An X-ray spectrum estimation method from transmission measurement combined with scatter correction

Published:April 23, 2021DOI:


      • This study aims to apply the scatter correction in x-ray spectrum estimation.
      • Unknown x-ray spectrum can be successfully estimated using the proposed method.
      • Scatter correction helps to estimate a more accurate spectrum.
      • The proposed method has potential in several diagnostic x-ray imaging applications.



      Conventional x-ray spectrum estimation methods from transmission measurement often lead to inaccurate results when extensive x-ray scatter is present in the measured projection. This study aims to apply the weighted L1-norm scatter correction algorithm in spectrum estimation for reducing residual differences between the estimated and true spectrum.


      The scatter correction algorithm is based on a simple radiographic scattering model where the intensity of scattered x-ray is directly estimated from a transmission measurement. Then, the scatter-corrected measurement is used for the spectrum estimation method that consists of deciding the weights of predefined spectra and representing the spectrum as a linear combination of the predefined spectra with the weights. The performances of the estimation method combined with scatter correction are evaluated on both simulated and experimental data.


      The results show that the estimated spectra using the scatter-corrected projection nearly match the true spectra. The normalized-root-mean-square-error and the mean energy difference between the estimated spectra and corresponding true spectra are reduced from 5.8% and 1.33 keV without the scatter correction to 3.2% and 0.73 keV with the scatter correction for both simulation and experimental data, respectively.


      The proposed method is more accurate for the acquisition of x-ray spectrum than the estimation method without scatter correction and the spectrum can be successfully estimated even the materials of the filters and their thicknesses are unknown. The proposed method has the potential to be used in several diagnostic x-ray imaging applications.


