A novel technique is proposed for the direct two-dimensional phase derivatives estimation based on the matrix pencil approach in digital holographic interferometry. The interference field is represented as a two-dimensional complex sinusoidal signal in an analysis window around each pixel. The method provides high resolution frequency estimates and does not require the two-dimensional search in the spectral domain. A simple denoising procedure is proposed based on singular value decomposition of the interference field. The uncertainty in the frequency estimate is utilized as a parameter to identify the regions containing high fringe concentration on the object surface. Simulation and experimental results are provided to show the noise robustness and the practical applicability of the proposed method.