correction and preprocessing methods
DESCRIPTION
Correction and Preprocessing Methods. Veselin Dikov Moscow-Bavarian Joint Advanced Student School 19-29. March 2006 Moscow, Russia. Outline. Beam hardening Scattered radiation Ring artefacts References. Beam hardening. Monochromatic vs. Polychromatic X-ray source - PowerPoint PPT PresentationTRANSCRIPT
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
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Outline
● Beam hardening
● Scattered radiation
● Ring artefacts
● References
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Beam hardening
● Monochromatic vs. Polychromatic X-ray source● Absorption of low energy photons● Additive detector● Mean energy higher - beam hardening
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Thickness measurement
rayind dsyxNN ),(exp
● Monochromatic
● Polychromatic
d
in
ray N
Ndsyx ln),(
d
in
N
Nl ln for homogenous medium
dEdsEyxESN
rayind ),,(exp)(
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Thickness measurement
● “Non-linear” deviation of the polychromatic signal
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Beam hardening artefacts
● Cupping● Simulated skull
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Beam hardening artefacts
● Streaks● Hard (e.g. bone) tissues
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Correction Strategies
● Preprocessing On projection data
● Postprocessing On reconstructed data
● Dual-energy imaging Considered most elegant
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Preprocessing
● Select “appropriate” absorber
● Measured value A is corrected to A’
● Assumes “homogeneous” medium
● Fails if bone present
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
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
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
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
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
● 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
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Outline
● Beam hardening
● Scattered radiation
● Ring artefacts
● References
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Scattered radiation
● Scattered radiation● Components of
scatter Off-focus radiation
(OFR) Scattered radiation in
the patient Veiling glare
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Scatter measure
● SPR – Scatter-to-Primary-Ratio● Broad beam model estimation for SPR
22
222 12sR
sRLRLLSPR st
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Scatter artefacts – loss of contrast
● Loss of contrast Contrast without scatter
Contrast with scatter
SPRe
SPRC
bb t
)(
1ln
bb tC )(
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Scatter artefacts – loss of sharpness
● Loss of sharpness Transmitted radiation
- blurring kernel - 2D convolution
srpt III
srpsr hISPRI
srh
dudvvyuxhvugyxhg ),(),(),)((
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Scatter artefacts – loss of sharpness
● Loss of sharpness Veiling glare contribution
vgttd hIII )1(
vgsrppsrppd hhISPRIhISPRII )())(1(
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
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:
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
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
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
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
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Correction schemes – Scatter sampling
●Sampling of the scatter measurement Opaque discs arrays Aperture grid
●Interpolation of the smooth surface -6 dB
vgsrppsrppd hhISPRIhISPRII )())(1(
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
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
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Results
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Outline
● Beam hardening
● Scattered radiation
● Ring artefacts
● References
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Ring artefacts
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Ring Artefacts
● Reason
● 4G vs. 3G
● Postprocessing correction only
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Correction scheme
1. ROI
2. I P
3. Artefact pattern
4. Artefact subtraction
5. P I
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
ROI
● Select ROI with morphological operations
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Find artefact pattern
● Scan for irregularities Use variance of signal or Use median of signal etc.
● Extract ring pattern
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
Results
Moscow-Bavarian Joint Advanced Student School19-29 March 2006, Moscow, Russia
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!