In this paper, a method for adaptive pure interpolation (PI) in the frequency domain, with gradient auto-regularization, is proposed. The input image is transformed into the frequency domain and convolved with the Fourier transform (FT) of a 2D sampling array (interpolation kernel) of initial size L rows by M columns. The inverse Fourier transform (IFT) is applied to the output coefficients and the edges are detected and counted. To get a denser kernel, the sampling array is interpolated in the frequency domain and convolved again with the transform coefficients of the original image of low resolution and transformed back into the spatial domain. The process is repeated until a maximum number of edges is reached in the output image, indicating that a locally optimal magnification factor has been attained. In a next step a maximum ascend–descend gradient auto-regularization method is designed and the edges are sharpened. For the gradient management, a new strategy is proposed, referred to as the natural bi-directional gradient field (NBGF). It uses a natural following of a pair of directional and orthogonal gradient fields. Finally we find a novel procedure based on the observation of auto-regularized gradient management (ARG) in which a direct and compact mathematical proposition is applied effectively. A development of series of derivatives constructs directly the gradient field without parameters of experimental initialization. The proposed procedure is comparable to novel algorithms reported in the state of the art with good results for high scales of amplification.