imaging

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imaging

EMISSION COMPUTED TOMOGRAPHY AND

IMAGE RECONSTRUCTION METHODS

Benjamin M.W. Tsui, Ph.D.*

Division of Medical Imaging Physics

The Russell H. Morgan Department of Radiology and Radiological Science

*Joint appointments in Department of Electrical and Computer Engineering and Department Environmental Health Sciences

Adjunct in Department of Biomedical Engineering


INTRODUCTION

• SPECT (Single-Photon Emission Computed

Tomography) is a combination of nuclear medicine

imaging technique and methods of image

reconstruction from projections


2D PLANAR (PROJECTION) IMAGING

• Single projection view

– Difficult to differentiate

overlapping structures

• Multiple oblique views

– Provides limited depthof-field

& some

differentiation of

overlapping structures

– Time consuming &

difficult


IMAGE RECONSTRUCTION PROBLEM

Projection Data Acquisition

Image Reconstruction

from Projections

‘Forward Problem’

‘Radon Transform’

‘Inverse Problem’

‘Inverse Radon Transform’


SPECT IMAGE RECONSTRUCTION METHODS

•Goal

– Obtain an estimate of ‘true’ radioactivity in vivo

• Methods

– Use 2D projections from different projections

around the patient

– Apply 3D image reconstruction techniques


IMAGE RECONSTRUCTION PROBLEM

Single planar view

Dual Oblique views

Tomographic Images


IMAGE RECONSTRUCTION

FROM PROJECTIONS

• Three general approaches

– Simple backprojection

– Analytical techniques (Nobel prize)

(solution of the inverse Radon transform problem)

• Filtered of the backprojection

• Backprojection of the filtered projection

(filtered backprojection)

– Iterative reconstruction techniques


SIMPLE BACKPROJECTION

• Intuitive approach

• First applied in the 60s

• Backproject intensity at each

projection bin uniformly

across the reconstructed

image space

• Disadvantage

– Blurred reconstructed images


SIMPLE BACKPROJECTION

Object

distribution

Reconstructed

Images:

Increment of

23 o (8 views)

Up to 180 o

(64 views)


ANALYTICAL METHODS

(Convolution and Filtered Backprojection Technique)

• From solution of inverse Radon transform

– a Nobel prize winning mathematic problem

• Major steps

– Apply ‘special function’ to projections

– Backproject ‘processed’ or ‘filtered’ projection

• Special functions

– Spatial domain (convolution)

• function w/ big central peak & small side lobes

– Spatial frequency domain (multiplication)

• Ramp function


STEPS OF FILTERED PROJECTION

(Frequency domain operation)

1. Fourier transform

each projection


MUSICOLOGY

(Tuning fork sound ‘images’ in the time domain)

Single

tuning

fork

C4 (261.63 Hz) E4 (329.63 Hz) G4 (392 Hz)

C4 E4 G4

C4, E4, G4

Multiple

tuning

fork


Sound image in time domain

(Tuning forks)

ANALOGY OF MUSIC

C4, E4, G4

Fourier

Transform

Sound image in frequency domain

(Tuning forks)


STEPS OF FILTERED PROJECTION

(Frequency domain operation)

1. Fourier transform

each projection

2. Multiply by a ‘ramp’ function


STEPS OF FILTERED PROJECTION

(Frequency domain operation)

3. Inverse Fourier transform to obtain

‘processed’ or ‘filtered’ projection

4. Backproject the ‘filtered’

projections from all views

to obtain the reconstructed

image


FILTERED BACKPROJECTION

(noise-free)

Object

distribution

Reconstructed

Images:

Increment of

23 o (8 views)

Up to 180 o

(64 views)


SIMULATION DATA USING

REALISTIC COMPUTER-GENERATED PHANTOM

3D NCAT Phantom

Simulated ideal SPECT projection data

3D radioactivity distribution

3D attenuation coefficient distribution


IMAGE RECONSTRUCTION IN MYOCARDIAL SPECT

Simulation study under ideal conditions

3D

radioactivity distribution

Filtered backprojection images

from ideal projection data

(i.e., without image degrading factors)


ADDITIONAL FILTERING

USED IN IMAGE RECONSTRUCTION

Ramp Function

(from image reconstruction)

Additional Filters

(for noise smoothing &

image enhancement)

Combined Filters


EFFECTS OF DIFFERENT FILTERS

Hann Butterwoth Metz

Noise smoothing Noise smoothing

Edge preservation

Edge enhancement


SIMULATION DATA USING

REALISTIC COMPUTER-GENERATED PHANTOM

3D NCAT Phantom

Simulated SPECT projection data with

effects of image degrading factors*

3D radioactivity distribution

3D attenuation coefficient distribution

* collimator-detector response and

photon attenuation and scatter


NOISY PROJECTIONS FROM 3D NCAT PHANTOM

Noise level:

~15 Kcounts/view


RECONSTRUCTED IMAGES FROM REALISTIC

PROJECTION DATA OF 3D NCAT PHANTOM

From noise-free projection data

using the ramp function

From noisy projection using the ramp function

and the Hann smoothing filter

0.1 0.2 0.3 0.4 0.5

Cut-off Frequency (cycle/pixel)


BUTTERWORTH SMOOTHING FILTER

reletive magnitude

Relative Magnitude

1.2

1

0.8

0.6

0.4

0.2

0

n=2,fc=0.1

n=8,fc=0.1

n=32,fc=0.1

n=2,fc=0.3

n=8,fc=0.3

n=32,fc=0.3

-0.2

0 0.1 0.2 0.3 0.4 0.5

Spatial Frequency (cycle/pixel)


RECONSTRUCTED IMAGES OF

REALISTIC NOISY PROJECTION DATA

Using the ramp function and the Butterworth smoothing filter

Order

n=2

n=8

n=32

0.1 0.2 0.3 0.4 0.5

Cut-off Frequency (cycle/pixel)

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