稀疏表示是一种有潜力的图像信息表示方法，已应用于图像目标检测。正交匹配追踪算法(OMP)求解稀疏系数过程计算复杂，不能满足快速处理的要求，因此引入Kalman滤波器的递归思想，提出了一种计算稀疏系数的快速OMP(FastOMP)算法。利用Hermitian引理，从上一时刻的状态更新当前信息，避免了高维矩阵数据的重复计算。为提高算法的执行效率，提出了基于GPU/CUDA(图形处理器/统一计算设备架构)的并行计算方法，充分利用GPU的并行计算能力，提高了FastOMP算法的计算速度。实验结果表明，与传统OMP算法相比，FastOMP算法可大幅度缩短计算时间并提高检测精度。

Sparse representation is a potential image representation method, which has been applied to target detection for images. The process to calculate sparse coefficients is complex when the orthogonal matching pursuit (OMP) algorithm is used, which cannot satisfy the requirement of rapid processing. An idea of recursive Kalman filter is introduced, and a fast OMP (FastOMP) algorithm is proposed to calculate the sparse coefficient. The Hermitian lemma is used to update the current information from the last status. The FastOMP algorithm can avoid repeated calculation of higher-dimension matrix data. In order to further improve the efficiency of the algorithm, the parallel computation method is proposed based on GPU/CUDA (graphics processing unit/compute unified device architecture). The parallel computation capacity of GPU is utilized to accelerate the FastOMP algorithm. The experimental results show that the FastOMP algorithm saves the processing time notably and improves the detection accuracy compared to the traditional OMP algorithm.