An L1-regularized variational approach for NDVI time-series reconstruction considering inter-annual seasonal similarity

Long-term normalized difference vegetation index (NDVI) data are extensively applied in environmental and ecological researches. However, cloud-induced interference and contamination seriously affects the quality of the current NDVI products, bringing huge uncertainty for subsequent applications. Although plenty of temporal methods have been developed to reconstruct NDVI time series, they still struggle to solve the challenge of temporally continuous gaps, due to the insufficient utilization of the prior characteristics in the time series. This paper develops a variational-based method to reconstruct multi-year NDVI time series by jointly regularizing local smoothness and inter-annual Seasonal similarity using the L1-norm (termed the SeasonL1 method). The proposed method innovatively introduces the information from adjacent years combined with assistance from temporal neighbors, and the L1-norm is imposed to establish the two corresponding regularization terms, to better characterize their statistical distributions. Simulated and real-data experiments were conducted in the Yangtze River Economic Belt of China using Moderate Resolution Imaging Spectroradiometer (MODIS) NDVI data, to validate the performance of the SeasonL1 method by comparing with five classic methods. The results demonstrate that the proposed SeasonL1 method can achieve a satisfactory performance with an acceptable time cost in terms of both the quantitative indicators and spatio-temporal visual effect. In particular, the SeasonL1 method shown obvious advantages in recovering temporally continuous missing values and preventing over -smoothing in the inflection points of vegetation growth. We expect that the SeasonL1 method will become a useful filtering approach for obtaining high-quality NDVI time-series data in large-scale applications.