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. 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. 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 0.04 seconds to 0.11 seconds

unlike the cyclic boundary algorithm. The time consumed for the iterative restoration algorithm decreases by several seconds. Experimental results indicate that utilizing the ringing effects suppression algorithm with sine integral fitting to suppress the ringing effect preserves the image edge completely and ensures less calculation

which is superior to other traditional methods.