Fabrication of independent virtual lines for reconstruction of 2D source distribution with high spatial resolution equal to that of limited projections

Abstract

In order to improve the quality of tomography reconstruction for ill-posed problems with limited projections, a new idea of fabricating virtual lines of sight which are consistent with, but not lineally dependent on, the measured lines of sight is proposed in this paper. Using a scheme of equilateral triangle plane meshes whose edge length equals twice the width of the lines of sight, based on the spatial continuity of the source term distribution, some independent virtual lines of sight are fabricated by an interpolation method described in this paper. Non-negative linear least squares method is used to solve the reconstruction problem. As the times of interpolation for virtual lines approach a critical level (it is 6 for the case in this paper) the condition number of the matrix of the forward problem drops obviously, indicating that the independent interpolation method may effectively overcome the `ill-posed-ness' of the problem. Accordingly, if the times of interpolation for virtual lines are less than the critical level, the shape of the assumed source distribution, obviously could not be reconstructed; as the times of interpolation become larger than the critical level, the shape of the assumed source distribution has been recovered visually. With 10 times of interpolation for virtual lines, most of the relative errors near the four peaks are below 10 %, thus the effectiveness of the interpolation method is reasonably verified. In addition, the reconstruction method has good noise immunity.