  Estimation of the parameters of a 2-dimensional sinusoidal model is a
fundamental problem in digital signal processing and time series analysis. In
this paper, we propose a robust least absolute deviation (LAD) estimators for
parameter estimation. The proposed methodology provides a robust alternative to
non-robust estimation techniques like the least squares estimators, in
situations where outliers are present in the data or in the presence of heavy
tailed noise. We study important asymptotic properties of the LAD estimators
and establish the strong consistency and asymptotic normality of the LAD
estimators of the signal parameters of a 2-dimensional sinusoidal model. We
further illustrate the advantage of using LAD estimators over least squares
estimators through extensive simulation studies. Data analysis of a
2-dimensional texture data indicates practical applicability of the proposed
LAD approach.
