Iteratively reweighted optimum linear regression in the presence of generalized Gaussian noise

Generalized Gaussian distribution (GGD) is one of the most prominent and widely used parametric distributions to model the statistical properties of various phenomena. In this paper, we consider the linear regression problem in the presence of GGD noise employing the iteratively reweighted least squares (IRLS) algorithm. For the standard IRLS algorithm, an ℓp-norm minimization problem is solved iteratively. However, its performance depends on a properly chosen norm parameter p. To solve this problem, we propose a modified IRLS algorithm with a variable p, which is noise distribution dependent and can be updated online. Numerical studies show that the proposed method can normally converge within a few iterations. Furthermore, optimal performance is achieved in terms of normalized mean square error for different GGD noise models.