Iterative Reweighted <i>l</i>₁ Penalty Regression Approach for Line Spectral Estimation

Abstract

In this paper, we proposed an iterative reweighted <i>l</i>₁ penalty regression approach to solve the line spectral estimation problem. In each iteration process, we first use the ideal of Bayesian lasso to update the sparse vectors ; the derivative of the penalty function forms the regularization parameter. We choose the anti-trigonometric function as a penalty function to approximate the <i>l</i>₀ norm. Then we use the gradient descent method to update the dictionary parameters. The theoretical analysis and simulation results demonstrate the effectiveness of the method and show that the proposed algorithm outperforms other state-of-the-art methods for many practical cases.