lecture05 - 2009.ppt
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TRANSCRIPT
BMED-4800/ECSE-4800Introduction to
Subsurface Imaging Systems
Lecture 5: X-ray Imaging (cont.)Kai E. Thomenius1 & Badri Roysam2
1Chief Technologist, Imaging Technologies, General Electric Global Research Center
2Professor, Rensselaer Polytechnic Institute
Center for Sub-Surface Imaging & Sensing
Review of Last Lecture
• Quick historical review of X-rays was given.• Block diagrams, key components defined.• Brief discussion of x-ray scattering• An X-ray beam, traversing through an object, is
attenuated by the exponential Lambert-Beer Law.• The product of the attenuation coefficient and the path
length of the x-ray beam in such a target is critical in establishing detectability.
• Today: – Digital Detectors, X-ray Metrics
Outline of Course Topics
• THE BIG PICTURE– What is subsurface imaging?– Why a course on this topic?
• EXAMPLE: Projection Imaging – X-Ray Imaging– Computer Tomography
• COMMON FUNDAMENTALS– Propagation of waves– Interaction of waves with
targets of interest
• PULSE ECHO METHODS– Examples
• MRI– A different sensing modality
from the others– Basics of MRI
• MOLECULAR IMAGING– What is it?– PET & Radionuclide Imaging
• IMAGE PROCESSING & CAD
www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf
Digital Detector Front End
www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf
Detector Details
www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf
Selenium based Detector
www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf
Performance Metrics
Signal-to-noise Ratio (SNR)• SNR determines the
detectability of an object• Signal derived from x-ray
quanta• Noise comes from a
variety of sources:– X-ray quantum statistics,
Poisson distribution– Electronic noise– Sampling noise– Anatomical noise
• Signal processing steps critical to image quality– Correction for detector
variability, defects– Post-process filtering
FP vessel12 mm large cell lung cancer
Quantum noise• For a digital x-ray detector
system with square pixels– if the average number of
x-rays recorded in each pixel is N,
– then the noise (per pixel) will be
• Statistical distribution associated with x-rays is the Poisson distribution.– The above relation falls
out directly from this fact.
N
Poisson Distribution• Poisson Distribution is a probability
distribution given by
!
exp,k
kfk
If the expected no. of occurrences in a space is, then the probability that there are exactly k occurrences is given by f(k,)
Signal-to-noise ratio• The signal-to-noise ratio (SNR) is given by
• When the number of x-rays, N, is increased, the radiation dose also increases.
• To double the SNR, the dose to the patient needs to be increased by a factor of 4
• Contrast-to-noise ratio (CNR) for any two intensities (I1 and I2) at a detector is given by
– Here N is the nominal value of photons reaching the detector.
NNNN
SNR
CNR I1 I2
I1 I2
N
Other Measures of Image Quality
• Limiting Spatial Resolution (LSR)– The highest frequency that can be visualized
• Modulation Transfer Function (MTF)– Measures how the detector passes signal, as a function of
spatial frequency
MTF = Modulation at detector outputModulation at detector input
Spatial Frequency (cycles/mm)
MTF 1.0
00.03 - 0.05
LSR
MTF=1
in
out
ContrastContrastMTF
in out
q(x)
2A(f))
q(x)
2A(f))
Source: http://203.64.251.39/info/download/etc/breastx/93/93-04.ppt
MTF=0.5
• Modulation Transfer Function (MTF) / Spatial resolution:An imaging system’s ability to render the contrast of an object as a function of object detail.
in
out
ContrastContrastMTF
in out
q(x)
2A(f))
I(x)
2Aout(f)
MTF
Modulation Transfer Function•LSR– Screen-film has LSR » 20 lp/mm
• corresponds to 25 m pixel• Digital (GE) 100 m pixel
•Sources of MTF degradation– Lateral spread of light in scintillator
• limited by CsI needles• increases with scintillator
thickness– Lateral spread of secondary x-rays
• not significant away from k-edges of Cs and I
– Sampling aperture of pixel: sinc(fx*a)sinc(fy*a)
Spatial Frequency (cycles/mm)
MTF
Digital Imager
Film-Screen
If film’s LSR is better than digital why do we see improved performance in digital?
MTF For Direct, Indirect, and Screen Film
Measures of Image Quality-DQE
• Detective Quantum Efficiency, DQE
• SNR gives the transfer function of both signal and noise
DQE = SNR2 at detector output
SNR2 at detector input
SNR2 at detector output
Patient Dose
DQE
Spatial Frequency (cycles/mm)
DQE
Digital Imager
Film-Screen
1.0
High DQE in low-to-mid frequencies aids detection.High DQE in high frequencies aids characterization.
The higher the DQE,the higher the SNR,and the greater theprobability of detection.
where f is the spatial frequency (lp/mm), X is the exposure (mR) and :
S = Median Signal Level (cts), i.e. amplitude of information
MTF = Modulation Transfer Function
NPS = Noise Power Spectrum (cts^2 * mm^2)
C = Incident Xray Fluence (xrays / (mm^2 * mR)
DQE describes the measured SNR in relation to an ideal detector.
