Robust high resolution image spectral analysis
This paper deals with a 2-D high resolution frequency estimation method dedicated to corrupted image by outliers. Outliers are particular data points that do not obey the assumed model. In this framework the well-known model of the sum of complex exponentials fails for the smallest fraction of a data set, which causes the classical estimators to produce inaccurate results. To alleviate this drawback, we propose a new robust iterative Levenberg-Marquardt (LM)-based method. The three main steps of the method we propose are as follows. First, we define a weight function based on the influence function which allows one to detect and correct the "wrong" data. The influence function measures the influence of a datum on the value of the parameter estimate. It is inspired from the so-called M-estimator. Second, a 2-D extension of the large sample approximation of the Maximum likelihood (ML) estimator is developed in order to estimate the image parameters. Third, the Levenberg-Marquardt (LM) technique is used to ensure the convergence of the ML estimator by performing the detection of "wrong" data for each iteration. The effectiveness of the proposed method is illustrated by some numerical simulations.