Few-Projection Tomography. II. Radioastronomical Method CLEAN for Three-Dimensional Problems

The radioastronomical method CLEAN is extended to problems of three-dimensional (3D) tomographic reconstruction. We consider two options, namely, 3D1D (reconstruction using one-dimensional projections) and 3D2D (reconstruction based on using two-dimensional projections). Deconvolution with the use of the synthesized beam (equivalent total transfer function) makes it possible to reduce several times the number of aspects in comparison with the conventional approach. We point out the relationship between the maximum level of sidelobes of the synthesized ray constructed for the Gaussian transfer functions and the number of used projections. In the case of 3D2D-reconstruction, the reconstruction quality similar to that for the 2D1D case is only achieved if the same number of uniformly distributed projections are used in both cases. The use of one-dimensional projections for the 3D1D-reconstruction requires doubling of the number of projections. The reconstruction process is illustrated by an example of the three-dimensional model of an optically thin radiating object. We consider the possibilities of using the developed approach in astrotomography and remote sensing based on introducing the transfer functions which determine resolution of the receiving beam patterns and spectrographs, as well as temporal resolution of the sensing profiles.