New methods of image enhancement

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 different 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 a-rooting method and other known methods. The selection of such splitting-signals is described.