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Time-series data of normalized difference vegetation index (NDVI), derived from satellite sensors, can be used to support land-cover change detection and phenological interpretations, but further analysis and applications are hindered by residual noise in the data. As an alternative to a number of existing algorithms developed to compensate for such noise, we develop a simple but computationally efficient method (which we call the changing-weight filter method) to reconstruct a high-quality NDVI time series. The new algorithm consists of two major procedures: (1) detecting the local maximum/minimum points in a growth cycle along an NDVI temporal profile based on a mathematical morphology algorithm and a rule-based decision process and (2) filtering an NDVI time series with a three-point changing-weight filter. This method is tested at 470 test points for 55 vegetation types and a test region in China using a 250-m 16-day Moderate Resolution Imaging Spectroradiometer (MODIS) NDVI product. Comparing our results to those of three other well-known methods-asymmetric Gaussian function fitting, double logistic function fitting, and Savitzky-Golay filtering-the new method has many of the advantages of existing methods, while in some cases, the changing-weight filter method more effectively preserves the curve shape as well as the timing and the amplitude of the local maxima/minima in the NDVI time series for a broad range of phenologies. Moreover, the response of the filtering algorithm is relatively insensitive to the exact values of its design parameters, making the new method more flexible and effective in adjusting to fit a variety of classes of NDVI time series.