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Hyper spectral imager (HSI) on dasiaHJ-1psila Chinese satellite is a kind of Fourier transform imaging spectrometer (FTIS). In order to realize the fast reconstruction processing of HSI data, the authors designed the fast reconstruction algorithms using OpenMP parallel computing. The results show that the framework based on OpenMP can use the multi-core CPU hardware resources competently and can enhance the efficiency of spectrum reconstruction processing significantly. It has already been used on the data processing service of HSI at China Center for Resource Satellite Data and Applications successfully. If this framework is applied to more cores workstation in parallel computing, a single computer to implement real-time data reconstruction of FTIS will be possible.