中文摘要：

目的 图像修复在图像处理中起着举足轻重的地位，针对目前大部分图像修补算法在修复划痕时存在纹理修复不够突出的缺陷，提出了两种基于连分式插值的修补算法，可以较好保持图像纹理的特性。方法 该算法基于连分式插值理论，采用图像破损点周围像素信息来插值出破损点的像素值。根据插值函数和插值窗口的不同，提出了两种插值方法，即Thiele型修补算法与Newton-Thiele型修补算法，解决不同纹理类型图像的划痕修补问题，并对插值过程中出现的奇异点问题和平移问题提出了行之有效的解决办法。结果 对大量的划痕图像进行实验测试，并通过主观评价和客观评价进行评估。客观评价包括峰值信噪比（PSNR）和运行时间的比较。相对于目前流行的一些修补方法来说，本文算法有更好的视觉效果，更高的峰值信噪比和更短的运行时间，峰值信噪比为44.79 dB，运行时间为0.53 s。结论 Thiele型修补算法更加擅长处理纹理垂直于划痕的图像，而Newton-Thiele型修补算法适用于复杂纹理的图像。

英文摘要：

Objective Image inpainting is crucial for image processing. However, image inpainting methods produce restored images with unsatisfactory textures. Therefore, to effectively maintain image textures, we propose two image inpainting algorithms based on continued fraction interpolation.Methods The proposed algorithms are based on continued fraction interpolation. The intensity of a damaged point is interpolated from the information of the surrounding pixel points. The two proposed interpolation methods are based on different interpolation functions and interpolation windows to repair different types of scratching texture images：the inpainting algorithm based, which is based on Thiele interpolation, and the inpainting algorithm, which is based on Newton-Thiele interpolation. Moreover, we propose the solutions to singular point and translation problems in interpolation.Results To demonstrate the superiority of the proposed algorithms, several experiments were conducted with scratching images. Subjective and objective evaluations were employed. The objective evaluation compared the peak signal-to-noise ratio （PSNR） and running time among algorithms. The experimental results showed that the proposed algorithms exhibited better visual effect, higher PSNR, and shorter running time than those of current popular inpainting algorithms. The PSNR of the proposed algorithm was 44.79 dB, and its running time was 0.53 s.Conclusion The proposed inpainting algorithm, which is based on Thiele interpolation, is more suitable for scratching images with perpendicular textures. By contrast, the inpainting algorithm, which is based on Newton-Thiele interpolation, is more appropriate for complex texture images.