Reconstruction of x-ray images into basis function components using multiple-energy sources

A method of operating an inspection system adapted to acquire an array of measurements, each measurement representative of a region of a plurality of regions of an item under inspection, the method comprising:

• a) moving the item under inspection relative to an X-ray data acquisition system to acquire the array of measurements;
• b) with a computer, forming an array of computed values, each computed value representative of a region of the plurality of regions, the array formed according to a method:
• i) comprising, for each measurement, computing a plurality of weighting coefficients, the weighting coefficients computed so that the measurement is represented by a combination of a plurality of basis functions, each of the basis functions being weighted in the combination by a respective weighting coefficient of the plurality of weighting coefficients;
• ii) wherein:
• A. the plurality of basis functions comprises at least three basis functions, each basis function defining a relationship between a measured parameter and a parameter of operation of the X-ray data acquisition system;
• and
• B. each computed value in the array of computed values comprises a weighting coefficient computed for a measurement in the array of measurements, the weighting coefficients in the array being computed for the same basis function of the plurality of basis functions;
• c) making an inspection decision concerning the item under inspection based at least in part on the at least one array of computed values.