SNR2 is deduced from the ratio of MTF^2 (signal^2) to the NPS (noise^2)
DQE : Definition
www.aapm.org/meetings/amos2/pdf/26-5959-83142-414.pdf
Calibration of Digital Detector
•Dark Image Offset
•Diode leakage•FET charge
retention•Electronic
noise
Calibration of Digital Detector
•Offset Corrected Dark Image
•Electronic Noise
Calibration of Digital Detector
•Offset Calibrated
•Amplifier gainvariation
•Pixel-to-pixel gain variation
Calibration of Digital Detector
•Offset and Gain calibratedFlood exposed image
•Poisson statistical x-ray noise
•Electronic noise
Apply Corrections• Low dose: before and After Offset
Correction
Apply Corrections
• High dose
Tomosynthesis
Advanced Applications• Tomosynthesis- 3D X-ray
3D Breast Imaging - Tomosynthesis
• 3D imaging addresses the major problem with mammography today – superimposed tissue
• 3D imaging may enable compression reduction– Tissue immobilization vs. compression– Compliance with screening protocols
• Single tomo exam in MLO position may replace conventional mammography, potentially enabling dose reduction
Tomosynthesis Concept
Prototype System Parameters
• Prototype based on GEMS Senographe DMR, Revolution flat panel detector, motorized tube motion assembly
• 11 projections over +/- 25 degrees • 7.5 sec patient exam time• Total dose
– 1.5x a single mammographic view– 0.75x a standard mammographic screening
exam• 100 micron pixels• 1 mm (3d) slice separation
Tomosynthesis•Goal:• Limited 3-D reconstruction to remove
overlying/underlying structure• All image planes visualized using a single
acquisition
•Acquisition:• Vertical tube motion • Total tube angle: 5 -15°• Number of Projected Images: 15 – 25• Exam length: 5 -10 sec (single breath-
hold)• Slice thickness: ~1 cm• Enabled by GE Revolution™ detector:
Courtesy of Duke University and Wake Forest Medical Center
Rotational Axis
Tube vertical motion
Small Changes to Rad System allows for 3D Imaging!
Image Reconstruction in Tomo
• Data incompleteness– From a CT perspective, data is very sparse– Limited angular range (z-resolution)– Insufficient angular sampling (streaks)– Truncated projections (inconsistency)
Reconstruction Concept – Shift and Add
Add
Reconstruction of single plane
Projections at different angles
Shift
Vertical slice through object
Reconstruction of vertical slice through object
Artifacts: Out-of-plane structures appear as N low-contrast copies (N = # of projections). Contrast / “blurring” of artifacts depends on N, projection angles / tube trajectory, etc.
An Example…Standard 2D
x-ray
Images courtesy of Dr. Dan Kopans- MGH
Tomosynthesis – Missed Cancer
Spiculated Lesion
Standard MammogramMLO
Tomo SliceMLO
Tomosynthesis
Images courtesy of Dr. Dan Kopans- MGH
An Example…
3D Tomosynthe
sis
Images courtesy of Dr. Dan Kopans- MGH
Rad Tomo Example
Low Dose 3D Imaging!
Receiver Operating Characteristics
Receiver Operating Characteristic (ROC) curves
• Most basic task of the diagnostician is to separate abnormal subjects from normal subjects
• In many cases there is significant overlap in terms of the appearance of the image– Some abnormal patients have normal-looking films– Some normal patients have abnormal-looking films
• ROC curves are a tool for assessing the performance of a hypothesis testing algorithms.
2 x 2 Decision MatrixActually
AbnormalActually Normal
Diagnosed as
Abnormal
True Positive
(TP)
False Positive
(FP)Diagnosed as Normal
False Negative
(FN)
True Negative
(TN)
ROC curves (cont.)
• For a single threshold value and the population being studied, a single value for TP, TN, FP, and FN can be computed
• The sum TP + TN + FP + FN will be equal to the total number of normals and abnormals in the study population
• “True” diagnosis must be determined independently, based on biopsy confirmation, long-term patient follow-up, etc.
Summary•Design of digital x-ray detectors was
described.•Performance metrics (MTF, DQE) for x-
ray performance were given.– Justification for digital detectors was based
on these.•Tomosynthesis concept introduced.•Brief review of ROC methods for
hypothesis testing was given.
•Next time: Introduction to CT Scanners
Homework
• Using web resources (or sources given below), describe the key steps of the direct conversion process with amorphous Selenium. How are x-rays converted to electrons?
• What is the relative performance (MTF or DQE) with respect to the CsI-Photodiode approach?
• Which would you buy and why?– http://www.dondickson.co.uk/download/Challenges_
of_Direct_Digital_Radiology.pdf– Hoheisel et al., “Modulation transfer function of a
selenium-based digital mammography system”, IEEE Proc. Nuclear Science Symposium, 2004, 3589-3593
Instructor Contact Information
Badri RoysamProfessor of Electrical, Computer, & Systems EngineeringOffice: JEC 7010Rensselaer Polytechnic Institute110, 8th Street, Troy, New York 12180Phone: (518) 276-8067Fax: (518) 276-6261/2433Email: [email protected]: http://www.ecse.rpi.edu/~roysabm Secretary: Laraine Michaelides, JEC 7012, (518) 276 –
8525, [email protected]
Instructor Contact Information
Kai E ThomeniusChief Technologist, Ultrasound & BiomedicalOffice: KW-C300AGE Global ResearchImaging TechnologiesNiskayuna, New York 12309Phone: (518) 387-7233Fax: (518) 387-6170Email: [email protected], [email protected] Secretary: TBD