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.

翻译：二维正弦模型参数估计是数字信号处理和时间序列分析中的基本问题。本文针对参数估计问题，提出了稳健的最小绝对偏差（LAD）估计量。当数据中存在异常值或重尾噪声时，所提出的方法为最小二乘估计等非稳健估计技术提供了稳健的替代方案。我们研究了LAD估计量的重要渐近性质，并建立了二维正弦模型信号参数LAD估计量的强一致性和渐近正态性。通过大量模拟研究进一步说明了LAD估计量相对于最小二乘估计量的优势。对二维纹理数据的分析表明，所提出的LAD方法具有实际应用价值。