multiplexed fluorescence unmixing

Multiplexed Fluorescence Unmixing

Marina Alterman, Yoav Schechner

Aryeh Weiss

Technion, Israel

Bar-Ilan, Israel

2

Natural Linear Mixing

Raskar et al. 2006.

i Xc=

ImageJ image sample collection.

c

c i

i

c

i

3

Natural Linear Mixing i Xc=?


c+ noise

Raskar et al. 2006.

c i

i

+ noise

How do you measure i?

c

i

+ noise

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

5

Why Multiplexing?

+ noiseSNR

Trivial Measurements

SNR

Multiplexed Measurements

Same acquisition time

Intensity vector

i

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

7

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

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

9

Linear Mixing

Molecules per pixel

More molecules per pixel

Brighter pixelc

i

i cµi = x c∙


10

Linear Mixing

{cd}

i

vector of concentrations (spatial distribution)

For each pixel: i = x x x∙ ∙ ∙1 2 Ndyes

cc∙∙∙c

12

Ndyes


11

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}


For each pixel:

12

Linear Mixing

i Xc=

s=1i

vector of intensities Mixing matrix

For each pixel:

s=2i21

{cd} {cd}


Fluorescent Microscope


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)

unmix1

Intensity imageFluorescent Microscope


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

unmix1

unmix2

mix

Problem Definition15

Unmix

Intensity image (mixed)

+ noisenoise

How to multiplex for least noisy unmixing?

Fluorescent specimen


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


multiplexed unmixing

Look closer - again17

a W

Xci

Estimate c not i

i – single source intensitiesη - noise


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

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


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.


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.


Wi≠Wc



1

1.2

1.4

1.6

1.8

2

2.2

22

GAINc ai

c

W c




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

24

Natural Linear Mixing i Xc=?


c+ noise

Raskar et al. 2006.

c i

i

+ noisec

i

+ noise

=a Wi

= +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


multiplexed fluorescence unmixing

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