Algorithms for robust linear regression by exploiting the connection to sparse signal recovery

In this paper, we develop algorithms for robust linear regression by leveraging the connection between the problems of robust regression and sparse signal recovery. We explicitly model the measurement noise as a combination of two terms; the first term accounts for regular measurement noise modeled as zero mean Gaussian noise, and the second term captures the impact of outliers. The fact that the latter outlier component could indeed be a sparse vector provides the opportunity to leverage sparse signal reconstruction methods to solve the problem of robust regression. Maximum a posteriori (MAP) based and empirical Bayesian inference based algorithms are developed for this purpose. Experimental studies on simulated and real data sets are presented to demonstrate the effectiveness of the proposed algorithms.