Medical Imaging

Dr. Mohammad Dawood

Department of Computer Science

University of MünsterGermany

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Recap

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

α decay β- decay β+ decay

Gamma scintigraphy PET Sinogram

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound / Sonography

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

The frequency range of sound above 20kHz is known as ultrasound

Sound spectrum

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Sound wave propagation

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound

- is produced through the conversion of electrical energy into mechanical energy

- is detected by the reverse process, by converting mechanical energy into electrical energy.

- The transducer is a device that is both a transmitter and receiver of the ultrasound signal and it serves a dual role in pulse echo imaging.

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Inge Edler und Helmut Hertz (1954)

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reflexion Scatter Transmission

Ultrasound

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Frequency

DepthResolution

Ultrasound

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Medium Speed of sound m/s

Air 331

Water 1483

Tissue 1540-1595

Liver 1549

Blood 1570

Glycerin 1923

Bones (Compact) 3600

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound

- A mode (amplitude)

- B mode (brightness)

- M mode (moving)

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Ultrasound

- no functional information

- fast

- cheap

- no radiation

- portable

- no injection

- Bone / gas

- Obesity

- Operator dependence

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Image Reconstruction

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

x-ray source

collimator

object

detector

Reconstruction

Tomography

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Law of Attenuation

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Parallel projections of a plane

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

x

y

r

s

θ

n

Reconstruction

Radon Transformation f

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Radon Transformation (Line Integrals at different angles)

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Radon Transformations

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Radon Transformation 32

128

512

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Inverse Radon Transformation

H: Hilbert transform

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Inverse Radon Transformation

Problems with Missing data and Noise!

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Filtered Back Projection

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

A B

D C

A+B

C+D1

A+D B+C

3

2

BA+C

D

Reconstruction

Projections

A

B+D

C

4

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

? ?

? ?

Reconstruction

Back projections

A+B

C+D1

A+B A+B

C+D C+D

2

BA+C

D

2A+B+C A+2B

C+2D A+2C+D

A+D B+C

3

3A+B+C+D

A+3B+C

A+C+3D

A+B+3C+D

A

B+D

C

4

4A+B+C+D

A+4B+C+D

A+B+C+4D

A+B+4C+D

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

4A+B+C+D

A+4B+C+D

A+B+C+4D

A+B+4C+D

Reconstruction

Back projections

3A 3B

3D 3C

- (A+B+C+D) = / (n-1) =A B

D C

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Filtered Back Projection

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

1=Ram-Lak (ramp), 2=Shepp-Logan, 3=Cosine, and 4=Hamming

Reconstruction

FBP: Commonly used filters

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Projections

Backproject

Filter 1D

Filter 2D

Backproject

Image

Reconstruction

Filtered Back Projection

2D/3D filtering is costly

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Fourier slice theorem

Take a two-dimensional function f(r), project it onto a line, and do a Fourier transform of that projection

Take that same function, but do a two-dimensional Fourier transform first, and then slice it through its origin parallel to the projection line

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

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Medical Imaging, SS-2014

Dr. Mohammad Dawood

Reconstruction

Iterative Reconstruction

Kaczmarz Method (=ART: Algebraic Reconstruction Technique)

1. Start by setting x(0) = 0

2. Compute the forward projection

3. Update the current estimate

4. Iterate steps 2,3 until the difference between new forward projection, computed in 2, and the old one is below tolerance

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Medical Imaging, SS-2014

Dr. Mohammad Dawood