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Alessio - BIO508

Bioengineering 508:Physical Aspects of Medical Imaginghttp://courses.washington.edu/bioen508/

Organizer: Paul Kinahan, PhDAdam Alessio, PhDRuth Schmitz, PhD

Lawrence MacDonald, PhD

Imaging Research Laboratoryhttp://depts.washington.edu/nucmed/IRL/

Department of RadiologyUniversity of Washington Medical Center

Alessio - BIO508

Bioengineering 508:Physical Aspects of Medical Imaging

Introduction to Medical Imaging1. Medical Imaging Modalities2. Modern Image Generation3. Intro to Image Quality

Adam Alessio, PhDDepartment of Radiology

University of Washington Medical Centeraalessio@u.washington.edu

Alessio - BIO508

Nature of Medical Imaging

For this class:Medical Imaging: Non-invasive imaging of internal

organs, tissues, bones, etc.

Focus on:1. Macroscopic not microscopic2. in vivo (in the body) not in vitro (“in glass”, in the lab)3. Primarily human studies4. Primarily clinical diagnostic applications

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Nature of Medical Imaging

QUICK CAVEAT

• Powerpoint Slides are just a vehicle for major topics• These do not have all the information discussed in

class!• Taking notes to supplement slides is probably a

good idea!

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Types of Medical Imaging (Modalities)

Grouped by underlying physics:• X-Ray/CT• Ultrasound• Magnetic Resonance Imaging (MRI)• Nuclear Medicine• Optical• Magnetic Field• Electric Field• Thermal• Optoacoustic• Elastography

Major 4 that dominateclinical imaging, focusof this course

Primarily microscopic

Mainly research based

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Types of Medical Imaging (Modalities)

Nuclear medicineElectromagnetic Spectrum

For comparison, this iswavelength/frequency range of US,but US is NOT electromagnetic!

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Types of Medical Imaging (Modalities)

Classifications of Medical Images1. Anatomical vs. Functional

• Anatomy/Structure/Features vs. Physiology2. Emission vs. Transmission

• Where does energy imaged originate?3. Projection vs. Tomographic

• Projection--> 2D imaging, single plane, no depthinformation

• Tomographic (“tomo” = slice, graphy=image) --> volumetric

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Modern Image Generation

From continuous real world to a meaningful image(on computer):

1. Sampling Continuous Information– Information and sampling technique varies widely for each

modality- Topic for later lectures– Computer can only hold discrete chunks of data– Pixel = a single picture element; Voxel = a single volume

element2. Quantizing Samples

– Each discrete chunk must be represented by certain numberof bits

3. Visualization Techniques of quantized, sampled imagevolumes

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1. Sampling Continuous Information

Given a signal such as a sine wave withfrequency 1 Hz:

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Intro to Sampling Theory

We can sample the points at a uniform rate of 3Hz and reconstruct the signal:

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Intro to Sampling Theory

We can also sample the signal at a slower rate of2 Hz and still accurately reconstruct the signal:

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Intro to Sampling Theory

However, if we sample below 2 Hz, we don’t haveenough information to reconstruct the signal, and infact we may construct a different signal (an alias):

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Intro to Sampling Theory• Aliasing

– occurs when your sampling rate is not high enough to capture theamount of detail in your image

– Can give you the wrong signal/image—an alias– Where can it happen in graphics?

• During image synthesis:– sampling continuous signal into discrete signal– e.g. ray tracing, line drawing, function plotting, etc.

• During image processing:– resampling discrete signal at a different rate– e.g. Image warping, zooming in, zooming out, etc.

• Nyquist criterion: Must sample at two times the highest frequency in thesignal for the samples to uniquely define the given signal

– Sampling below the Nyquist frequency can cause aliasing (CD sampling example)

�

FNyquist =SamplingRate

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Intro to Sampling Theory

• To perform sampling correctly in image space, needto understand structure of data/image

• Fourier: “Any periodic function can be rewritten as a weightedsum of sines and cosines of different frequencies.” - FourierSeries

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A sum of sines

• Our building block:•

• Add enough of them to getany signal f(x) you want

• Which one encodes thecoarse vs. fine structure ofthe signal?

• What would an image looklike with a lot of highfrequency content?

• What could you do to reducespeckled noise from animage?

)+!"xAsin(

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Fourier Transform

1D Example:• A signal composed of two sine

waves with frequency 2 Hz and 50Hz

• The Fourier Transform of thesignal shows these twofrequencies

frequency

Fourier Transform of f(x)

Signal f(x)

Low Freq

High Freq

High FreqHigh Freq

High Freq

In 2D:• Usually represent low

frequencies near origin, highfrequencies away from origin

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2D Fourier TransformsImage in space domain Image in frequency domain

(magnitude of frequency component)Image in frequency domain

(log magnitude of frequency component)

Original

After low-pass

After high-pass

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2D Fourier TransformsImage in space domain Image in frequency domain

(magnitude of frequency component)Image in frequency domain

(log magnitude of frequency component)

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Frequency Content

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Frequency Content

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Modern Image Generation

From continuous real world to a meaningful image(on computer):

1. Sampling Continuous Information– Information and sampling technique varies widely for each

modality- Topic for later lectures– Computer can only hold discrete chunks of data– Pixel = a single picture element; Voxel = a single volume

element2. Quantizing Samples

– Each discrete chunk must be represented by certain numberof bits

3. Visualization Techniques of quantized, sampled imagevolumes

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2. Quantization

• Only have finite storage available for each pictureelement

• Digital images have “digitized” intensity values.Continuous values are quantized into discrete values.– Example: “Truecolor” on computer displays use 24 bits for

each pixel (8bits blue, 8 bits red, 8bits green=256x256x256possible colors)

– Many medical imaging modalities use intensity values of 12bits per pixel. (2^12=4096 possible gray levels)

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Color depth8 bits per pixel 5 bits per pixel 4 bits per pixel

3 bits per pixel 2 bits per pixel 1 bit per pixel