Incremental backprojection algorithm: modification of the searching flow scheme and utilization of the relationship among projection views

A two-dimensional (2-D) search flow scheme is proposed for the incremental backprojection algorithm. In this scheme, the searching direction in a beam is determined only by the distance from the current pixel to the corresponding ray; no pixels outside the beam are involved in the procedure. In addition, the geometrical relationships between the image grids and the projection rays in different views are fully exploited to further reduce the search operations. It is found that backprojection of four views can be performed at the same time, and the search operation is only required for one of them if the number of views is even. Thus, backprojection is accomplished on a quartet-by-quartet of views basis as well as on beam-by-beam basis. These approaches not only minimize the number of search operations but also possess a simple algorithm structure. Implementation results obtained with an AST-386 computer for the incremental backprojection algorithm using this search flow scheme and the relationship among projection views show that the processing time can be reduced by a factor of about 2.