Enhancement of Medical Images by the Paired Transform

In this paper, we discuss the application of the two-dimensional paired representation for processing medical images. This representation leads to the effective solution of the discrete as well as continuous model of image reconstruction from their projections, and to the image enhancement. These two applications can be combined in order to receive high quality images. The method of paired representation of two-dimensional (2D) images is considered with respect to the 2D discrete Fourier transform (DFT). Basis functions of the paired transformation are defined completely by parallel projections. At the same time, the paired representation describes the image as a set of short 1D real signals (splitting-signals) which completely determine the 2D DFT of the image at disjoint subsets of frequency-points. The image enhancement procedure is thus can be reduced to processing splitting-signals and such process requires only a few spectral components of the image. For instance, the traditional alpha-rooting method of image enhancement can be fulfilled through processing the splitting-signals defined for only 3N - 2 frequency-points, when the image has the size N times N, and N is a power of two. It is shown, that processing one or a few splitting signals leads to a high image enhancement.