      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


      Subscribe to Physica Medica: European Journal of Medical Physics
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • DeMarco J.J.
        • Cagnon C.H.
        • Cody D.D.
        • Stevens D.M.
        • McCollough C.H.
        • O'Daniel J.
        • et al.
        A Monte Carlo based method to estimate radiation dose from multidetector CT (MDCT): Cylindrical and anthropomorphic phantoms.
        Phys Med Biol. 2005; 50: 3989-4004
        • Jia X.
        • Gu X.
        • Graves Y.J.
        • Folkerts M.
        • Jiang S.B.
        GPU-based fast Monte Carlo simulation for radiotherapy dose calculation.
        Phys Med Biol. 2011; 56: 7017-7031
        • Christ G.
        Exact treatment of the dual-energy method in CT using polyenergetic x-ray spectra.
        Phys Med Biol. 1984; 29: 1501-1510
        • Kim G.
        • Park S.
        • Park C.
        • Kang S.
        • Kim K.
        • Cho H.
        • et al.
        Projection-based dual-energy digital tomosynthesis and its image characteristics.
        Instrum Sci Technol. 2019; 47: 248-263
        • Chang S.
        • Li M.
        • Yu H.
        • Chen X.i.
        • Deng S.
        • Zhang P.
        • et al.
        Spectrum estimation-guided iterative reconstruction algorithm for dual energy CT.
        IEEE Trans Med Imaging. 2020; 39: 246-258
        • Beam C.
        • Hsieh J.
        • Molthen R.
        • Dawson C.A.
        • Johnson R.H.
        An iterative approach to the beam hardening.
        Med Phys. 2000; 27: 23-29
        • Jin P.
        • Bouman C.A.
        • Sauer K.D.
        A model-based image reconstruction algorithm with simultaneous beam hardening correction for X-Ray CT.
        IEEE Trans Comput Imaging. 2015; 1: 200-216
        • Long Y.
        • Fessler J.A.
        Multi-material decomposition using statistical image reconstruction for spectral CT.
        IEEE Trans Med Imaging. 2014; 33: 1614-1626
        • Liu X.
        • Chen H.
        • Bornefalk H.
        • Danielsson M.
        • Karlsson S.
        • Persson M.
        • et al.
        Energy calibration of a silicon-strip detector for photon-counting spectral CT by direct usage of the X-ray tube spectrum.
        IEEE Trans Nucl Sci. 2015; 62: 68-75
        • Fritz S.G.
        • Shikhaliev P.M.
        • Matthews K.L.
        Improved x-ray spectroscopy with room temperature CZT detectors.
        Phys Med Biol. 2011; 56: 5735-5751
        • Tucker D.M.
        • Barnes G.T.
        • Chakraborty D.P.
        Semiempirical model for generating tungsten target x-ray spectra.
        Med Phys. 1991; 18: 211-218
        • Boone J.M.
        • Seibert J.A.
        An accurate method for computer-generating tungsten anode x-ray spectra from 30 to 140 kV.
        Med Phys. 1997; 24: 1661-1670
        • Gallardo S.
        • Ródenas J.
        • Verdú G.
        Monte Carlo simulation of the Compton scattering technique applied to characterize diagnostic x-ray spectra.
        Med Phys. 2004; 31: 2082-2090
        • Maeda K.
        • Matsumoto M.
        • Taniguchi A.
        Compton-scattering measurement of diagnostic x-ray spectrum using high-resolution Schottky CdTe detector.
        Med Phys. 2005; 32: 1542-1547
        • Silberstein L.
        Determination of the spectral composition of X-ray radiation from filtration data*.
        J Opt Soc Am. 1932; 22: 265-280
        • Sidky E.Y.
        • Yu L.
        • Pan X.
        • Zou Y.u.
        • Vannier M.
        A robust method of x-ray source spectrum estimation from transmission measurements: Demonstrated on computer simulated, scatter-free transmission data.
        J Appl Phys. 2005; 97: 124701
        • Lin Y.
        • Ramirez-Giraldo J.C.
        • Gauthier D.J.
        • Stierstorfer K.
        • Samei E.
        An angle-dependent estimation of CT x-ray spectrum from rotational transmission measurements.
        Med Phys. 2014; 41: 062104
        • Duan X.
        • Wang J.
        • Yu L.
        • Leng S.
        • McCollough C.H.
        CT scanner x-ray spectrum estimation from transmission measurements.
        Med Phys. 2011; 38: 993-997
        • Juste B.
        • Morató S.
        • Miró R.
        • Prieto A.I.
        • Verdú G.
        • Genoves R.
        • et al.
        Development of a reconstruction methodology for the X-Ray spectrum of a medical LinAc positioning flat panel.
        Radiat Phys Chem. 2020; 167: 108307
        • Zhao W.
        • Niu K.
        • Schafer S.
        • Royalty K.
        An indirect transmission measurement-based spectrum estimation method for computed tomography.
        Phys Med Biol. 2015; 60: 339-357
        • Zhao W.
        • Xing L.
        • Zhang Q.
        • Xie Q.
        • Niu T.
        Segmentation-free x-ray energy spectrum estimation for computed tomography using dual-energy material decomposition.
        J Med Imaging. 2017; 4: 023506
        • Floyd E.
        • Beatty P.T.
        • Ravin C.E.
        Scatter compensation in digital chest radiography using Fourier deconvolution.
        Invest Radiol. 1989; 24: 30-33
        • Ducote J.L.
        • Molloi S.
        Scatter correction in digital mammography based on image deconvolution.
        Phys Med Biol. 2010; 55: 1295-1309
        • Zbijewski W.
        • Beekman F.J.
        Efficient Monte Carlo based scatter artifact reduction in cone-beam micro-CT.
        IEEE Trans Med Imaging. 2006; 25: 817-827
        • Jia Feng S.S.
        • Sechopoulos I.
        A software-based x-ray scatter correction method for breast tomosynthesis.
        Med Phys. 2011; 38: 6643-6653
        • Kim K.
        • Kang S.
        • Kim W.
        • Park C.
        • Lee D.
        • Cho H.
        • et al.
        A new software scheme for scatter correction based on a simple radiographic scattering model.
        Med Biol Eng Comput. 2019; 57: 489-503
      1. Boyd S. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. now Publishers Inc, 2010
      2. Cranley K, Gilmore BJ, Fogarty GWA, Desponds L. IPEM Report 78: Catalogue of diagnostic x-ray spectra and other data. 1997.

      3. Hubbell JH, Seltzer SM. NIST Standard Reference Database 126. Gaithersburg, MD Natl Inst Stand Technol 1996.