simple sinogram interpolation

adds new projections to a sparse sinogram, improves the quality of the tomographic reconstruction

When only few projection images are taken with a sparse angular sampling around the object undergoing X-ray tomography, sinogram interpolation (impingement) can be used to treat the sparse sinogram and produce a denser sinogram with an impact on the quality of the reconstructed slice. In simple words, new projections are generated within the range of the set of available projections.
The present code considers a sparse tomographic acquisition with only 45-projections (theta = 0:4:176) or 90-projections (theta = 0:2:178) and interpolates to produce 180 projections (theta = 0:1:179). (We assume a monochromatic beam: projection at 0 degrees == projection at 180 degrees)
The code assumes that the few (experimental) projections are true & reliable tomographic data, uses the back projection of the sparse sinogram to reconstruct a poor quality tentative slice and uses the slice forward-projection to generate a denser synthetic sinogram. The few experimental data replaces the correspondent columns of the computed synthetic sinogram. The dense sinogram resulting from the ‘implant’ gives a slice-image quality better than that from the sparse sinogram.
The Structural Similarity Index and the Mean-Squared Error computed with respect to a reference image (target slice) computed via filtered back projection of a dense sinogram (180 projections) or with respect the phantom show that the simple ‘interpolation’ improves the slice quality.