Biomedical Imaging Hyperspectral Imaging Charles A. DiMarzio & Eric M. Kercher EECE–4649 Northeastern University Universidad de los Andes June 2019
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Biomedical Imaging
Hyperspectral Imaging
Charles A. DiMarzio & Eric M. Kercher
EECE–4649
Northeastern University
Universidad de los Andes
June 2019
Why Spectral?
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–1
Why Hyperspectral
Right ≈ North, Down = [400 to 2400 nm] (not Linear)
South Bay of California; 101 curves down on the left.
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–2
Why Hyperspectral
Right ≈ North, Down = [400 to 2400 nm] (not Linear)
Where are the Shrimp?
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–3
Hardware
• Tunable Filter (Lyot Filter, Pronounced “Leo”)
– x, y on camera
– λ with time
• Grating spectrometer with Pinhole
– λ on Camera
– x, y with time (whiskbroom: Slow)
∗ Slit, Grating and 2D Camera
· x, λ on camera
· y with time (pushbroom)
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–4
Applications
• Military (Where’s the Tank in the Trees?)
• Law Enforcement (Which crop is illegal?)
• Environmental (e.g. Deep Horizon)
• Biomedical
– Fluorescence Spectroscopy (Multiple, Overlapping Fluo-
rophores)
– Hemoglobin Spectroscopy
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–5
Forward Models
• Monte–Carlo
• Diffusion
• FDTD
• Linear Spectral Prediction
Yλ =N∑
n=1
Mλ,nXn
• Backscatter
Y = µa M = κn (λ)
• Fluorescence
Y = Eλ M = Eλ,n
• Intuitive Backscatter
1
W=
µs + µa
µs
1
W= 1+
µa
µs
• or µaℓeff = ln (1/T )
• Linear Superposition
µa (λ) =N∑
n=1
κn (λ)Xn
• Fluorescence
Source Powers Add
Eλ (λ) =N∑
n=1
Eλ,n (λ)Xn
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–6
Some CommonAbsorbers
200 300 400 500 600 700 800 900 1000
,Wavelength, nm
10-4
10-3
10-2
10-1
100
101
102
103
104
a,
Ab
sorp
tio
n C
oef
f, /
cm
Oxy in Skin
Deoxy
Oxy in Blood
Deoxy
Water
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–7
Some CommonFluorophores
200 300 400 500 600 700
, Wavelength, nm
-2
0
2
4
6
8
10
12
a,
Sp
ecif
ic A
bso
rpti
on
(cm
M)
- 1
104 Dye Spectra (file m10254.m)
488 514 633
Hoechst 33258
FITC Isomer 1
Mito Green FM
Mito CMXRos
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–8
Matrix Methods
• Forward Problem
Y = MX
• Typical Example
Y (λ1)
Y (λ2)
Y (λ3)
Y (λ4)...
Y (λ200)
=
M1,1 M1,2 M1,3
M2,1 M2,2 M2,3
M3,1 M3,2 M3,3
M4,1 M4,2 M4,3... ... ...
M200,1 M200,2 M200,3
X1
X2
X3
• Inverse Problem
X = M−1Y Oh No!!!
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–9
Variance, Covariance
• Variance:
Mean of Squared Difference from Mean
• Covariance:
Mean of Squared Difference
• Each Pixel (k) is a Column
Y =
Y1 (λ1) Y2 (λ1) . . .
Y1 (λ2) Y2 (λ1) . . .
Y1 (λ3) Y2 (λ1) . . .... . . .
Y1 (λ200) Y2 (λ200) . . .
COV (Y) = YY†
• We can visualize this in 3D space
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–10
Variance, Covariance,Principal Components
• Covariance
COV (Y) = YY†
• Find Eigenvalues and Eigenvectors
• Arrange in Eigenvalue Order Decending
• Remember Y = MX for a pixel or Y = MX for an image
• It’s Possible from this to Guess
– M, the basis comonent spectra in columns
– X , the strength of each component in each pixel
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–11
Non–Negative LeastSquares
Real–Time NLSS
Eric M. Kercher
NU Physics Ph.D. Candidate
DOC Teaching Assistant 2018
Application to Skin Imaging
Jaime Prieto & Matias Rivera
(UAndes)
Everett O’Malley (NU, UCSB)
June 2019 Chuck DiMarzio, Northeastern University 12286..slides7–12
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