What is a tomogram?
A tomogram is an image of a plane or slice within the body
Explain the basic mechanism of CT.
One way to think about the basic mechanism of Computed Tomography (CT) is to image taking a series of conventional chest x-rays, where the patient is rotated slightly around the axis running from head to foot between each exposure.
The projection data from CT is used for?
The projection data is used to reconstruct crosssectional images.
Compared to Radiographic Imaging, CT eliminates which artifacts?
Compared to Radiographic Imaging, CT eliminates the artifacts from overlaying tissues.
When was the first CT scanner developed?
The first clinical CT scanner developed by Houndsfield in 1971
How many generations of CT-scanners are presented in the lectures?
7 generations of CT-scanners.
Explain X-ray Source and Collimation for CT.
X-ray Source and Collimation
- Similar to those using for Projection Radiography
- CT system (Fan beam 30 – 60 degree) requires collimation and filtration that is different to radiography system (Cone Beam)
- Collimation (beam restriction) is accomplished by using two pieces of lead that form a slit between them
Give examples of CT Detectors?
CT Detectors
- Solid-state Detector
- Xenon Gas detector
Describe Solid-state Detector.
Solid-state Detector
- X-ray interacts with crystal by photoelectric effect (similar to phosphor in an intensifying screen)
- Electrons are excited and emitted visible light when they spontaneously de-excite.
- Such scintillation process results in a burst of light
- The light is converted to electric current using photo-diode
Explain Xenon Gas detector.
Xenon Gas detector
- Small and highly directional detectors required for 3G system
- Use Xenon gas in long, thin tubes.
- When Xenon gas ionized, it generates current between an anode and cathode.
- Less efficient, but highly directional.
- For same performance, solid state detectors must be accomplished by external collimations
What is Parallel Beam projection?
Parallel Beam Projection
Explain the Line integral.
Line integral
For Parallel Beam Projection, if the l=1 and \theta=0, what does the integral become?
Parallel Beam Projection,
What is g(l,\theta) when \theta is fixed and l varies?
Parallel Beam Projection
g(l,\theta) is then a projection.
What is an image of g(l,\theta) called?
Parallel Beam Projection
- An image of g(l,\theta) with l and \theta as rectilinear coordinates is called a sinogram.
- g(l,\theta) is also known as the radon transform of f(x,y) .
Explain Back Projection.
Back Projection
- Intuition tells us that if g(l,\theta) takes on a large value at \theta=\theta0, then f(x,y) must be large over the line L(l,\theta).
- One way to reconstruct an image with this property is to simply assign every point on the value L(l,\theta).
- The resultant function is called the back projection image and is given by:
- b\theta(x,y)=g(xcos(\theta)+ysin(\theta),\theta)
- To incorporate information about the projections at other angles, we can simply add up (integrate) their back projection images, which results:
- fb(x,y)=int(0->\pi)b\theta(x,y)d\theta
Explain Projection-Slice Theorem.
Projection-Slice Theorem (Fourier Slice Theorem)
- G(w,\theta)=F(w*cos(\theta),w*sin(\theta))
- w= the spatial frequency
- The 1-D Fourier Transform of a projection equals a line passing through the origin of the 2-D Fourier Transform at an angle corresponding to the projection.
- It forms the basis of three image reconstruction methods.
- Fourier Method
- Filtered Back Projection
- Convolution Back Projection
- Consider the 1-D Fourier Transform of a projection with respect to l:
- G(w,\theta)=F1D[g(l,\theta)=int(-inf->inf)g(l,\theta)e-j2\pi*w*ldl
Explain the Fourier Method.
Fourier Method
- A conceptually simple reconstruction method based on Projection-Slice Theorem.
- f(x,y)=F2D-1[G(w,\theta)}
- Problems:
- Interpolating polar data onto Cartesian Grid
- Time consuming to compute the 2D Inverse Fourier Transform
- Not widely used in CT
What are the differences in the results between back-projection, filtered back-projection or filtered back-projection using a Hamming Window?
Back Projection
Explain Filtered Back Projection
Filtered Back Projection
What is the flow of reconstructing images using filtered back projection with a HP-rampfilter?
Reconstructing images using filtered back projection with a HP-rampfilter
Explain Convolution Back Projection
Convolution Back Projection
- The filtered backward projection can be rewritten as:
- f(x,y)=int(0->\pi)[F1D1(|w|)*g(l\theta)] l=xcos(\theta)+ysin(\theta)d\theta
Explain Fan Beam Reconstruction.
Fan-Beam Reconstruction
- Fan-Beam Reconstruction
- (i) equal angles between the measured raypaths
- (ii) equal detector spacing
- (iii) both equal angles and equal detector spacing
- Advantage: Faster
- Disadvantage: More complicated Algorithm
Name some examples of artifacts related to CT
Artifacts associated with CT:
- Polychromaticity Artifacts in X-Ray CT
- Artifacts due to insuffucient views
- Artifacts due to strong scatterers
- Metal artifacts
- Aliasing artifact and noise
- Electronic or system drift
- Mis-calibration or Gain Drift
- Detector Faulty
- X-ray Scatter
- Strong Scatter that blurs the image
- Motion
- Typical scan takes 1 to 10 second
- Heart Beats, breathing
- Gate data acquisition so that data will be taken only at a certain stage in the cardiac cycle and/or breathing cycle.
