Decomposition of multi-energy scan projections using multi-step fitting

A method for decomposition of projection data acquired by scanning a set of objects using at least two x-ray spectra, said projection data including low energy projection data (PL) and high energy projection data (PH), said method comprising:

• A. performing a calibration procedure using at least some simulated data or measured data or a combination of simulated and measured data, including:
• i. generating low energy iso-transmission contours for known values of PL and high energy iso-transmission contours for known values of PH;
• ii. generating a polynomial gL that represents the shape of the low energy iso-transmission contour for each PL, wherein gL includes a set of coefficients gLi determined at said known values of PL;
• iii. generating a polynomial gH that represents the shape of the high energy iso-transmission contour for each PH, wherein gH includes a set of coefficients gHi determined at said known values of PH;
• iv. generating polynomials hL that represents the variation of the coefficients of the polynomial gL as a function of PL;
• v. generating polynomials hH that represents the variation of the coefficients of the polynomial gH as a function of PH;
• vi. determining the minimum and maximum values of PH for each transmission line corresponding each PL;
• vii. generating a polynomial mH that represents the variation of the minimum value of PH as a function of PL;
• and
• viii. generating a polynomial nH that represents the variation of the maximum value of PH as a function of PL;
• B. solving the projections PL and PH to determine a photoelectric line integral (Ap) component of attenuation and a Compton line integral (Ac) component of attenuation of the set of scanned objects using a multi-step fitting procedure, including:
• i. computing the values of each coefficient gLi using a polynomial function hLi(PL) and computing the values of each coefficient gHi using a polynomial function hHi(PH);
• and
• ii. determining Ac and Ap as a function of PL and PH, using the coefficients of gL and the coefficients of gH;
• and
• C. reconstructing a Compton image Ic and a photoelectric image Ip from Ac and Ap.

A system for decomposing projection data for a set of scanned objects acquired using at least two x-ray spectra, said system comprising:

• A. media for storing low energy projection data (PL) and high energy projection data (PH);
• B. a decomposition module configured to determine a photoelectric line integral (Ap) component of attenuation and a Compton line integral (Ac) component of attenuation for PL and PH using multi-step fitting;
• and
• C. an image construction module configured to construct a Compton image (Ic) and a photoelectric image (Ip) from the Ap and Ac.

A system for decomposing projection data for a set of scanned objects acquired using at least two x-ray spectra, said system comprising:

• A. media for storing low energy projection data (PL) and high energy projection data (PH);
• B. a calibration module configured to calibrate the decomposition module using at least some simulated data or measured data or a combination of simulated and measured data, and configured to:
• i. generate a low energy iso-transmission contour corresponding to PL and a high energy iso-transmission contour corresponding to PH;
• ii. generate a polynomial gL that represents the shape of the low energy iso-transmission contour, wherein gL includes a set of coefficients gLi determined at said known values of PL;
• iii. generate a polynomial gH that represents the shape of the high energy iso-transmission contour, wherein gH includes a set of coefficients gHi determined at said known values of PH;
• iv. generate polynomials hL that represents the variation of the coefficients of the polynomial gL as a function of PL;
• v. generate polynomials hH that represents the variation of the coefficients of the polynomial gH as a function of PH;
• vi. determine the minimum and maximum values of PH for each transmission line corresponding each PL;
• vii. generate a polynomial mH that represents the variation of the minimum value of PH as a function of PL;
• and
• viii. generate a polynomial nH that represents the variation of the maximum value of PH as a function of PL;
• C. a decomposition module configured to determine a photoelectric line integral (Ap) component of attenuation and a Compton line integral (Ac) component of attenuation for PL and PH using multi-step fitting, and configured to:
• i. compute the values of each coefficient gLi using a polynomial function hLi(PL) and to compute the values of each coefficient gHi using a polynomial function hHi(PH);
• and
• ii. determine Ac and Ap as a function of PL and PH using the coefficients of gL and the coefficients of gH;
• and
• D. an image reconstruction module configured to reconstruct a Compton image (Ic) and a photoelectric image (Ip) from the Ap and Ac.