Satellite-borne high-resolution imaging spectrometers， employed as payloads on atmospheric observation satellites， utilize frame transfer CCDs to measure the concentration and distribution of atmospheric components on Earth. However， the Smear effect inherent in frame transfer CCDs compromises the accuracy of spectral measurements. Traditional Smear removal algorithms， which rely on matrix representations of 2D images， are computationally complex and unsuitable for implementation in ground test systems requiring real-time performance. This study proposes an algebraic Smear removal algorithm by modeling the Smear process in accordance with the operational principles of frame transfer CCDs. The algorithm eliminates the need for matrix operations inherent in conventional methods， reducing processing time to 1/500th of that required by matrix-based approaches. It is particularly well-suited for ground test platforms that demand high real-time performance and focus on Smear removal in static images. The paper begins by analyzing the causes of Smear in frame transfer CCDs and subsequently derives an algebraic Smear removal algorithm based on this analysis. Compared to the matrix-based algorithm implemented using the Eigen library， the proposed method reduces processing time from 8 s to 16 ms. The algorithm has been successfully applied to the ground test system of a satellite-borne imaging spectrometer， enabling real-time Smear removal during image processing.