multiplexed fluorescence unmixing
DESCRIPTION
Multiplexed Fluorescence Unmixing. Marina Alterman , Yoav Schechner. Technion , Israel. Aryeh Weiss. Bar- Ilan , Israel. Natural Linear Mixing. i. c. i. c. Raskar et al. 2006. i. c. ImageJ image sample collection. Natural Linear Mixing. ?. + noise. i. c. i. + noise. - PowerPoint PPT PresentationTRANSCRIPT
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Multiplexed Fluorescence Unmixing
Marina Alterman, Yoav Schechner
Aryeh Weiss
Technion, Israel
Bar-Ilan, Israel
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Natural Linear Mixing
Raskar et al. 2006.
i Xc=
ImageJ image sample collection.
c
c i
i
c
i
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3
Natural Linear Mixing i Xc=?
ImageJ image sample collection.
c+ noise
Raskar et al. 2006.
c i
i
+ noise
How do you measure i?
c
i
+ noise
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Single Source Excitation
Multiplexed Excitation
4demultiplex
i1
i2
i3
1 2 3
1 2 3
1 2 3
1
a31 1 0 1 0 1 0 1 1
2
3
Beamcombiner
a11 1 0 1 0 1 0 1 1
1
2
a21 1 0 1 0 1 0 1 1
3
31
2 a = 0 1 1 ia 1 1 0 i
a 1 0 1 i
1
2
3
1
2
3
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Why Multiplexing?
+ noiseSNR
Trivial Measurements
SNR
Multiplexed Measurements
Same acquisition time
Intensity vector
i
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Multiplexing - Look closer6
a W
Xci
i – single source intensitiesη - noise
estimation1
ˆ Wi a
acquisition
2 1
sources
Var traceˆT
NW W
i
( )var h
Minimum W=?
Estimate c not i
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a i
Wi
a i c
Wc
Common Approach This Work
c
Concentrations
Single sourceintensities
Acquired multiplexed intensities
efficient acquisition
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
Ndyes=3Nsources=7size(i)=7
Nmeasure=3
Nmeasure=7
Wi≠Wc
Multiplexing: a=Wi, Mixing: i=Xc
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Fluorescence8
http://www.microscopyu.com/galleries/fluorescence, http://www.microscopy.fsu.edu/primer/techniques/fluorescence/fluorogallery.html
Cell structure and processes
Corn GrainFleaIntestine Tissue
Horse Dermal Fibroblast Cells
Fluorescent Specimen
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Linear Mixing
Molecules per pixel
More molecules per pixel
Brighter pixelc
i
i cµi = x c∙
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
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Linear Mixing
{cd}
i
vector of concentrations (spatial distribution)
For each pixel: i = x x x∙ ∙ ∙1 2 Ndyes
cc∙∙∙c
12
Ndyes
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
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Linear Mixing
s=1i
vector of intensities Mixing matrix
cc∙∙∙c
12
Ndyes
1s=2
i2
i = x x x∙ ∙ ∙1,1 1,2 1,Ndyes1
i = x x x∙ ∙ ∙2,1 2,2 2,Ndyes2
i = x x x∙ ∙ ∙s,1 s,2 s,Ndyess
∙∙∙
{cd} {cd}
vector of concentrations (spatial distribution)
For each pixel:
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Linear Mixing
i Xc=
s=1i
vector of intensities Mixing matrix
For each pixel:
s=2i21
{cd} {cd}
vector of concentrations (spatial distribution)
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Fluorescent Microscope
Fluorescent Specimen
DichroicMirror
EmissionFilter
unmix1
Intensity image
unmix1
Blue
d=1
L2(λ)
13
300 400 500 600 700 λ
300 400 500 600 700 λ
Excitation Sources
Excitation Filter
s=1
s=2
s=3
s=4
=5s
s: illumination sources
e(λ)
e(λ)
300 400 500 600 700 λ
α(λ)
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unmix1
Intensity imageFluorescent Microscope
Fluorescent Specimen
DichroicMirror
EmissionFilter
unmix2
Green
d=2
L2(λ)300 400 500 600 700 λ
300 400 500 600 700 λ
Excitation Sources
Excitation Filter
s=1
s=2
s=3
s=4
=5s
s: illumination sources
300 400 500 600 700 λ
α(λ)
e(λ)
e(λ)
Cross-talk
Cross-talk
14
Unmixing required
Intensity image(mixed)
unmix1
Blue
d=1
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unmix1
unmix2
mix
Problem Definition15
Unmix
Intensity image (mixed)
+ noisenoise
How to multiplex for least noisy unmixing?
Fluorescent specimen
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
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Sum up the concepts
ciamixing
unmixing
multiplexing
demultiplexing
Concentrations
Single sourceImage intensities
Acquired multiplexed image intensities
X
X-1
W
W-1
NatureMan made
16
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
multiplexed unmixing
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Look closer - again17
a W
Xci
Estimate c not i
i – single source intensitiesη - noise
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
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Multiplexed Unmixing
acquisition
Minimum Variance in c W=?
For each pixel
18
i
c= +a
acquired measurements
Wmultiplexing
matrixX
mixingmatrix
η
noise
estimation1
ˆ c W X a
OR Weighted Least Squares
WX is not square
Other estimatorsOR
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Generalizations19
2 1
sourcesˆVar trace T
NiW W
( )var h
2 1
dyes
Var trace ( )ˆT
NWX WXc
( )var h
11
noisedyes
1Var traceˆT
NWX WXc
var(η) = constant
var(η) = constant
i =?
( )cov h
c =?
c =? var(η) ≠ constant
Image intensities
concentrations
Minimum Var W=?
η - noise
Details in the paper
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
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Generalized Multiplex Gain
trivialˆ
ˆ
VarGAIN
Var=c
c
c=W I
20
What is the SNR gain for unmixing?
Only Unmixing
Unmixing +
Multiplexing
VS.
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
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Significance of the Model
Nsources=Nmeasure3 4 5 6 7
1
1.2
1.4
1.6
1.8
2
2.2
21
GAINc a i c
Wc
a i c
Wi
VS.
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
Wi≠Wc
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Significance of the Model
Nsources=Nmeasure3 4 5 6 7
1
1.2
1.4
1.6
1.8
2
2.2
22
GAINc ai
c
W c
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
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Significance of the Model
Nsources=Nmeasure3 4 5 6 7
1
1.2
1.4
1.6
1.8
2
2.2
23
GAINc
GAIN < 1
For specific 3 dyes, camera and filter characteristics
a i c
Wi
ai
c
W c
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Natural Linear Mixing i Xc=?
ImageJ image sample collection.
c+ noise
Raskar et al. 2006.
c i
i
+ noisec
i
+ noise
=a Wi
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= +a X cW
Multiplexed Unmixing
25
η
a W iXc
The goal is unmixing
Efficient Acquisition
Exploit all available sources
SNR improvement
Generalization of multiplexing theory
Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing