Multiplexed Fluorescence Unmixing Marina Alterman Yoav Schechner Technion
- Slides: 25
Multiplexed Fluorescence Unmixing Marina Alterman, Yoav Schechner Technion, Israel Aryeh Weiss Bar-Ilan, Israel
2 Natural Linear Mixing i c c i Raskar et al. 2006. i c Image. J image sample collection.
Natural Linear Mixing e s i i o n + c 3 ? c Raskar et al. 2006. + i How do you measure i? c + o n si e i si e Image. J image sample collection.
Single Source Excitation 1 Multiplexed Excitation demultiplex i 1 2 a 1 Beam combiner 1 2 3 i 2 i 3 a 1 a 2 = a 3 3 i 1 i 2 i 3 1 1 0 0 1 1 1 0 1 3 a 2 1 a 3 2 4
Why Multiplexing? i + noise Intensity vector Trivial Measurements Multiplexed Measurements SNR Same acquisition time 5
Multiplexing - Look closer acquisition i Xc i – single source intensities η - noise 6 Estimate c not i estimation Minimum W=?
Multiplexing: a=Wi, Mixing: i=Xc Common Approach Acquired multiplexed intensities 7 This Work Single source intensities Concentrations ˆi a Wi size(i)=7 Nmeasure=7 cˆ a Wi≠Wc Ndyes=3 Nsources=7 ˆi cˆ Wc Nmeasure=3 efficient acquisition Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
8 Fluorescence Cell structure and processes Fluorescent Specimen Horse Dermal Fibroblast Cells Intestine Tissue Corn Grain Flea http: //www. microscopyu. com/galleries/fluorescence, http: //www. microscopy. fsu. edu/primer/techniques/fluorescence/fluorogallery. html
9 Linear Mixing i c More molecules per pixel Brighter pixel Molecules per pixel c i i= x∙c Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
10 Linear Mixing i {cd} For each pixel: i = x 1 x 2 ∙ ∙ ∙ x. N dyes c 1 c 2 ∙∙ ∙ c Ndyes vector of concentrations Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing (spatial distribution)
11 Linear Mixing i 1 s=2 {cd} For each pixel: {cd} i 1= x 1, 1 x 1, 2∙ ∙ ∙ x 1, N dyes i 2= x 2, 1 x 2, 2∙ ∙ ∙ x 2, N ∙∙ ∙ dyes i s= x s, 1 x s, 2 ∙ ∙ ∙ x s, N vector of intensities i 2 Mixing matrix dyes c 1 c 2 ∙∙ ∙ c Ndyes vector of concentrations (spatial distribution)
12 Linear Mixing i 1 s=1 {cd} i 2 s=2 {cd} For each pixel: vector of intensities Mixing matrix vector of concentrations (spatial distribution)
Fluorescent Microscope 13 Intensity image e(λ) 300 400 500 600 700 λ Emission Filter s= 1 s= 2 s= 3 e(λ) 300 400 500 600 700 λ Dichroic Mirror s= 4 L 2(λ) s=5 Excitation Filter Fluorescent Specimen Excitation Sources s: illumination sources Blue α(λ) 300 400 500 600 700 λ
Fluorescent Microscope 14 Intensity image (mixed) e(λ) 300 400 500 600 700 λ ired u q e r g n i x i m n U Emission Filter s= 1 s= 2 e(λ) Cross-talk 300 400 500 600 700 λ s= 3 Dichroic Mirror s= 4 L 2(λ) Excitation Filter Fluorescent Specimen Green s=5 Excitation Sources s: illumination sources Blue α(λ) Cross-talk 300 400 500 600 700 λ
Problem Definition Fluorescent specimen Intensity image (mixed) e s i o n + Unmix How to multiplex for least noisy unmixing? Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing n e s oi 15
Sum up the concepts Acquired multiplexed image intensities a de a m an M Single source Image intensities W multiplexing demultiplexing -1 W 16 e r u t Na X i mixing unmixing Concentrations c X-1 multiplexed unmixing Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
17 Look closer - again i – single source intensities η - noise i Xc Estimate c not i Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
Multiplexed Unmixing acquisition For each pixel estimation i acquired measurements a = W multiplexing matrix X 18 noise c + mixing matrix WX is not square OR Weighted Least OR Squares Minimum Variance in c W=? Other estimators
Generalizations Image intensities 19 Minimum Var W=? η - noise i =? var(η) = constant c =? concentrations var(η) = constant c =? var(η) ≠ constant Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing Detai ls in t pape he r
20 Generalized Multiplex Gain What is the SNR gain for unmixing? Only Unmixing VS. Unmixing + Multiplexing Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
21 Significance of the Model GAINc 2. 2 a 2 1. 8 ˆi Wc Wi≠Wc cˆ VS. 1. 6 ˆi a 1. 4 1. 2 cˆ Wi 1 3 4 5 6 7 Nsources=Nmeasure Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing
22 Significance of the Model GAINc 2. 2 a 2 ˆc ˆi Wc 1. 8 1. 6 1. 4 1. 2 1 3 4 5 6 Nsources=Nmeasure Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing 7
23 Significance of the Model GAINc 2. 2 a 2 ˆc ˆi Wc 1. 8 ˆi a 1. 6 cˆ Wi 1. 4 1. 2 1 GAIN < 1 3 4 5 6 Nsources=Nmeasure For specific 3 dyes, camera and filter characteristics 7
Natural Linear Mixing e s i i o n + c 24 ? c Raskar et al. 2006. + i c + o n si e i si e Image. J image sample collection.
25 Multiplexed Unmixing Xc i Generalization of multiplexing theory The goal is unmixing SNR improvement Efficient Acquisition Exploit all available sources a = W Alterman, Schechner & Weiss, Multiplexed Fluorescence Unmixing X c + η
