Topic 15: SPECT-PET - iterative image reconstruction and attenuation & scatter

Question 1

Acitivity decays exponentially what is the decay rate characterised by?

Answer 1

the half-life. and activity is the number of decays per second (Bq)

Question 2

Radioactivity is a ____ process. and has to be described using _____

Answer 2

random and probabilities

Question 3

Most detected counts follow a ________ distribution unless____

Answer 3

possion distribution unless measurement time frame is much longer than the half life.

Question 4

for poisson random variable variance = ? and CV = ?

Answer 4

variance = mean, and CV = 1/Sqrt

Question 5

What factors influence image quality?

Answer 5

Biology/tracer Movement Scanner technology Counts!!!!!!! Image reconstruction and processing ( including filtering)

Question 6

Forward back project is based on an _________ ___ ____ of the x-ray transform

Answer 6

FBP is based on an analytic inversion formula of the X-ray transform

Question 7

The FBP can be derived from the ____ ___ theorem which equates a line through the origin of the 2D FT of the image with the 1D FT of the projections at given angle)

Answer 7

The fBP Can be derived from the Central Slice Theorem (which equates a line through the origin of the 2D FT of the image with the 1D FT of the projections at given angle).

Question 8

What is the slight issue with back-projection images and what can be done to recover the true image?

Answer 8

Back-projection in itself gives very smooth images. A specific sharpening filter (called the ramp filter) needs to be applied to recover the true image.

Question 9

What do smoothing filters do to the image?

Answer 9

Reduce resolution but reduces noise

Question 10

FBP issues?

Answer 10

Need to discretise analytic formulas- after all only discrete detectors are available Analytic methods ignore: - noise - finite detector size - limited angles

Question 11

what are the components of “iterative reconstruction”?

Answer 11

1. Forward model 2. Goodness-of-fit function 3. Iterative scheme to improve the fit (i.e. reduce the goodness of fit)

Question 12

What does the data have that reduces the quality of the image?

Answer 12

Projections, Attenuation, scatter Defective detector block Gaps Noise

Question 13

What is the basic idea around the iterative image reconstruction?

Answer 13

We want to find an image such that the estimated data fits the measured data. make a system model with noise, acquisition etc. etc. then you make it once.

Question 14

Maximum likelihood/Goodness of fit?

Answer 14

Needs to take noise into account. Statistical estimation. Find the most probable image using poisson probability.

Question 15

Two examples of iterative reconstruction algorithms?

Answer 15

OLEM AND MLEM

Question 16

Advantages and disadvantages of FBP?

Answer 16

Fast but inflexible

Question 17

The noise increases with each iteration, how does MLEM AND FBP algorithms compare?

Answer 17

the MLEM is more “grainy” whilst FBP is more streaky

Question 18

Why does the FBP have streaks?

Answer 18

FBP back projects then filters. the mlem will give you the intersections and fbp will give you all the lines.

Question 19

How do you reduce noise in FBP?

Answer 19

filtering - smoothing filters, less noise

Question 20

what do people do with iterative reconstruction in clinical practice ?

Answer 20

• Early stopping( at fixed number of iterations) - Apply some post-filtering.

Question 21

Problems with early stopping?

Answer 21

quantification - wrong values of positions.

Question 22

What rule is used for calculating how likely an image is given the data in MAP?

Answer 22

Bayes rule

Question 23

What are the MAP advantages over MLEM?

Answer 23

Results are no longer dependent on interation number. Results are easier to predict - results independent of initial image and of exact algorithm that was used. - Can be analysed theoretically Iterative problem is easier to solve - algorithm can be designed to need less iterations for MAP than MLEM.

Question 24

MAP disadvantages?

Answer 24

More choice:

• which penalty are we going to use?
• what parameters are we going to use?

Effect of the penalty is more complicated than you would hope

• The balance between the “fitting” term and the penalty depends on the whole object, not just the local edges.

Question 25

What is the noise determined by

Answer 25

data: the amount of detected counts

Image: data quality and choice of image reconstruction algorithm

Question 26

MLEM/osem trade off?

Answer 26

MLEM is very flexible but slow. OSEM (using early-stopping) is much faster and is currently most popular.

Question 27

MAP tradeoff?

Answer 27

algorithm are very flexible and promise more reliable quantification

Question 29

What is MLEM?

Answer 29

MLEM is a commonly used example of an iterative reconstruction algorithm. It is an iterative procedure for estimating the Maximum Likelihood (ML) for the Poisson distribution (EM stands for “Expectation Maximisation” which is a general method for maximising a probability).