The research focuses on considering the possibility of computational speedup during image reconstruction based on the SART algorithm through application of the nonlinear voxel grid. Motion scheme of linear tomosynthesis served as foundation, with a non-linear voxel grid being used in the reconstruction area.
The proposed method allows calculating the coefficients of the SART system matrix for only 2 planes, thus significantly reducing the computation time (up to 6-fold). Besides that, the amount of data stored decreases (approximately 295 times). This method allows performing parallel computations for each vertical layer in the reconstruction area, which provides a 10-fold gain in reconstruction rate.
The aim of tomographic synthesis is to reconstruct the internal structure of a three-dimensional object from a set of its projections in a space of smaller dimension. The foundation of the three-dimensional reconstruction is the operation of backprojection, without additional transformations; however, its result features a low contrast and is significantly blurred due to the overlap effect. The quality of reconstruction is also affected by the number of projections of the object, the range of viewing angles, and the instrumental error of the geometrical configuration of the X-ray unit upon obtaining each of the projections. This work is aimed at studying the influence of the latter factor. By instrumental error in this context, one should understand the positioning accuracy of X-ray source and detector, the projection angle, focus point positioning.
The study was carried out on a three-dimensional mathematical phantom. For the reconstruction we used the algorithm of filtered reverse projections (Feldkamp algorithm) and algebraic reconstruction algorithm (ART). In the process of reconstruction, noise with a specified RMS was added to the data reflecting the angles of obtaining the projection, as well as the position of the focus point. The result of the study are the dependences of the normalized mean square error and the normalized absolute error of reconstruction for different layers from the NMS of the introduced noise.