Surround subtraction - ISR

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24 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

68 εμφανίσεις

Miguel Lourenço Rodrigues

Master’s thesis in Biomedical Engineering

December

2011

1

2

Outline

1.

Introduction

and

Objectives

2.

Methods
:
Problem

Formulation
,
Simulations

and

Real Data

3.
Results

and

Discussion

4.

Conclusions


Outline

1.

Introduction

2.

Literature

Review

3.

Problem

Formulation

4.

Experimental
Results

and

Discussion

5.

Conclusions


3

4

Introduction

-
Cerebral
Blood

Flow

(CBF):

Volume
of

blood

flowing

per

unit

time
[2]

-
Perfusion
:

CBF
per

unit

volume
of

tissues

Arterial
Spin

Labeling

(ASL):

-
Non

invasive

technique

for
generating

perfusion

images

of

the

brain

[1]

Se [1]
e

[2]
são

refs,
deviam

aparecer

antes com
nome

e

ano

5

Introduction

Labeled

acquisiton

1.
Labeling

of

inflowing


arterial
blood

2.
Image

acquisition


ASL:

Este slide
e

o

seguinte

deviam

ser
1


6

Introduction

ASL

Control

acquisiton

3. No
labeling

4.
Image

acquisition


7

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.

[C
1
, L
1
, C
2
, L
2
,…,
C
n
/2
,
L
n
/2
]

n
length

vector

C
i



i
th

control

image

L
i



i
th

labeled

image

P
-

perfusion

8

Introduction

ASL
signal

processing

methods

Pair
-
wise

subtraction
:

[P
1
, P
2
,…,
P
n
/2
]=[C
1
-

L
1
, C
2
-

L
2
,…,
C
n
/2
-
L
n/2
]

Surround

subtraction
:

[P
1
, P
2
,…,
P
n
/2
]=[C
1
-

L
1
, C
2
-

(L
1
+L
2
),…,
C
n
/2
-
(L
(n/2)
-
1
-
L
n/2
)]

2

2

Sinc
-
interpolated

subtraction
:

[P
1
, P
2
,…,
P
n
/2
]=[C
1
-

L
1/2
, C
2
-

L
3/2
,…,
C
n
/2
-
L
n/2
-
1/2
]

9

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
)

10

Outline

1.

Introduction

2.

Literature

Review

3.

Problem

Formulation

4.

Experimental
Results

and

Discussion

5.

Conclusions


11

Problem

Formulation

Mathematical

model

Y(t)=F+D(t)+v(t)ΔM+
Γ
(t)



Y
(
NxMxL
)


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,
σ
y
2
)


(1)

12

Problem

Formulation

Mathematical

model

Y(t)=F+D(t)+v(t)ΔM+
Γ
(t)

(1)

13

Problem

Formulation

Algorithm

implementation

Y(t)=F+D(t)+v(t)ΔM+
Γ
(t)

(1)

Vectorization

Y=fu
T
+D+
Δmv
T
+
Γ

Y
(NM x L)

f
(NM x1)

u
(L x 1)

D
(NM x L)

v
(L x 1)

Δm
(NM x 1)

Γ
(NM x 1)

(2)

14

Problem

Formulation

Algorithm

implementation

Since

noise

is

AWGN,

p(
Y
)~
N
(
μ
,

σ
y
2
),
where


μ
=
fu
T
+D+
Δmv
T

Maximum

likelihood

(ML)
estimation

of

unknown

images
,
θ
={
f
,
D
,

Δm
}
=
θ
=arg

min

E
y
(
Y
,
v
,
θ
)

θ

Ill
-
posed

problem

(3)

15

Problem

Formulation

Algorithm

implementation

Using

the

Maximum

a posteriori
(MAP)
criterion
,
regularization

is

introduced

by

the

prior
distribution

of

the

parameters

θ
=arg

min

E
y
(
Y
,
v
,
θ
)

θ

(3)

θ
=arg

min

E

(
Y
,
v
,
θ
)

θ

(4)

E

(
Y
,
v
,
θ
)
=E
y

(
Y,v
,

θ
) + E
θ
(
θ
)

(5)

Data


fidelity

term

Prior
term

16

Problem

Formulation

Algorithm

implementation

Figure
from

[11]

17

Problem

Formulation

Algorithm

implementation

E

(
Y
,
v
,
θ
)
=E
y

(
Y,v
,

θ
) + E
θ
(
θ
)

