Surround subtraction

Report
Miguel Lourenço Rodrigues
Master’s thesis in Biomedical Engineering
December 2011
1
Outline
1. Introduction and Objectives
2. Methods: Problem Formulation,
Simulations and Real Data
3. Results and Discussion
4. Conclusions
2
Outline
1. Introduction
2. Literature Review
3. Problem Formulation
4. Experimental Results and Discussion
5. Conclusions
3
Introduction
Arterial Spin Labeling (ASL):
Se [1] e [2] são refs, deviam
aparecer antes com nome e ano
-Non invasive technique for generating perfusion images of the brain
[1]
-Cerebral Blood Flow (CBF):
Volume of blood flowing per unit time[2]
-Perfusion:
CBF per unit volume of tissues
4
Introduction
ASL:
Labeled acquisiton
Este slide e o
seguinte deviam ser
1 só
2. Image acquisition
1. Labeling of inflowing
arterial blood
5
Introduction
ASL
Control acquisiton
4. Image acquisition
3. No labeling
6
Introduction
ASL
Control image
Labeled image
CBF
A number of control-label repetitions is required in order to achieve
sufficient SNR to detect the magnetization difference signal, hence
increasing scan duration.
n length vector
Ci – ith control image
[C1, L1, C2, L2,…, Cn/2, Ln/2]
Li – ith labeled image
P- perfusion
7
Introduction
ASL signal processing methods
Pair-wise subtraction:
[P1, P2,…, Pn/2]=[C1- L1, C2- L2,…, Cn/2-Ln/2]
Surround subtraction:
[P1, P2,…, Pn/2]=[C1- L1, C2- (L1+L2),…, Cn/2-(L(n/2)-1-Ln/2)]
Sinc-interpolated subtraction:
2
2
[P1, P2,…, Pn/2]=[C1- L1/2, C2- L3/2,…, Cn/2-Ln/2-1/2]
8
Objectives
Objectives
-Increase image Signal to Noise Ratio (SNR)
-Reduce acquisition time
Approach
- New signal processing model
- Bayesian approach
- spatio-temporal priors
No drastic signal variatons
(except in organ boundaries)
9
Outline
1. Introduction
2. Literature Review
3. Problem Formulation
4. Experimental Results and Discussion
5. Conclusions
10
Problem Formulation
Mathematical model
Y(t)=F+D(t)+v(t)ΔM+Γ(t)
Y
(NxMxL)
(1)
– Sequence of L PASL images
F (NxM) – Static magnetization of the tissues
D(NxM x L) – Slow variant image (baseline fluctuations of the signal – Drift)
v(L x 1) - Binary signal indicating labeling sequences
ΔM(NxM ) - Magnetization difference caused by the inversion
Γ(NxM xL) – Additive White Gaussian Noise ~N (0,σy2)
11
Problem Formulation
Mathematical model
Y(t)=F+D(t)+v(t)ΔM+Γ(t)
(1)
12
Problem Formulation
Algorithm implementation
Y(t)=F+D(t)+v(t)ΔM+Γ(t)
(1)
Vectorization
Y=fuT+D+ΔmvT+Γ
Y(NM x L)
f(NM x1)
u(L x 1)
D(NM x L)
(2)
v(L x 1)
Δm(NM x 1)
Γ(NM x 1)
13
Problem Formulation
Algorithm implementation
Since noise is AWGN,
p(Y)~N (μ, σy2), where μ=fuT+D+ΔmvT
Maximum likelihood (ML) estimation of unknown images, θ={f,D, Δm}
θ=arg min Ey(Y,v,θ)
θ
(3)
Ill-posed problem
14
Problem Formulation
Algorithm implementation
θ=arg min Ey(Y,v,θ)
θ
(3)
Using the Maximum a posteriori (MAP) criterion, regularization is
introduced by the prior distribution of the parameters
θ=arg min E (Y,v,θ)
θ
(4)
E (Y,v,θ)=Ey (Y,v, θ) + Eθ(θ)
Data – fidelity term
(5)
Prior term
15
Problem Formulation
Algorithm implementation
Figure from [11]
16
Problem Formulation
Algorithm implementation
E (Y,v,θ)=Ey (Y,v, θ) + Eθ(θ)
(5)
E (Y,v,θ)= ½ Trace [(Y-fuT-D-ΔmvT) T (Y-fuT-D-ΔmvT)]
+αTrace[(φhD)T(φhD)+(φvD)T(φvD)+(φtD)T(φtD)]
+β(φhf)T(φhf)+(φvf)T(φvf)
(6)
+γ(φhΔm)T(φhΔm)+(φvΔm)T(φvΔm)
17
Problem Formulation
Algorithm implementation
-In equation (6), the matrices φh,v,t are used to compute the horizontal,
Vertical and temporal first order differences, respectively
Φ=
1
0
0
.
-1
-1
1
0
.
0
0
-1
1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0
0
0
.
-1
1
0
-α, β and γ are the priors.
