Evaluation of Estimation Method of X-ray Spectral Distribution by Attenuation Data

This paper describes a method for estimating spectral distributions from X-ray attenuation data obtained by inserting metal filters in the beam. First, the principle of the estimation method is briefly outlined. The spectral distribution is approximated by a histogram with an appropriate number of cells whose heights are estimated by recursive algorithm. The algorithm is based on a gradient method that seeks the minimum of a least-square criterion function. Next, the following two problems to which special attention should be paid in practical applications are discussed: 1) appearance of discontinuity in estimated distribution; and 2) termination criterion of iterative computation. The problem 1) is investigated theoretically and the improved algorithm is devised. Computer simulation is performed for the problem 2), and a proper termination criterion based on the decreasing curve of the least-square criterion function is given. The validity of estimation results is illustrated about the spectral distribution of 140 kV constant potential X-ray source.