Comparison of doubling the size of image algorithms

In this paper the comparative analysis for quality of some interpolation non-adaptive methods of doubling the image size is carried out. We used the value of a mean square error for estimation accuracy (quality) approximation. Artifacts (aliasing, Gibbs effect (ringing), blurring, etc.) introduced by interpolation methods were not considered. The description of the doubling interpolation upscale algorithms are presented, such as: the nearest neighbor method, linear and cubic interpolation, Lanczos convolution interpolation (with $a=1, 2, 3$), and $17$-point interpolation method. For each method of upscaling to twice optimal coefficients of kernel convolutions for different down-scale to twice algorithms were found. Various methods for reducing the image size by half were considered the mean value over $4$ nearest points and the weighted value of $16$ nearest points with optimal coefficients. The optimal weights were calculated for each method of doubling described in this paper. The optimal weights were chosen in such a way as to minimize the value of mean square error between the accurate value and the found approximation.
A simple method performing correction for approximation of any algorithm of doubling size is offered. The proposed correction method shows good results for simple interpolation algorithms. However, these improvements are insignificant for complex algorithms ($17$-point interpolation, Lanczos $a=3$). According to the results of numerical experiments, the most accurate among the reviewed algorithms is the $17$-point interpolation method, slightly worse is Lanczos convolution interpolation with the parameter $a=3$ (see the table at the end).