(5)

½ Trace [(
Y
-
fu
T
-
D
-
Δmv
T
)

T

(
Y
-
fu
T
-
D
-
Δmv
T
)]


E

(
Y
,
v
,
θ
)=

+
α
Trace[(
φ
h
D
)
T
(
φ
h
D
)+(
φ
v
D
)
T
(
φ
v
D
)+(
φ
t
D
)
T
(
φ
t
D
)]

+
β
(
φ
h
f
)
T
(
φ
h
f
)+(
φ
v
f
)
T
(
φ
v
f
)

+
γ
(
φ
h
Δm
)
T
(
φ
h
Δm
)+(
φ
v
Δm
)
T
(
φ
v
Δm
)

(6)

18

Problem

Formulation

Algorithm

implementation

-
In

equation

(6),
the

matrices

φ
h,v,t


are
used

to compute
the

horizontal,

Vertical
and

temporal
first

order

differences
,
respectively

1

0

0

.

-
1

-
1

1

0

.

0

0

-
1

1

0

.

.

.

.

.

.

.

.

.

.

.

.

.

.

0

0

0

.

-
1

1

Φ
=

-
α
,
β

and

γ

are
the

priors
.

19

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

20

Outline

1.

Introduction

2.

Literature

Review

3.

Problem

Formulation

4.

Experimental
Results

and

Discussion

5.

Conclusions


21

Experimental
Results

and

Discussion

Synthetic

data

-
Brain

mask

(64x64)

-
Axial
slice

-
White

matter

(WM)
and

Gray

matter

(GM)

ISNR=SNR
f
-
SNR
i



100

NxM

N,M

i=1,j=1

|x
i,j
-
x
i,j
|

x
i,j

^

Mean

error
(%)=

SNR=

A
signal

A
noise

2

-

;

-

22

Experimental
Results

and

Discussion

Synthetic

data

Control

acquisition

Labeled

acquisition

Parameters
:

σ
=1

Δm
Ed䴩=1
=
Δm
(WM)=0.5

D
=[
-
1,1]

F
=10000

α=0

β
=0

γ
=0

23

Experimental
Results

and

Discussion

Synthetic

data

Proposed


algorithm

Pair
-
wise

subtraction

Surround

Subtraction

Parameters
:

σ
=1

Δm
Ed䴩=1
=
Δm
(WM)=0.5

D
=[
-
1,1]

F
=10000

α=0

β
=0

γ
=0

24

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

25

Experimental
Results

and

Discussion

Synthetic

data

Prior
optimization

26

Experimental
Results

and

Discussion

Synthetic

data

Prior
optimization

Incresasing

prior
value

27

Experimental
Results

and

Discussion

Synthetic

data

Prior
optimization

28

Experimental
Results

and

Discussion

Synthetic

data

Prior
optimization

β
=1

γ
=5

29

Experimental
Results

and

Discussion

Synthetic

data

Parameters
:

σ
=1

Δm
Ed䴩=1
=
Δm
(WM)=0.5

D
=[
-
1,1]

F
=10000

α=1

β
=1

γ
=5

Proposed


algorithm

Pair
-
wise

subtraction

Surround

Subtraction

30

Experimental
Results

and

Discussion

Synthetic

data

Parameters
:

σ
=1

Δm
Ed䴩=1
=
Δm
(WM)=0.5

D
=[
-
1,1]

F
=10000

α=1

β
=1

γ
=5

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

32

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

7%

23%

-
30%

33

Experimental
Results

and

Discussion

Synthetic

data

Monte
Carlo

Simulation

for
different

noise

levels

34

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

-
201
repetitions

-
spatial

resolution
: 3.5x3.5x7.0 mm
3

-
Matrix

size
: 64x64x9

35

Control

image

Labeled

image

Experimental
Results

and

Discussion

Real data

36

Experimental
Results

and

Discussion

Real data

Proposed


algorithm

Pair
-
wise

subtraction

Surround

Subtraction

37

Experimental
Results

and

Discussion

Real data

-
Influence

of

the

number

of

iterations

38

Proposed


algorithm

Pair
-
wise

subtraction

Surround

Subtraction

Experimental
Results

and

Discussion

Real data

39

Experimental
Results

and

Discussion

Real data

40

Outline

1.

Introduction

2.

Literature

Review

3.

Problem

Formulation

4.

Experimental
Results

and

Discussion

5.

Conclusions


41

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

42

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43

Questions