Symmetric quadratic tetration interpolation using forward and backward operation combination

Abstract

The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.