ABSTRACT

This chapter discusses the decomposition of the image by direction images, which is based on the concept of the tensor representation and its advanced form, the paired representation. The tensor and paired representations in the frequency-and-time domain define the image as a set of 1-D splitting-signals. Each of such splitting-signals is calculated as the sum of the image along the parallel lines, and it defines the direction image as a component of the original image. The unique decomposition of the image by direction images is described and formulas for the inverse tensor and paired transforms are given. These formulas can be used for image reconstruction from projections. The number of required projections is uniquely defined by the tensor representation of the image. The chapter describes the system of basic functions of the inverse tensor transform, and shows how to calculate these functions by the basic functions of the tensor transform.