A new rational bi-quartic spline interpolation scheme is constructed in this study. This rational bi-quartic spline has six free parameters that can be used to refine the final interpolating surface. The degree of smoothness attained is C1 continuity. Image interpolation is one of the methods in image processing that is used to rescale the images, either downscaling or upscaling. The proposed rational bi-quartic spline will be used to interpolate the missing pixel in image interpolation. We employ an algorithm that will speed up the process as well as be able to produce the quality upscaling images. We measure the quality of the proposed method by calculating peak-signal-to-noise-ratio (PSNR). Based on numerical comparison, the proposed scheme gives higher PSNR (consequently smaller RMSE) unlike some existing schemes. Thus, the new rational bi-quartic spline with six parameters is better than the existing scheme via an efficient algorithm. All numerical simulations and graphical results are presented using MATLAB.

中文翻译：

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用于表面插值的六参数有理双四次样条在图像放大中的应用

本研究构建了一种新的有理双四次样条插值方案。这个有理双四次样条具有六个自由参数，可用于细化最终的插值曲面。获得的平滑度是 C1 连续性。图像插值是图像处理中的一种方法，用于重新缩放图像，缩小或放大。提出的有理双四次样条将用于在图像插值中对丢失的像素进行插值。我们采用了一种算法，可以加快过程并能够生成高质量的图像。我们通过计算峰值信噪比（PSNR）来衡量所提出方法的质量。基于数值比较，与一些现有方案不同，所提出的方案提供更高的 PSNR（因此更小的 RMSE）。因此，具有六个参数的新有理双四次样条通过有效算法优于现有方案。所有数值模拟和图形结果均使用 MATLAB 呈现。