The Construction Of Vector Valued Interpolants By Multi-branched Continued Fractions And Applications In The Image Zooming

Vector valued rational interpolation (i.e. vector rational interpolation, hereinafter) issue was proposed by Wynn in 1963, when he noticed that by adopting e algorithm and implementing Samelson inverse on a vector, one could obtain the same accurate result as the scalar method did. Since 1983, Graves-Morris has done some research about univariate vector valued rational interpolation under practical application background (such as machine vibration data analysis and so forth) and established a few methods about interpolation. Vector valued rational interpolation is now extended to some cases in which multiple variables are involved and some significant results are obtained. As for the image zooming, the following interpolation methods are usually adopted: (1) nearest neighborhood interpolation; (2) bilinear interpolation; (3) cubic B-spline interpolation; (4) general bicubic spline interpolation; (5) adaptive interpolation; (6) wavelet interpolation; (7) fractal interpolation. The first four interpolation methods are developed fully and have been applied to many image processing softwares, while the remainders bear some shortcomings and call for further investigation.In this thesis, we focus our attention on introducing the methods and theory related to multivariate vector valued branched continued fractions, and providing corresponding construction method and characteristic theorem on the basis of principal theory of continued fractions. Finally, we apply the bivariate vector valued rational interpolation to the image zooming successfully. The method presented in this thesis has considerable merits in reserving the sharpness of the image.