Reconstruction methods

Question 1

Backprojection

Answer 1

• 2D count profiles are transformed to a 3D image
• Counts from the individual projections are projected back over an image matrix
• projected at same angle which they were acquired
• photon information received from one
  pixel is translated to all other pixels
  perpendicular to the detector
• Creates a star artifact that needs to be removed by applying a filter

Question 2

Filtered backprojection

Answer 2

• Filter is applied prior to backprojection
• faster and simpler
• fewer artifacts
• uses the fourier slice theorem
• ramp filter applied in frequency domain
• performed post-acquisiton

Question 3

FBP image quality concerns

Answer 3

• effects of sampling on image quality
• sampling coverage and consistency requirements
• SNR and CNR

Question 4

Final resolution of a FBP image depends on…

Answer 4

• Linear sampling distance
• Angular sampling intervals
• Cut-off frequency of filter
• Spatial resolution of system

Question 5

Iterative reconstruction (the iterative cycle)

Answer 5

1) Guesses RP distribution; assuming uniform distribution based on backprojection or other techniques
2) makes 1st estimated 3D matrix
3) makes estimate on 2D projections based on assumed RP distribution
4) compares measured 2D projections to estimated 2D projections
5) Differences between estimated and modified projections are used to modify the estimated 3D matrix
6) Modified matrix is used as the starting point for the next iteration
7) process repeated until convergance

Question 6

What are the four most common iterative methods

Answer 6

• Maximum likelihood expectation
  maximization (MLEM)
• Ordered subset expectation
  maximization (OSEM)
• Least squares
• Algebraic reconstruction technique (ART)

Question 7

MLEM

Answer 7

1) attempts to maximize a statistical value called the liklihood
2) goal is to find activity distribution with the highest probability of generating the measured projections
3) uses all projections in each iteration causing it to converge slowly
4) each iteration requires more time than FBP
5) Gives more control over noise
6) require 50-100 iterations

Question 8

OSEM

Answer 8

1) breaks a whole set of 2D projections into a large number of subsets (measured and estimated)
2) compares subset of estimated projections to its corresponding measured subset
3) 3D matrix is updated, where next projection is considered
4) a full iteration is made once all subsets are considered
5) convergence occurs more quickly than MLEM

Question 9

Least squares

Answer 9

• Minimizes the difference between the
  measured and calculated projections by
  using least squares
• Algorithm needs 10-15 iterations to
  reach convergence
• Includes attenuation correction

Question 10

ART

Answer 10

• Algebraic reconstruction technique
• Simplest method
• Treats one projected point at a time
• Corrections can be additive by adding
  subtracting from each point or, multiplicative by applying a factor to all
  points