New formula for image reconstruction from projections by the 2-D paired transformation

To solve the problem of image reconstruction from projections, we describe an effective representation of the image by the paired transform which is a frequency and time representation of 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 calculating the Fourier transforms. The image is reconstructed directly from the paired image-signals which can be calculated from projection data. A new concept of direction images is introduced, that define the decomposition of the image by directions. The proposed method of image reconstruction has been implemented and applied for modeled images of sizes up to 256 × 256.