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In digital speckle pattern interferometry, the denoising of speckle fringe patterns is of vital importance for quantitative extraction of phase distribution. A filtering method of fast discrete curvelet transform based on weighted average thresholding technique is proposed in this paper for noise removal in speckle fringe patterns. Both computer-simulated and experimental digital speckle pattern interferometry fringe patterns are adopted to evaluate the performance of the proposed filtering method. In addition, a widely used and representative filtering method, windowed Fourier filter, is introduced for making a comparison and validation in the image processing effect, and the parameter of peak signal noise ratio is also used for assessment of denoising effect. It is shown from the filtered results that the filtering method of fast discrete curvelet transform is effecitve to remove speckle noises and simultaneously preserve fringe structure information.