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. 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. 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. 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.