Topic 15: SPECT-PET - iterative image reconstruction and attenuation & scatter Flashcards
Acitivity decays exponentially what is the decay rate characterised by?
the half-life. and activity is the number of decays per second (Bq)
Radioactivity is a ____ process. and has to be described using _____
random and probabilities
Most detected counts follow a ________ distribution unless____
possion distribution unless measurement time frame is much longer than the half life.
for poisson random variable variance = ? and CV = ?
variance = mean, and CV = 1/Sqrt
What factors influence image quality?
Biology/tracer Movement Scanner technology Counts!!!!!!! Image reconstruction and processing ( including filtering)
Forward back project is based on an _________ ___ ____ of the x-ray transform
FBP is based on an analytic inversion formula of the X-ray transform
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)
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).
What is the slight issue with back-projection images and what can be done to recover the true image?
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.
What do smoothing filters do to the image?
Reduce resolution but reduces noise
FBP issues?
Need to discretise analytic formulas- after all only discrete detectors are available Analytic methods ignore: - noise - finite detector size - limited angles
what are the components of “iterative reconstruction”?
- Forward model 2. Goodness-of-fit function 3. Iterative scheme to improve the fit (i.e. reduce the goodness of fit)
What does the data have that reduces the quality of the image?
Projections, Attenuation, scatter Defective detector block Gaps Noise
What is the basic idea around the iterative image reconstruction?
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.
Maximum likelihood/Goodness of fit?
Needs to take noise into account. Statistical estimation. Find the most probable image using poisson probability.
Two examples of iterative reconstruction algorithms?
OLEM AND MLEM
Advantages and disadvantages of FBP?
Fast but inflexible
The noise increases with each iteration, how does MLEM AND FBP algorithms compare?
the MLEM is more “grainy” whilst FBP is more streaky
Why does the FBP have streaks?
FBP back projects then filters. the mlem will give you the intersections and fbp will give you all the lines.
How do you reduce noise in FBP?
filtering - smoothing filters, less noise
what do people do with iterative reconstruction in clinical practice ?
- Early stopping( at fixed number of iterations) - Apply some post-filtering.
Problems with early stopping?
quantification - wrong values of positions.
What rule is used for calculating how likely an image is given the data in MAP?
Bayes rule
What are the MAP advantages over MLEM?
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.
MAP disadvantages?
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.
What is the noise determined by
data: the amount of detected counts
Image: data quality and choice of image reconstruction algorithm
MLEM/osem trade off?
MLEM is very flexible but slow. OSEM (using early-stopping) is much faster and is currently most popular.
MAP tradeoff?
algorithm are very flexible and promise more reliable quantification
What is MLEM?
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).
