A 2-D robust high-resolution frequency estimation approach

This paper deals with a 2-D high-resolution frequency estimation method dedicated to images corrupted by outliers. Outliers are considered here as particular data points that do not fit an assumed model. We propose an efficient subspace estimation algorithm for 2-D complex sinusoids. In this framework the well-known model using the sum of complex exponentials fails for a small fraction of the data set causing the classical estimators to produce inaccurate results. To alleviate this drawback, we propose a new robust iterative Levenberg-Marquardt (LM) approach based method. The proposed approach operates in three main steps. First, we define a weight function based on the influence function which allows the “wrong” data to be detected and corrected. The influence function, which is inspired from the so-called M-estimator, measures the influence of a datum on the value of the estimated parameter. Second, a 2-D extension of the large sample approximation of the maximum likelihood (ML) estimator is developed in order to estimate image parameters. Third, the Levenberg-Marquardt (LM) technique is used to ensure the convergence of the ML estimator by detecting “wrong” data for each iteration. The effectiveness of the proposed method is illustrated by numerical simulations.