Decomposition by series direction images: image reconstruction and enhancement
Artyom M. Grigoryan · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
In this paper, we focus on the effective representation of the image, which is called the paired representation and reduces the image to the set of independent 1-D signals and splits the 2-D DFT into a minimal number of 1-D DFTs. The paired transform is a frequency and time representation of the image. Splitting-signals carry the spectral information in disjoint subsets of frequencies, which allows for enhancing the image by processing splitting-signals separately and changing the resolution of periodic structures composing the image. We present a new effective formula for the inverse 2-D paired transform, which can be used for solving the algebraic system of equations with measurement data for image reconstruction without using the Fourier transform technique. The image is reconstructed directly from the splitting-signals which can be calculated from projection data. The same inverse formula can be used for image enhancement, such as the known method of α-rooting. A new concept of direction images is introduced, that define the decomposition of the image by directions.