Robust estimators of two dimensional sinusoidal model parameters

Abstract

In this paper we consider the two dimensional (2-D) sinusoidal model. This particular model has several applications in the statistical signal processing and in texture analysis. Extensive work has been done in developing several efficient procedures and establishing their properties. The least squares estimators (LSEs) are known to be the most efficient estimators in presence of additive noise. But it is observed that the LSEs are quite sensitive in presence of outliers. In this paper we propose to use the weighted least squares estimators (WLSEs) of the unknown parameters in presence of additive white noise. It is observed that in presence of outliers, the WLSEs are more robust than the least squares estimators (LSEs) and they behave very similarly to some of the other well known robust estimators, for example the least absolute deviation estimators (LADEs). It is observed that developing the properties of the LADEs is not immediate. We derive the consistency and asymptotic normality properties of the WLSEs. Extensive simulations have been performed to show the effectiveness of the proposed method. One synthetic data set has been analyzed to illustrate how the proposed method can be used in practice.