18
Problem Formulation
Algorithm implementation
-MAP solution as a global mininum
-Stationary points of the Energy Function – equation (6)
- Equations implemented in Matlab and calculated iteratively
19
Outline
1. Introduction
2. Literature Review
3. Problem Formulation
4. Experimental Results and Discussion
5. Conclusions
20
Experimental Results and Discussion
Synthetic data
-Brain mask (64x64)
-Axial slice
-White matter (WM) and Gray matter (GM)
- SNR=
Asignal
2
Anoise
- Mean error(%)=
;
ISNR=SNRf-SNRi
100
NxM
∑
N,M
^
|xi,j-xi,j|
xi,j
i=1,j=1
21
Experimental Results and Discussion
Synthetic data
Parameters:
σ=1
Δm(GM)=1
Δm(WM)=0.5
D=[-1,1]
F=10000
α=0
β=0
γ=0
Control acquisition
Labeled acquisition
22
Experimental Results and Discussion
Synthetic data
Parameters:
σ=1
Δm(GM)=1
Δm(WM)=0.5
D=[-1,1]
F=10000
α=0
β=0
γ=0
Proposed
algorithm
Pair-wise
subtraction
Surround
Subtraction
23
Experimental Results and Discussion
Synthetic data
Method
ISNR(dB)
Mean Error (%)
Proposed algorithm
13.906
24.658
Pair-wise subtraction
13.906
24.658
Surround Subtraction
13.999
24.393
24
Experimental Results and Discussion
Synthetic data
Prior optimization
25
Experimental Results and Discussion
Synthetic data
Prior optimization
Incresasing prior value
26
Experimental Results and Discussion
Synthetic data
Prior optimization
27
Experimental Results and Discussion
Synthetic data
Prior optimization
β=1
γ=5
28
Experimental Results and Discussion
Synthetic data
Parameters:
σ=1
Δm(GM)=1
Δm(WM)=0.5
D=[-1,1]
F=10000
α=1
β=1
γ=5
Proposed
algorithm
Pair-wise
subtraction
Surround
Subtraction
29
Experimental Results and Discussion
Synthetic data
Parameters:
σ=1
Δm(GM)=1
Δm(WM)=0.5
D=[-1,1]
F=10000
α=1
β=1
γ=5
30
Experimental Results and Discussion
Synthetic data
Method
ISNR(dB)
Mean Error (%)
Proposed algorithm
16.990
17.807
Pair-wise subtraction
14.026
24.492
Surround Subtraction
14.103
24.269
31
Experimental Results and Discussion
Synthetic data
Method
ISNR(dB)
Mean Error (%)
Proposed algorithm
16.990
17.807
Pair-wise subtraction
14.026
24.492
Surround Subtraction
14.103
24.269
3dB
23%
7%
-30%
32
Experimental Results and Discussion
Synthetic data
Monte Carlo Simulation for different noise levels
33
Experimental Results and Discussion
Real data
-One healthy subject
-3T Siemens MRI system (Hospital da Luz, Lisboa)
-PICORE-Q2TIPS PASL sequence
-TI1/TI1s/TI2=750ms/900ms/1700ms
-GE-EPI
-TR/TE=2500ms/19ms
-spatial resolution: 3.5x3.5x7.0 mm3
-201 repetitions
-Matrix size: 64x64x9
34
Experimental Results and Discussion
Real data
Control image
Labeled image
35
Experimental Results and Discussion
Real data
Proposed
algorithm
Pair-wise
subtraction
Surround
Subtraction
36
Experimental Results and Discussion
Real data
-Influence of the
number of iterations
37
Experimental Results and Discussion
Real data
Proposed
algorithm
Pair-wise
subtraction
Surround
Subtraction
38
Experimental Results and Discussion
Real data
39
Outline
1. Introduction
2. Literature Review
3. Problem Formulation
4. Experimental Results and Discussion
5. Conclusions
40
Conclusion
-The proposed bayesian algorithm showed improvement of SNR and ME
-SNR increased by 3db (23%)
-ME decreased by 7% (30%)
-Applied to real data
Future work:
-Automatic prior calculation
-Reducing the number of control acquisitions
-Validation tests on empirical data
41
Bibliography
[1] T.T. Liu and G.G. Brown. Measurement of cerebral perfusion with arterial spin labeling: Part 1. Methods. Journal of the International
neuropsychological Society, 13(03):517-525, 2007.
[2]A.C. Guyton and J.E. Hall. Textbook of medical physiology. WB Saunders (Philadelphia),1995.
[3]D.S. Williams, J.A. Detre, J.S. Leigh, and A.P. Koretsky. Magnetic resonance imaging of perfusion using spin inversion of arterial water.
Proceedings of the National Academy of Sciences, 89(1):212, 1992.
[4]ET Petersen, I. Zimine, Y.C.L. Ho, and X. Golay. Non-invasive measurement of perfusion: a critical review of arterial spin labeling
techniques. British journal of radiology, 79(944):688, 2006.
[5]R.R. Edelman, D.G. Darby, and S. Warach. Qualitative mapping of cerebral blood flow and functional localization with echo-planar mr
imaging and signal targeting with alternating radio frequency. Radiology, 192:513-520, 1994.
[6]DM Garcia, C. De Bazelaire, and D. Alsop. Pseudo-continuous ow driven adiabatic inversion for arterial spin labeling. In Proc Int Soc
Magn Reson Med, volume 13, page 37, 2005.
[7]E.C. Wong, M. Cronin, W.C. Wu, B. Inglis, L.R. Frank, and T.T. Liu. Velocity-selective arterial spin labeling. Magnetic Resonance in Medicine,
55:1334{1341, 2006.
[8]W.C. Wu and E.C. Wong. Feasibility of velocity selective arterial spin labeling in functional mri. Journal of Cerebral Blood Flow &
Metabolism, 27(4):831{838, 2006
[9]GK Aguirre, JA Detre, E. Zarahn, and DC Alsop. Experimental Design and the Relative Sensitivity of BOLD and Perfusion fMRI.
NeuroImage, 15:488{500, 2002.
[10]E.C. Wong, R.B. Buxton, and L.R. Frank. Implementation of Quantitative Perfusion Imaging Techniques for Functional Brain Mapping
using Pulsed Arterial Spin Labeling. NMR in Biomedicine, 10:237{249, 1997.
[11] J.M. Sanches, J.C. Nascimento, and J.S. Marques. Medical image noise reduction using the Sylvester-Lyapunov equation. IEEE
transactions on image processing, 17(9), 2008.
42
Questions
43

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