Accurate Estimation of Single Counts from Axially Compressed Random Data

Abstract

The use of the ordinary Poisson iterative reconstruction algorithm requires the estimation of mean random counts. In a clinical environment, random data are acquired as separate scans. When axial compression (span) is used to produce projection data, the random equation is complicated by the axial rebinning of a few lines-of-response (LOR). Previously developed methods, which were designed for basic random equations as a product of single counts, are not directly applicable. The accurate estimation of single counts per crystal from random data (in the case of axial compression) is suggested. This method utilizes the fact that the border planes of the projection segments use only one axial LOR to form an axial projection plane. The Defrise method, which solves the system of nonlinear equations, is used for border planes. The next axial planes use more LORs, but the equations are linear, if crystal singles estimations are used from the previous step. Since the number of unknown singles is significantly lower than the number of random data, various systems of equations can be constructed. In this work, 2D data (segment zero) are used for random smoothing. Computer simulations are used to verify method performance.