Dual Energy

Introduction

• Reduce false alarms from EDS using dual energy techniques

• Use density and (effective) atomic number to identify harmful objects

• Limitations include : approximation error, boundary constraints, image artifacts, x-ray spectral drift

Overview of dual-energy

• μ(x, y, z, E) = ac(x, y, z)fKN(E) + ap(x, y, z)fp(E)

Compton scatterphotoelectric effect

• fP(E) = E^-3 and fKN(E) is the Klein-Nishina cross section

• 2 logarithmic projects are then found, pL, pH

• Atomic number is then calculated

CDM (Constrained Decomposition Method)

Goal: decompose the dual energy projection PL and PH into AC (Compton projection) and AP (photoelectronic projection)

Problem: find (AC, AP) = arg min (PL (AC, AP) - PL)^2 + (PH (AC, AP) - PH)^2s.t. AC >= 0, AP >= 0

CDM vs. indirect polynomial approximation Method (AM)Approach

Results: Error percentage was calculated for both methods

CDM error is due to numerical errorAM error is due to the approximation error

Conclusion: AM should not be used for dual energy CT due to the big dynamic range of photoelectronic coefficients

AC AM

AM 1.5% 238.25%

CDM 0.00008% 0.0002%

14,400 (AC, AP) calibration points generated

(PL , PH) calculated for each (AC, AP)

calibration points reduced by 8,997 by setting max bound

Solved 8,997 linear equations for AMfor 16 polynomial coefficients

Newton – Raphson for CDM method was used

CDM vs. Truncation Method for handling the Boundary Conditions (TM)

Approach:

Results: Number of error cases : TM – 6,355 cases, CDM – 3,119 cases

Scatter CorrectionResults:

random (AC, AP) pairs were generated

(PL , PH) calculated for each (AC, AP)

noise modeled by Poisson process was added

TM used 2D Newton –Raphson iterative method to solve for (AC, AP)

100,000 truncation cases were identified

Destreaking

Spectral Correction

DISCUSSION

•Constrained decomposition algorithm•Spectral correction algorithm•Adaptive scatter collection algorithm

Limitations:

•Conversion gain factor and charge collection efficiency different for high and low energy x-ray data - correction operations include offset, air and monitor correction -noise in the photoelectric image compensated by destreaking algorithm and adaptive filters

Dual energy CT scanner used in this paper passes the TSA explosive detection certification test