GPU implementation for rapid iterative
image reconstruction algorithm
and its applications in nuclear medicine
Jakub Pietrzak Krzysztof Kacperski
Department of Medical Physics, Maria Skłodowska-Curie Memorial Cancer Center -
Institute of Oncology, Warsaw, Poland
Institute of Experimental Physics, Faculty of Physics, University of Warsaw
Outline
• Single Photon Emission Tomography
• Why do we need more computational power?
• Our software
• Results and efficiency comparison
Outline
• Single Photon Emission Tomography
• Why do we need more computational power?
• Our software
• Results and efficiency comparison
Single Photon Emission Tomography
(SPECT)
Emission Tomography, Miles N. Wernick and John N. Aarsvold
Single Photon Emission Tomography
(SPECT)
Gamma emission
Detector
Radioisotope
SPECT / CT SPECT
• Radiation source inside the
patient,
• functional images of metabolic
processes.
CT
• Radiation source outside the
patient,
• structure of body organs,
(attenuation coefficient).
123I-MIBG SPECT
CT
SPECT/CT
Single Photon Emission Tomography
(SPECT)
series of 100 projections 3d reconstructed data
Single Photon Emission Tomography
(SPECT)
3d reconstructed data
Two approaches to image reconstruction :
Analytical methods FBP
fast but approximate
Statistical (iterative) Reconstruction
MLEM
accurate but more computational power
needed
x
l s
f
p(f,s)
f(x,y)
y
ff2
0
1
1 ),( dPFf(x,y)
g
M
f
OSEM, 30 subs., 2 iter. Phantom
OSEM, 30 subs., 20 iter. FBP
Why Statistical Iterative Reconstruction ?
SPECT:
Why Statistical Iterative Reconstruction ?
• The application of iterative reconstruction methods in SPECT allows to reduce the time of data acquisition process (for instance from 30 to 15 minutes).
• Reduce the radiation dose,
• Enable to use more sophisticated hardware (modeling of hardware physics)
MR collimator (3.5HR), 10 min. with RR, 48 iter. HR collimator, 25 min. with RR, FBP
Outline
• Single Photon Emission Tomography
• Why do we need more computational
power?
• Our software
• Results and efficiency comparison
Taking a single projection.
Geometric collimator response function
Septal penetration, scatter, …
detector
f
g M
g = Mf
Numerical complexity of the full iterative
reconstruction
Typical problem size:
Spatial resulution of SPECT: ~1cm,
Pixel size: 4-8 mm,
Typical reconstruction matrix size: 643 - 1283,
Number of image voxels: ~106 (4 byte values),
Number of iterations: from 20 to 1000,
Number of non-zero elements of M: ~109-1012.
7 × 1013 (r/w operations)
several hours on
standard PC!
1. rotation 2. Gaussian blur 3. projection
.. and aritmethic matrix operations
Numerical operations (rotation based projector)
Image estimate
More iterations?
Ba
ckp
rojectio
n
Image estimate update
?
=
Compare
Measured data
Start Image
Rotation Gaussian blur
Pro
jection
w
ith a
ttenu
atio
n
Projector
Reconstructed Image
measured estimated
Reconstruction
Rotator
Bilinear
(inverse mapping)
Gaussian
( forward mapping )
An Optimal Rotator for Iterative Reconstruction, Jerold W. Wallis and Tom R. Miller
Why do we use CUDA?
• Projection operator is simple to parallelize, values of
projection pixels can be computed independently at the
same time,
• Fast floating point mathematical functions and cashed arrays
can speed up the projection, correction and filtering processes,
• Linear Texture Interpolation (used in rotations),
Outline
• Single Photon Emission Tomography,
• Why do we need more computational power?
• Our software
• Results and efficiency comparison.
Our software
• Complete simulator of the SPECT scanner modeling the physics of emission tomography (xSpect scanner),
• Image reconstruction module (xSpect reconstructor),
• Two versions of the software: GPU and CPU only.
xSpect scanner
xSpect reconstructor
Reconstruction (1)
Reconstruction (2)
Reconstruction (4)
Reconstruction (8)
Reconstruction (16)
Reconstruction (32)
High resolution collimator 32 iterations
High sensitivity collimator 200 iterations
Software applications:
• Investigating properties of reconstruction algorithms
• Simulating different hardware configurations and researching optimal scanning parameters,
• Education/Training in the field of nuclear
medicine imaging.
Outline
• Single Photon Emission Tomography
• Why do we need more computational power?
• Our software
• Results and efficiency comparison
Software tested on:
• PC with Intel Core i7 950,
• 24GB RAM,
• GTX 480,
Results
For the one iteration we gain:
• 45 times faster reconstruction for matrix size 64 x 64 x 64. • 78 times faster reconstruction for matrix size 128 x 128 x 128.
(Gaussian rotator)
17 h
13,5 min 22,9min
0.34min
Tota
l re
const
ructi
on t
ime [
min
]
Collimator
Tim
e [s
]
Matrix size [px]
Matrix size reconstruction time dependence for the 2.2 x HR collimator
Matrix size [px]
Tim
e [
s ]
(bilinear rotator)
Matrix size [px]
Tim
e [
s ]
Matrix size reconstruction time dependence for the 2.2 x HR collimator
(bilinear rotator)
Reconstruction time breakup (bilinear rotator)
10 iterations, high sensitivity collimator, image size: 1283
GPU CPU
10 iterations, high sensitivity collimator, image size: 1283
GPU CPU
Reconstruction time breakup (Gaussian rotator)
Conclusions
• GPU implementation reduces the computation time of the statistical image reconstruction in SPECT by a factor of about ~80 for typical image sizes.
• The speed-up factor grows with the size of image size; it may approach 200 for large images.
• For GPU implementation reducing the dimensions of image matrix may not be an effective way of decreasing the reconstruction time. Similarly, using non pixel based image representations, e.g. blobs, may be suboptimal to just applying a finer pixel grid.
• For standard SPECT 1283 seems to be the optimal image size, readily suitable to apply the fast FFT based filtering.
• Even higher speed gains could be obtained in CT, where typical image sizes are of the order of 10003
Backup
Low dose CT 120 kVp; 3.75-mm slice thickness
FBP ASIR
Adaptive Statistical Iterative Reconstruction Technique for Radiation Dose Reduction in Chest CT: A Pilot Study. Singh S, Kalra, MK Radiology May
1, 2011 259:565-573
Why Statistical Iterative Reconstruction ?
CT:
Why Statistical Iterative Reconstruction ?
• The application of iterative reconstruction methods in computer tomography (CT) allows to reduce radiation dose by 60% with the
same image quality.
150mAs FBP 40mAs ASIR
Abdominal CT: Comparison of Low-Dose CT With Adaptive Statistical Iterative Reconstruction and Routine-Dose CT With Filtered Back Projection in 53 Patients Am. J. Roentgenol. September 1, 2010 195:713-719
25 mGy 12 mGy
X-ray computed tomography (CT)
Maximum likelihood expectation
maximization
M
f
g
M
f
g
M
f
g
M
f
