Image Reconstruction from Projections

Abstract

The problem of reconstructing cross-sections from their projections, using Fourier transform processing, is considered in detail and is related to problems in medical tomography. A number of equations relating cross-sections to their projections are derived, and are used as the bases for algorithms which enable cross-sections to be reconstructed from a finite number of projections. Results of computations on analytically derived and radiographically measured projections demonstrate the usefulness of these techniques. A proposal for a new type of transverse tomographic system is described. It is demonstrated that images of crosssections may be restored from tomograms produced using this system, by the use of both optical and digital processing techniques. Image reconstruction techniques using Fourier transforms are shown to be of use for reconstructing three-dimensional radio-isotope distribution~ from scintigraphic projections measured with a gamma camera.

Solar Stereoscopy and Tomography

“…The first attempts of a tomographic reconstruction of the 3D density distribution of the solar corona, based on a daily series of ground-based coronagraph images and potential-field extrapolations from magnetograms, is described in Altschuler (1979), which shows multiple coronal streamers as viewed from above the solar north pole.…”

“…The first tomographic reconstruction of the 3D density distribution of the solar corona, based on a time series of coronagraph images from Skylab in white light has been accomplished by Altschuler (1979). Tomographic inversion of coronagraph images from Mark III K-coronameter on Hawaii and from LASCO C-1 were conducted by Zidowitz et al (1996), Zidowitz (1997), and Zidowitz (1999).…”

“…The first coronal tomographic reconstructions of Altschuler (1979) from Skylab data visualized a streamer belt map from a polar viewing angle. Tomographic inversion of Mark III K-coronameter data of the minimum corona revealed pronounced longitudinal density variations in the streamer belt (Zidowitz, 1999).…”