In this paper, applications of the tensor and paired representations of an image are presented for image enhancement. The proposed methods are based on the fact that the 2-D image can be represented by a set of 1-D "independent" signals that split the 2-D discrete Fourier transform (DFT) of the image into different groups of frequencies. Each splitting-signal carries information of the spectrum in a specific group. Rather than enhance the image by traditional methods of the Fourier transform (or other transforms), splitting-signals can be processed separately and the 2-D DFT of the processed image can be defined by 1-D DFTs of new splitting-signals. The process of splitting-signals related to the paired representation is very effective, because of no redundancy of spectral information carrying by ifferent splitting-signals. The effectiveness of such approach is illustrated through processing the image by the a-rooting method of enhancement. Images can be enhanced by processing only a few splitting-signals, to achieve enhancement that in many cases exceeds the enhancement by the α-rooting method and other known methods. The selection of such splitting-signals is described.