ℓ2,p-correlation and robust matching pursuit for sparse approximation

Abstract

Correlation is an index indicating the similarity of different data set, and a correct calculation of correlation or correlation coefficient is very important in science and engineering. However, in many real word applications, the signal will be contaminated by structured impulsive noise, then the generally used correlation or correlation coefficient will fail to correctly express the statistical relationship between two signals. In this paper, in order to reveal the correlation between two matrix signals in the presence of structured or group-wise outliers, we extend the definition of correlation to the ℓ2,p-space and define the ℓ2,p-correlation and its corresponding correlation coefficient. The properties of the ℓ2,p-correlation coefficient are also presented, and an iterative ℓ2,p-norm minimization algorithm is proposed to calculate the ℓ2,p-correlation accurately. The ℓ2,p-correlation is then applied to solve the problem of robust sparse signal recovery, and a greedy pursuit based algorithm is developed to approximate the signal. Furthermore, experiments are carried out on sparse signal recovery and direction of arrival (DOA) estimation to demonstrate the efficiency of the ℓ2,p-greedy pursuit approach in sparse approximation in the presence of group-wise outliers comparing to the state-of-the-art algorithms.