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CTSeeram Chapter
7:Image
Reconstruction
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Reconstruction:Solve for ’s
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14512 values
512values
100’s of diagonals @ 100’s of angles
***
Real Reconstruction ProblemIntensity (transmission)
measured Rays transmitted through
multiple pixelsFind individual pixel values
(question marks) from transmission data
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255 712199
Raw DataIntensity (transmission) measurements 534
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Image DataIndividual pixel
values (question marks)
Algorithm
Set of rules for getting a specific output (answer) from a specific input
Reconstruction algorithm examplesFourier TransformInterpolationConvolution (filtered back projection)
Fourier Transform
converts data from spatial domain to frequency domainbreaks any signal into frequency component
parts
C-major chord consists of C, E, & G notes
Fourier TransformTransforms any function to sum of sine &
cosine functions of various frequencies
+
+
Fourier TransformSin(x) + 1/3Sin(3x)
+-1.500
-1.000
-0.500
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0.500
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1.500
0.000 5.000 10.000 15.000 20.000
Fourier TransformSin(x) + 1/3 Sin (3x) + 1/5 sin (5x)
++
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Fourier TransformSin(x) + 1/3 Sin (3x) + 1/5 sin (5x) + 1/7 Sin (7x)
+++ -1.000
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Fourier Transform Reconstruction
Each set of projection data transformed to its frequency domaincombinations of sines & cosines at various
frequenciesFrequency domain image createdFrequency domain image transformed back
to spatial domaininverse Fourier Transform
Frequency Domain Image
Lends itself to computer calculationEasily manipulated (filtered)
edge enhancementemphasize higher frequencies
smoothingde-emphasize higher frequencies
Provides image quality data directly
Back Projection ReconstructionBack Projection Reconstruction
Reconstruction Problemconverting transmission data for
individual projections into attenuation data for each pixel
??????? 63
Back Projection ReconstructionBack Projection ReconstructionBack Projection
for given projection, assume equal attenuation for each pixel
repeat for each projection adding results
9999999 63
Back Projection ReconstructionBack Projection ReconstructionAssume actual image has 1 hot spot
(attenuator)Each ray passing through spot will
have attenuation back-projected along entire line
Each ray missing spot will have 0’s back-projected along entire line
Hot Spot
9999999 63
0000000 0
Back Projection ReconstructionBack Projection ReconstructionEach ray missing spot stays blankEach ray through spot shares some
densityLocation of spot appears brightest
Hot Spot
9999999 63
0000000 0
Back Projection ReconstructionBack Projection ReconstructionStreaks appears radially from spotstar artifact
HotSpot
Star Artifact Spokes
Iterative ReconstructionIterative ReconstructionStart with measured data
? ? ?
? ? ?
? ? ?
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Measurements
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Iterative ReconstructionIterative ReconstructionMake initial guess for first projections
by assuming equal attenuation for each pixel in a projection
Similar to back projection
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Initial guess based upon vertical projections
Measurements
? ? ?
? ? ?
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Measurements
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Iterative ReconstructionIterative Reconstructioncalculate difference between measured &
calculated attenuation for next projectioncorrect all pixels equally on current
projection to achieve measured attenuation
BUT!!!
Iterative ReconstructionIterative Reconstructionchanging pixels for one projection alters previously-calculated attenuation for others
corrections repeated for all projections until no significant change / improvement
Iteration ExampleIteration Example
8.33 4.33 4.33
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6.67 2.67 2.67
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Make correctionsbased onhorizontalProjections data
Low by 1; add .33 to each.
Low by 3; add 1 to each.
High by 4; subtract 1.33 from each.
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Initial guess based upon vertical projections
Iteration ExampleIteration Example
8 4.16 4.33
9.17 4.33 4.83
6.67 2.84 2.33
Make correctionsbased uponData measured ondiagonals
Low by .3; add .17 to each.
High by .33; subtract .17 from each.
High by 1; subtract .33 from each.
8.33 4.33 4.33
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6.67 2.67 2.67
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Iteration Image ReconstructionIteration Image Reconstruction
operationally slow and cumbersome, even for computers
not used
Stay tuned! We’ll be right back after a word about
filtered back-projection.
Filtered Back ProjectionFiltered Back Projectionenhancement of back
projection techniquefiltering function (convolution)
is imposed on transmission datasmall negative side lobes
placed on each side of actual positive data
negative values tend to cancel star artifact
Filtered back
projection
Unfiltered back
projection
*
Filtered Back ProjectionFiltered Back Projectionoperationally fast
reconstruction begins upon reception of first transmission data
best filter functions found by trial & error
Most common commercial reconstruction algorithm
The Resurrection of Iterative Reconstruction: General Electric Adaptive Statistical Iterative Reconstruction (ASIR)
22-66% reduction in dose in abdominal scans with no change in spatial or temporal resolution
No special operator trainingAs fast as filtered back-projectionJagged edge seen around liver when dose too lowImaging problems seen in thin patients when dose
too lowAlgorithm creates different texture
Appears artificialCreates a “new normal”
Claims & Observations
The Resurrection of Iterative Reconstruction: General Electric Adaptive Statistical Iterative Reconstruction (ASIR)
New algorithm being developedMBIRStill too slow for routine use.
Dual-energy CT may eliminate need for pre-contrast images.
Claims & Observations
The Resurrection of Iterative Reconstruction: Siemens Iterative Reconstruction in Image Space (IRIS)
Dose reduction up to 60% without quality loss
Fast reconstruction
Claims & Observations
The Resurrection of Iterative Reconstruction: Philips iDose
Dose reduction for coronary CT angiography more than 80% without quality loss
Reconstruction times of up to 20 images/second
Can improve image quality in typically high noise bariatric exams
Claims & Observations
Multi-plane reconstructionMulti-plane reconstructionusing data from multiple axial
slices it is possible to obtainsagittal & coronal planesoblique & 3D reconstruction
Non-spiral reconstructionPoor appearance if slice
thickness >>pixel sizemulti-plane reconstructions are
computer intensiveCan be slow
Saggital / Coronal Reconstructions
Saggital
Coronal
Axial
3D Reconstructions
Uses pixel data from multiple slicesAlgorithm identifies surfaces & volumesDisplay renders surfaces & volumes
Real-time motion auto-rotation user-controlled multi-plane rotation
3D Reconstructions
http://www.pumpkingutter.com/
*
InterpolationCalculating attenuation data for specific slice
from spiral raw dataTable moves continuallyAs tube rotates table constantly moves
Position at start of rotation
Position at start of rotation
Position of interest
Interpolation
Estimates value of function using known values on either side
When x = 50, y = 311When x = 80, y = 500
What will be the value of y when x=58? (50,311)
(80,500)?
58
Interpolation58 is 8/30ths of the way between points“y” when x=58 will be 8/30ths of the way
between 311 and 500
(50,311)
(80,500)?
58
?=311+8/30 (500-311)
The End
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