Fourier Reconstruction of Functions from their Nonstandard Sampled Radon Transform

Signal reconstruction from Fourier transform sign information

3D Fourier based discrete Radon transform

The Radon transform is a fundamental tool in many areas. For example, in reconstruction of an image from its projections (CT scanning). Recently A. Averbuch et al. [SIAM J. Sci. Comput., submitted for publication] developed a coherent discrete definition of the 2D discrete Radon transform for 2D discrete images. The definition in [SIAM J. Sci. Comput., submitted for publication] is shown to be ...

Sampled fourier transform hologram generated by computer.

A technique to determine a real nonnegative function representing the transmittance of a synthesized hologram is described. The technique uses the positions of the samples in the synthesized hologram to record the phase information of a complex wavefront. Synthesized holograms are displayed on a flying spot scanner and recorded on film. The transmittance of the synthesized hologram is quantized...

Reconstruction of Scalar and Vector Fields from Their Attenuated Radon Transform

In this paper we derive explicit inversion formulas for recovering scalar and vector fields supported on the unit disk from their 2D attenuated Radon transform in the framework of the fan-beam scanning geometry. The attenuation function is supposed to be known (from additional transmission measurements, for instance). It is known that in the vector case the kernel of the (unattenuated) Radon tr...

trace reconstruction by parabolic radon transform

due to some difficulties during seismic data acquisition, like natural obstacles (high voltage electricity cable, bad coupling of geophones with the ground) some of the traces cannot be recorded. since bad traces make the final stack unclear, usually bad traces go mute while processing. the final image of the earth’s crust is highly dependent of the quality and resolution of acquired data and m...