Algorithms for the estimation of noise level and the detection of noise model are proposed. They are applied to gene expression data for Drosophila embryos. The 2D data on gene expression and the extracted 1D profiles are considered. Since the 1D data contain processing errors, an algorithm for separation of these processing errors is constructed to estimate the biological noise level. An approach to discrimination between the additive and multiplicative models is suggested for the 1D and 2D cases. Singular spectrum analysis and its 2D extension are exploited for the pattern extraction. The algorithms are tested on artificial data similar to the real data. Comparison of the results, which are obtained by the 1D and 2D methods, is performed for Krüppel and giant genes.