Few-Projection Tomography. I. Radio-Astronomical Approach for the Problem and the 2-CLEAN DSA Method

We develop the radio-astronomical approach for solving the few-projection tomography problem. It is shown that the 2-CLEAN DSA method proposed for determination of the permissible solution area is an efficient way for solving this problem. The method is based on solving the deconvolution problem with allowance for the synthesized beam or the synthesized Green's function. The distortions due to the sidelobe responses of the synthesized transfer function are eliminated by using two realizations of the well-known iterative radio-astronomical CLEAN algorithm with nonlinear constraints. The proposed 2-CLEAN DSA method allows one to decrease the number of projections required for two-dimensional reconstruction by a factor of about 10 as compared with the conventional tomography approach, provided that a wide spatial-frequency spectrum limited from above is reconstructed. The method can easily be adapted to introducing additional constraints. Examples of astrotomography reconstruction are presented. We show that the proposed method is promising for a large number of remote sensing applications and compare it with other well-known reconstruction techniques. The papers by radio astronomers, who contributed significantly to the development of components of the method, are pointed out.