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

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Real Reconstruction ProblemIntensity (transmission)

measured Rays transmitted through

multiple pixelsFind individual pixel values

(question marks) from transmission data

534

417

364

555

501

355

255 712199

Raw DataIntensity (transmission) measurements 534

417

364

501

255 712199

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

0.000

0.500

1.000

1.500

0.000 5.000 10.000 15.000 20.000

Fourier TransformSin(x) + 1/3 Sin (3x) + 1/5 sin (5x)

++

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.600

0.800

1.000

0.000 5.000 10.000 15.000 20.000

Fourier TransformSin(x) + 1/3 Sin (3x) + 1/5 sin (5x) + 1/7 Sin (7x)

+++ -1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

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1.000

0.000 5.000 10.000 15.000 20.000

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

8 4 4

8 4 4

8 4 4

24 12 12

Initial guess based upon vertical projections

Measurements

? ? ?

? ? ?

? ? ?

24 12 12

Measurements

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159

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

9 5 5

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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8 4 4

8 4 4

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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

9 5 5

6.67 2.67 2.67

17

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12

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159

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