Multiplexed Fluorescence Unmixing - PowerPoint Presentation

Slide1

Multiplexed Fluorescence Unmixing

Marina Alterman, Yoav Schechner

Aryeh

Weiss

Technion

, Israel

Bar-

Ilan

, Israel

Slide2

2

Natural Linear Mixing

Raskar

et al.

2006.

ImageJ

image sample

collection.

c

c

i

i

c

i

Slide3

3

Natural Linear Mixing

?

ImageJ

image sample

collection.

c

+ noise

Raskar

et al.

2006.

c

i

i

+ noise

How do you measure

i

?

c

i

+ noise

Slide4

Single Source Excitation

Multiplexed Excitation

4

demultiplex

i

1

i

2

i

3

1

a

3

2

3

Beam

combiner

a

1

1

2

a

2

3

3

1

2

a

=

0

1 1

i

a

1

1 0

i

a

1

0 1

i

1

2

3

1

2

3

Slide5

Why Multiplexing?

+

noise

SNR

Trivial

Measurements

SNR

Multiplexed Measurements

Same acquisition time

5

Intensity vector

i

Slide6

Multiplexing - Look closer

6

Xc

i

i

– single source intensities

η

- noiseestimation

acquisition

Minimum

 W=?

Estimate

c

not

i

Slide7

7

a

i

ˆ

W

i

a

i

ˆ

c

ˆ

W

c

Common Approach

This Work

c

ˆ

Concentrations

Single source

intensities

Acquired multiplexed

intensities

efficient acquisition

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

N

dyes

=3

N

sources

=7

size(

i

)=7

N

measure

=3

N

measure

=7

W

i

≠

W

c

Multiplexing:

a=

Wi, Mixing:

i=Xc

Slide8

Fluorescence

8

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

Cell structure and processes

Corn Grain

Flea

Intestine Tissue

Horse Dermal Fibroblast Cells

Fluorescent Specimen

Slide9

9

Linear Mixing

Molecules per pixel

More molecules per pixel

Brighter pixel

c

i

i

c

i

=

x∙c

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

Slide10

10

Linear Mixing

{

c

d

}

i

vector of concentrations

(spatial distribution)

For each pixel:

i

= x

x

∙ ∙ ∙ x

1 2

N

dyes

c

c

∙

∙

∙

c

1

2

N

dyes

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

Slide11

11

Linear Mixing

s=1

i

vector of intensities

Mixing matrix

c

c

∙

∙

∙

c

1

2

N

dyes

1

s=2

i

2

i

= x

x

∙ ∙ ∙ x

1

,1

1

,2

1

,N

dyes

1

i

= x

x

∙ ∙ ∙ x

2

,1

2

,2

2

,N

dyes

2

i

= x

x

∙ ∙ ∙ x

s

,1

s

,2

s

,N

dyes

s

∙

∙

∙

{

c

d

}

{

c

d

}

vector of concentrations

(spatial distribution)

For each pixel:

Slide12

12

Linear Mixing

s=1

i

vector of intensities

Mixing matrix

For each pixel:

s=2

i

2

1

{

c

d

}

{

c

d

}

vector of concentrations

(spatial distribution)

Slide13

Fluorescent Microscope

Fluorescent

Specimen

Dichroic

Mirror

Emission

Filter

Intensity image

Blue

L

2

(

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

=

5

s

s

:

illumination sources

e(

λ

)

e(

λ

)

300 400 500 600 700

λ

α

(

λ

)

Slide14

Intensity image

Fluorescent Microscope

Fluorescent

Specimen

Dichroic

Mirror

Emission

Filter

Green

L

2

(

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

=

5

s

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)

Blue

Slide15

Problem Definition

15

Unmix

Intensity image (mixed)

+ noise

noise

How to multiplex for least noisy unmixing?

Fluorescent specimen

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

Slide16

Sum up the concepts

c

i

a

mixing

un

mixing

multiplexing

de

multiplexing

Concentrations

Single source

Image intensities

Acquired multiplexed

image intensities

X

X

-1

W

W

-1

Nature

Man made

16

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

multiplexed

unmixing

Slide17

Look closer - again

17

Xc

i

Estimate

c

not

i

i

– single source intensities

η

- noise

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

Slide18

Multiplexed Unmixing

acquisition Minimum Variance in c

 W=?

For each pixel

18

i

c

=

+

a

acquired measurements

W

multiplexing

matrix

X

mixing

matrix

noise

estimation

OR

Weighted Least Squares

WX is not square

Other estimators

OR

Slide19

Generalizations

19

var

(

η

) =

constant

var

(

η

) =

constant

i

=?

c =?

c =?

var

(

η

) ≠

constant

Image intensities

concentrations

Minimum

Var

 W=?

η

- noise

Details in the paper

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

Slide20

Generalized Multiplex Gain

20

What is the SNR gain for unmixing?

Only Unmixing

Unmixing

+ Multiplexing

VS.

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

Slide21

Significance of the Model

N

sources

=

N

measure

3

4

5

6

7

1

1.2

1.4

1.6

1.8

2

2.2

21

GAIN

c

a

i

ˆ

c

ˆ

W

c

a

i

ˆ

c

ˆ

W

i

VS.

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

W

i

≠

W

c

Slide22

Significance of the Model

N

sources

=

N

measure

3

4

5

6

7

1

1.2

1.4

1.6

1.8

2

2.2

22

GAIN

c

a

i

ˆ

c

ˆ

W

c

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing

Slide23

Significance of the Model

N

sources

=

N

measure

3

4

5

6

7

1

1.2

1.4

1.6

1.8

2

2.2

23

GAIN

c

GAIN < 1

For specific 3 dyes, camera and filter characteristics

a

i

ˆ

c

ˆ

W

i

a

i

ˆ

c

ˆ

W

c

Slide24

24

Natural Linear Mixing

?

ImageJ

image sample

collection.

c

+ noise

Raskar

et al.

2006.

c

i

i

+ noise

c

i

+ noise

Slide25

=

+

a

X

c

W

Multiplexed

Unmixing

25

η

i

Xc

The goal is unmixing

Efficient Acquisition

Exploit all available sources

SNR improvement

Generalization of multiplexing theory

Alterman

,

Schechner

&

Weiss,

Multiplexed Fluorescence

Unmixing