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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.

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multiplexed fluorescence unmixing

Multiplexed Fluorescence Unmixing

Marina Alterman, YoavSchechner

Technion, Israel

Aryeh Weiss

Bar-Ilan, Israel

slide2

Natural Linear Mixing

i

c

i

c

Raskar et al. 2006.

i

c

ImageJ image sample

collection.

slide3

Natural Linear Mixing

?

+ noise

i

c

i

+ noise

c

Raskar et al. 2006.

i

+ noise

How do you measure i?

c

ImageJ image sample

collection.

slide4

a1 1 0 i

1

1

a = 0 1 1 i

2

2

a1 0 1 i

3

3

Single Source Excitation

demultiplex

Multiplexed Excitation

i1

2

1

a1

1

3

i2

a2

2

1

3

i3

a3

3

Beam

combiner

2

why multiplexing
Why Multiplexing?

Trivial

Measurements

Multiplexed Measurements

i

+

noise

SNR

SNR

Intensity vector

Same acquisition time

multiplexing look closer

i – single source intensities

η - noise

Multiplexing - Look closer

Estimate c noti

Xc

i

acquisition

estimation

Minimum  W=?

slide7

Multiplexing: a=Wi, Mixing: i=Xc

Common Approach

This Work

Acquired multiplexed

intensities

Single source

intensities

Concentrations

ˆ

ˆ

ˆ

ˆ

c

c

i

i

a

a

Wi≠Wc

Wi

Wc

Ndyes=3

Nsources=7

Nmeasure=3

size(i)=7

efficient acquisition

Nmeasure=7

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

fluorescence
Fluorescence

Cell structure and processes

Fluorescent Specimen

Horse Dermal Fibroblast Cells

Corn Grain

Intestine Tissue

Flea

http://www.microscopyu.com/galleries/fluorescence, http://www.microscopy.fsu.edu/primer/techniques/fluorescence/fluorogallery.html

linear mixing
Linear Mixing

i

More molecules per pixel

Brighter pixel

c

i c

Molecules per pixel

i = x∙c

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

linear mixing1
Linear Mixing

i

{cd}

i = x x ∙ ∙ ∙ x

For each pixel:

c

c

c

1 2 Ndyes

1

2

Ndyes

vector of concentrations (spatial distribution)

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

linear mixing2
Linear Mixing

i

i

1

2

s=1

s=2

{cd}

{cd}

For each pixel:

i = x x ∙ ∙ ∙ x

i = x x ∙ ∙ ∙ x

i = x x ∙ ∙ ∙ x

c

c

c

1

2

s

2,1 2,2 2,Ndyes

1,1 1,2 1,Ndyes

s,1 s,2 s,Ndyes

1

2

Ndyes

vector of concentrations (spatial distribution)

vector of intensities

Mixing matrix

linear mixing3
Linear Mixing

i

i

1

2

s=1

s=2

{cd}

{cd}

For each pixel:

vector of concentrations (spatial distribution)

vector of intensities

Mixing matrix

fluorescent microscope
Fluorescent Microscope

Intensity image

e(λ)

Emission

Filter

s

=

1

s

=

2

s

=

3

e(λ)

s

=

4

Dichroic

Mirror

L2(λ)

s

=

5

Excitation

Excitation

Fluorescent

Filter

Sources

λ

λ

λ

300 400 500 600 700

300 400 500 600 700

300 400 500 600 700

Specimen

s: illumination sources

Blue

α(λ)

fluorescent microscope1
Fluorescent Microscope

Intensity image

(mixed)

Intensity image

e(λ)

Unmixing required

Emission

Filter

s

=

1

s

=

2

s

=

3

e(λ)

s

=

4

Dichroic

Mirror

L2(λ)

s

=

5

Excitation

Excitation

Fluorescent

Filter

Sources

λ

λ

λ

300 400 500 600 700

300 400 500 600 700

300 400 500 600 700

Specimen

s: illumination sources

Green

Blue

Cross-talk

α(λ)

Cross-talk

problem definition

Unmix

Fluorescent specimen

Problem Definition

Intensity image (mixed)

+ noise

noise

How to multiplex for least noisy unmixing?

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

sum up the concepts
Sum up the concepts

Man made

Nature

Acquired multiplexed

image intensities

Single source

Image intensities

W

X

a

i

Concentrations

multiplexing

mixing

c

unmixing

demultiplexing

W-1

X-1

multiplexed unmixing

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

look closer again
Look closer - again

i – single source intensities

η - noise

Xc

i

Estimate c noti

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

multiplexed unmixing
Multiplexed Unmixing

acquisition

For each pixel

i

acquired measurements

noise

estimation

a

X

W

c

WX is not square

+

=

Weighted Least Squares

Other estimators

OR

multiplexing

matrix

OR

mixing

matrix

Minimum Variance in c  W=?

generalizations
Generalizations

Minimum Var W=?

η - noise

Image intensities

i =?

var(η) =constant

Details in the paper

concentrations

c =?

var(η) =constant

c =?

var(η) ≠constant

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

generalized multiplex gain
Generalized Multiplex Gain

What is the SNR gain for unmixing?

Only Unmixing

VS.

Unmixing

+ Multiplexing

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

significance of the model

2.2

2

1.8

1.6

1.4

1.2

1

3

4

5

6

7

Nsources=Nmeasure

Significance of the Model

ˆ

ˆ

c

GAINc

ˆ

ˆ

c

i

i

a

a

VS.

Wi≠Wc

Wi

Wc

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

significance of the model1

2.2

2

1.8

1.6

1.4

1.2

1

3

4

5

6

7

Nsources=Nmeasure

Significance of the Model

ˆ

ˆ

c

GAINc

i

a

Wc

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing

significance of the model2
Significance of the Model

ˆ

ˆ

2.2

c

GAINc

ˆ

ˆ

c

i

i

a

2

a

1.8

1.6

Wi

1.4

1.2

1

Wc

3

4

5

6

7

GAIN < 1

Nsources=Nmeasure

For specific 3 dyes, camera and filter characteristics

slide24

Natural Linear Mixing

?

+ noise

i

c

i

+ noise

c

Raskar et al. 2006.

i

+ noise

c

ImageJ image sample

collection.

multiplexed unmixing1
Multiplexed Unmixing

Xc

i

Generalization of multiplexing theory

The goal is unmixing

SNR improvement

Efficient Acquisition

Exploit all available sources

a

X

+

=

c

η

W

Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing