中文摘要：

目的边缘振铃效应是影响运动模糊图像复原效果的重要因素之一。为了有效提高运动模糊图像复原的质量，针对运动模糊图像复原中由于图像边界截断而产生的振铃效应问题，提出一种正弦积分拟合的图像复原边界振铃效应抑制方法。方法首先，对待处理的模糊图像根据模糊核的大小进行边缘延展；然后，分别利用正弦函数积分方法和双正弦函数积分方法对单向过渡区域和双向过渡区域进行窗函数计算；进而，将延展图像进行加窗处理；最后，对加窗图像进行复原处理并提取出原始图像的部分作为复原结果。结果与现有的几种振铃效应抑制算法进行对比实验。在视觉效果方面，本文方法能有效抑制振铃效应；在峰值信噪比（PSNR）、归一化均方误差（NMSE）以及图像质量指数（Q）等图像质量评价指标方面，本文方法的PSNR值比最优窗算法提高了约0．17～0．76dB，NMSE值比最优窗算法降低了约0．0005～0．0007，Q值比最优窗算法提高了约o．023～o．029，本文方法在多数情况下得到的评价指标优于循环边界法；在耗时方面，本文方法对非迭代恢复算法的处理时间比循环边界算法降低了约0．04～0．11s，对迭代恢复算法处理时间减少达到数秒。结论通过大量实验发现，正弦积分拟合的图像复原边界振铃效应抑制方法在进行振铃效应抑制时，能有效控制计算量，且能完整地保留图像的边缘信息，图像恢复效果明显优于其他方法。

英文摘要：

Objective Border ringing effect is an important factor that influences the quality of motion-blurred image restoration. A deep analysis is performed to determine the causes of boundary ringing effects and improve the quality of image restoration. A new boundary ringing effects suppression algorithm with sine integral fitting is then proposed to suppress the ringing artifacts of the restored image caused by boundary truncation. Method First, the boundaries of the blurred image to be restored are extended according to the previously estimated blur kernel size. Second, window functions for one-direction and two-direction transition regions are calculated based on the sine integral and double sine integral methods, respectively.Third, the window function is applied to the extended image by multiplier operation. Finally, the windowed image is restored by restoration algorithms, and the original area is extracted as the restored result. Result Our proposed method is compared with several traditional algorithms that can lower the ringing effect. The proposed method in this study can suppress the ringing effect effectively in terms of visual quality. Peak signal-to-noise ratio （PSNR） , normalized mean square error （NMSE）, and image quality index （Q） are utilized to evaluate the image quality restored by our proposed method. The PSNR value of the image restored by the proposed method is 0. 17 to 0. 76 higher than that of the optimal window algorithm. The NMSE value of the image restored by the proposed method is 0. 000 5 to 0. 000 7 lower than that of the optimal window algorithm. The Q value of the image restored by the proposed method is 0. 023 to 0. 029 higher than that of the optimal window algorithm. Evaluation values of the proposed method are better than that of the cyclic boundary algorithm in most cases. Time consumption is applied to evaluate the efficiency of the proposed method. The processing time of the proposed method for the non-iterative restoration algorithm decreases by O. 04 seconds to 0. 1