8: Honochranatlc case where H, and H p are the Compton and photoelectric coefficients of the material being measured, expressed in Hounsfield units. The parameter Q, called spectral factor, depends only upon the X-ray spectrum used and may be obtained by performinga scan on acalibratingmaterial. A noteworthy feature of H, and H p is that they are both energy independent. Fig. 10. (a)Reconstructionfrompolychromaticprojection data ofa waterphantominsidea skull. Notethewhitening effect near the Equation (31) leads to the important result that if two difA quantitativeillustration of the effect in(a). Curve A ferent C images are reconstructed using two different incident skull. (b)thereconstructedvalues T represents on the middle horizontal line spectra (resulting in two different values of Q ), from the re(a): Curve E represents reconstructed the values on the same lme w t h monochromatic X-rays. sulting two measured Hounsfield units for a given point in the cross section, one may obtain H, and H p leading to a degree ofchemical identification of the material at that point. Inwas done stead of performing two different scans, one may also per- Phelps e t al.[981.Reconstructionfromthisdata using the filtered backprojection algorithm (Section 11-A) form only one scan with split detectors for this purpose[20]. with 10 1 projections and 101 parallel rays in each projection. C. Polychromaticity Artifacts in X-Ray CT Notethe"whitening"effect near the skull in Fig. lO(a). This is more quantitatively illustrated in Fig. 10(b) where the Beam hardening artifacts, whose cause was given above, are most noticeable in the CT images of the head, andinvolve two elevationof the reconstructed values near the skullboneis different types of distortions. Many investigators[ 151,[461, quite evident. When CT imaging was in itsinfancy this whiten[ 541,[go] have shown that beam hardening causes an eleva- ing effect used t o be mistaken for gray matter of the cerebral wehave also shown in Fig. 10(b) tionin CT numbersfor tissues close to the skull bone. To cortex.Forcomparison, illustrate t i artifact we have presented in Fig. 10 computer the reconstructed values obtained when the projectiond
ata hs simulation reconstructions of a water phantom inside a skull. was generated for monochromatic X-rays. The other artifact caused by polychromaticity is theappearThe projection data was generated on the computerusing Epp and Weiss[ 5 1] 105 keVp X-ray tube spectrum(Fig. 9). The en- ance of streaks and flares in the vicinity of thick bones and ergy dependence of the attenuation coefficients of the skull between bones[SO],[781,[831. (Note that streaks can also bone was taken from theICRU report[ 731 and of water from be caused by aliasing 121 I,[421.) This artifact is illustrated in
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PROCEEDINGS OF THE IEEE, VOL. 67, NO. 9, SEPTEMBER 1979Ideal case
(no beam hardening)
case
Thickness o f a homDgencous absorber
Fig. 12. The solid curve shows that the experimental measurement o f a ray integral depends nonlinearly on the thickness o f a homogeneous absorber.
cessing of the projection data and 2) postprocessing of the reconstructed image. Preprocessing techniques are based on the following rationale. If the assumption of the photons being monoenergetic was indeed valid, a ray integral would then be given by (25). For a homogeneous absorber of attenuation coefficient p this implies
(b) Fig. 1 1 . (a) Reconstruction frompolychromatic projection data o f a phantom that consists o f a skull with.four circular bones inside. The rest of the“tissue” inside the skull is water. The dark and wide streaks are caused by polychromaticity the of X-rays. (b)Reconstruction of the same phantom as in (a) from projections generated with monochromatic X-rays. The variations in the gray levels outside t o bone areas within the skull are less than 0.1 percent of the mean value. The image was displayed with a narrow window t o bring out these variations. Note the absence of dark streaks present in (a).
Fig. 11. The phantom used is a skull with water and four circular bones inside. Polychromaticprojectiondata was generated as before using the105 keVp X-ray spectrum. The reconstruction using this data is shown in Fig. 1l(a) with the same number of rays andprojections as before. Note the wide dark streaks between the bones inside the skull. Compare this image with the reconstruction shown in Fig. 1l(b) for the case when the X-rays are monochromatic. In X-ray CT of the head similar dark and wide streaks appearin those cross sections that include the petrous bones, andaresometimes called the interpetrouslucency artifact. Various schemes have been suggested for making these artifacts less apparent. These fall into two categories: 1) prepro-
where I is the thickness of the absorber. This equation says that under ideal conditionsthe experimental measurement ln(Nin/Na) should belinearly proportional to the absorber thickness. This is depicted in Fig. 12. However, under actual conditions a result like