-form update rules and provide an efficient implementation that leverages the low-rank nature of the Gram matrix of the dictionary so as to obtain a computational complexity of at most $\mathcal{O}(MN)$ per iteration where $M$ is the array size and $N$ is the length of the dictionary. We additionally provide a convergence guarantee for the DCA iterates of $SR\text{-}TL_{1}$. Experimental verification of the proposed framework shows a lower sensitivity of the regularization hyperparameter to the noise variance level and a competitive recovery performance compared to state-of-the-art baselines.
