Correction and Preprocessing Methods

Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia

Correction and Preprocessing Methods

Veselin Dikov

Moscow-Bavarian Joint Advanced Student School19-29. March 2006

Moscow, Russia


Outline

● Beam hardening

● Scattered radiation

● Ring artefacts

● References


Beam hardening

● Monochromatic vs. Polychromatic X-ray source● Absorption of low energy photons● Additive detector● Mean energy higher - beam hardening


Thickness measurement

rayind dsyxNN ),(exp

● Monochromatic

● Polychromatic

d

in

ray N

Ndsyx ln),(

d

in

N

Nl ln for homogenous medium

dEdsEyxESN

rayind ),,(exp)(


Thickness measurement

● “Non-linear” deviation of the polychromatic signal


Beam hardening artefacts

● Cupping● Simulated skull


Beam hardening artefacts

● Streaks● Hard (e.g. bone) tissues


Correction Strategies

● Preprocessing On projection data

● Postprocessing On reconstructed data

● Dual-energy imaging Considered most elegant


Preprocessing

● Select “appropriate” absorber

● Measured value A is corrected to A’

● Assumes “homogeneous” medium

● Fails if bone present


Postprocessing

● Iterative approach: first: preprocessing step second: threshold to identify hard structures third: forward-project the contribution of the hard

structures into projection data

● Good results


Dual-energy image

● Modeling of the attenuation coefficient

● Substitute in

● Gives

dEdsEyxESN

rayind ),,(exp)(

)(),()(),(),,( 21 EfyxaEgyxaEyx KN

ray ii

KNind

idsyxaA

dEEfAEgAESN

2,1),(

))()((exp)( 21

for , where

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f and g depend only on Eg - Photoelectronic absorptionf - Compton scatter contribution


● Two energies - two integral equations

● Reconstruct and Now can be reconstructed for any E

● Two scans?

Dual-energy image

dEEfAEgAESAAI

dEEfAEgAESAAI

KN

KN

))()((exp)(),(

))()((exp)(),(

212212

211211

),(1 yxa ),(2 yxa

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single scan with:- split detectors- changing tube voltage in alternating projections


Outline

● Beam hardening


● Ring artefacts

● References


Scattered radiation

● Scattered radiation● Components of

scatter Off-focus radiation

(OFR) Scattered radiation in

the patient Veiling glare

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3G vs 4G


Scatter measure

● SPR – Scatter-to-Primary-Ratio● Broad beam model estimation for SPR

22

222 12sR

sRLRLLSPR st

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dependence of SPR on thickness, air gap, beam width, so on


Scatter artefacts – loss of contrast

● Loss of contrast Contrast without scatter

Contrast with scatter

SPRe

SPRC

bb t

)(

1ln

bb tC )(


Scatter artefacts – loss of sharpness

● Loss of sharpness Transmitted radiation

- blurring kernel - 2D convolution

srpt III

srpsr hISPRI

srh

dudvvyuxhvugyxhg ),(),(),)((


Scatter artefacts – loss of sharpness

● Loss of sharpness Veiling glare contribution

vgttd hIII )1(

vgsrppsrppd hhISPRIhISPRII )())(1(

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weighted applying of two blurring kernels - all we need to know


Scatter reduction methods

●Anti-scatter grids 4G vs. 3G Higher voltage

●Air gaps Magnifying effects Increased blurring

●Beam collimation Complicated systems

22

222 12sR

sRLRLLSPR st

reminder:


Measurement of scatter

● Opaque disc techniques Scatter in the “shadow” Arrays of discs with decreasing size

● Aperture techniques Narrow beam “clean” of scatter Arrays of apertures

● Hybrid techniques● One vs. Two scan techniques


Correction schemes - Convolution Filtering

● Detected image

● Use as an estimation for

● Spatial vs. frequency domain filtering● Analytical vs. empirical approaches for filtering

schemes

sppspd hISPRIIII

spdp hISPRII

dI pI

)( sddp hIWII


Correction schemes – Scatter sampling

●Sampling of the scatter measurement Opaque discs arrays Aperture grid

●Interpolation of the smooth surface -6 dB

vgsrppsrppd hhISPRIhISPRII )())(1(


Correction schemes – Scatter sampling

●Interpolation schemes 2D least squares fitting Filtration with sinc and

jinc 2D polynomial fitting 2D bicubic splines

●Sampling rate depends on surface frequencies

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least squares - 15 % error on the pointsFiltration - aliasing artefactspolinomial - fine up-to 5x5 sample (6-deg poly)spline - fine for any sample size


Results


Outline

● Beam hardening


● Ring artefacts

● References


Ring artefacts


Ring Artefacts

● Reason

● 4G vs. 3G

● Postprocessing correction only


Correction scheme

1. ROI

2. I P

3. Artefact pattern

4. Artefact subtraction

5. P I


ROI

● Select ROI with morphological operations


Find artefact pattern

● Scan for irregularities Use variance of signal or Use median of signal etc.

● Extract ring pattern


Results


References

● T.Buzug, Einfürung in die Computertomographie, Springer-Verlag (2004)● A.Kak and M.Slaney, Principles of Computerized Tomographic Imaging,

IEEE Press (1988)● K.P.Maher and J.F. Malone, Computerized scatter correction in diagnostic

radiology, Contemporary Physics 38, 131-148 (1997).● J.Sijbers and A.Postnov, Reduction of ring artefacts in high resolution

micro-CT reconstructions, Physics in Medicine and Biology Vol. 49 (07/2004)

● M.Zellerhoff et al, Low contrast 3D-reconstruction from C-arm data, Medical Imaging SPIE, 646-655 (04/2004)

Thank you for your attention!

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Correction and Preprocessing Methods