A robust matching pursuit algorithm using information theoretic learning. (November 2020) - Zhang, Miaohua; Gao, Yongsheng; Sun, Changming; Blumenstein, Michael
Highlights: A robust matching pursuit algorithm based on a new ITL-Correlation and non-second order kernel minimization method is proposed. Different from the current matching pursuit algorithms, which only works under Gaussian conditions, the proposed ITL-Correlation can work under non-Gaussian conditions and is robust against heavy-tailed impulsive noise that is commonly associated with large-amplitude outliers. A non-second order loss is proposed to provide more flexibility in controlling the reconstruction error, which performs better in detecting occlusions and outliers in the data. A new classifier based on the non-second order statistic measurement is developed to minimize the effect from outliers and non-Gaussian noise for robust classification. Experimental results demonstrate the superiority of the proposed method in handling the challenging outlier and occlusion problems against the existing methods. Abstract: Current orthogonal matching pursuit (OMP) algorithms calculate the correlation between two vectors using the inner product operation and minimize the mean square error, which are both suboptimal when there are non-Gaussian noises or outliers in the observation data. To overcome these problems, a new OMP algorithm is developed based on information theoretic learning (ITL), which is built on the following new techniques: (1) an ITL-based correlation (ITL-Correlation) is developed as a new similarity measure which can better exploit higher-order statistics of the data, and is robust against many different types of noise and outliers in a sparse representation framework; (2) a non-second order statistic measurement and minimization method is developed to improve the robustness of OMP by overcoming the limitation of Gaussianity inherent in a cost function based on second-order moments. The experimental results on both simulated and real-world data consistently demonstrate the superiority of the proposed OMP algorithm in data recovery, image reconstruction, and classification.