Method and apparatus for multicolor unmixing through iterative mutual-information minimization in simultaneous channel update structure
Methods and apparatuses for multicolor unmixing may involve iterative mutual information minimization in a simultaneous channel update structure. A plurality of images may be obtained with respect to a plurality of fluorophores labeled on different biomolecules, respectively. Images of the fluorophores may be unmixed from the obtained images, respectively, while simultaneously minimizing mutual information shared between the obtained images based on all permutation combinations of the obtained images. Signals having three or more fluorophores whose emission spectra are overlapped in one spectral range can be more accurately unmixed.
1. A method performed by an electronic device, comprising:
obtaining a plurality of images with respect to a plurality of fluorophores labeled on different biomolecules, respectively; and
unmixing images of the fluorophores from the obtained images, respectively, while simultaneously minimizing mutual information shared between the obtained images based on all permutation combinations ( N P 2 ) of the obtained images;
wherein the unmixing of the images of the respective fluorophores comprises:
selecting two images of the obtained images based on one of all the permutation combinations ( N P 2 );
updating an update function wherein updating of the update function comprises processing the selected images as low-resolution images having lower resolution than the selected images as in [Equation i] below; and
u 1=IMG i
u 2=IMG j
v 1=pixelBinning( u 1 ,m )
v 2=pixelBinning( u 2 ,m ) [Equation i]
wherein the u1 and the u2 indicate the obtained images, the v1 and the v2 indicate the low-resolution images, and the m indicates a factor applied in order to process the obtained images as the low-resolution images, respectively;
calculating the variable from the low-resolution images as in [Equation iii] by using a loss function defined as in [Equation ii] below; and
L
(
α
)
=
I
(
v
1
;
v
2
-
α
×
v
1
)
[
Equation
ii
]
α
i
,
j
^
=
arg
min
α
L
(
α
)
=
arg
min
α
I
(
v
1
;
v
2
-
α
×
v
1
)
[
Equation
iii
]
wherein the indicates the variable;
updating the update function by applying the variable as in [Equation iv] below;
[
X
1
(
k
+
1
)
X
2
(
k
+
1
)
⋮
X
N
(
k
+
1
)
]
=
[
1
-
γ
α
^
1
,
2
(
k
)
…
-
γ
α
^
1
,
N
(
k
)
-
γ
α
^
2
,
1
(
k
)
1
⋱
⋮
⋮
⋱
⋱
-
γ
α
^
N
-
1
,
N
(
k
)
-
γ
α
^
N
,
1
(
k
)
…
-
γ
α
^
N
,
N
-
1
(
k
)
1
]
[
X
1
(
k
)
X
2
(
k
)
⋮
X
N
(
k
)
]
[
Equation
iv
]
wherein the k indicates an iteration number, the γ indicates an update ratio, and the X i(k+1) indicates an i-th channel image after a k-th iteration; and
obtaining a plurality of new images updated from the obtained images by using the update function, and X i(k+1) obtained in a previous step is used as an input image IMG i .
2. The method of claim 1 , wherein the obtaining of the plurality of images comprises obtaining the plurality of images in different detection spectral ranges distinguished from one another, respectively.
3. The method of claim 2 , wherein emission spectra of at least two of the fluorophores are overlapped in each of the detection spectral ranges.
4. The method of claim 1 , wherein the selecting of the two images of the obtained images and updating the update function are iterated based on all the permutation combinations ( N P 2 ), and
wherein, when the iteration is completed, the obtaining the plurality of new images updated from the obtained images is performed.
5. The method of claim 1 , wherein the obtaining of the plurality of new images updated from the obtained images is iterated by a predetermined number of times, and
wherein, when the iteration is completed, the obtained images are obtained as the images of the fluorophores, respectively.
6. The method of claim 1 , wherein
the obtaining of the plurality of new images updated from the obtained images is iterated until the mutual information between the obtained images is equal to or smaller than a reference value, and
wherein, when the iteration is completed, the obtained images are obtained as the images of the fluorophores, respectively.
7. The method of claim 1 , wherein the images of the respective fluorophores are obtained as in [Equation v] by imposing positive number restrictions on a solution obtained through the iterative operation;
X i,k =max( X i,k ,0) [Equation v].
8. An electronic device, comprising:
a memory; and
a processor connected to the memory and configured to execute at least one instruction stored in the memory,
wherein the processor is configured to:
obtain a plurality of images with respect to a plurality of fluorophores labeled on different biomolecules, respectively; and
unmix images of the fluorophores from the obtained images, respectively, while simultaneously minimizing mutual information shared between the obtained images based on all permutation combinations ( N P 2 ) of the obtained images;
wherein the processor is configured to:
select two images of the obtained images based on one of all the permutation combinations ( N P 2 );
process the selected images as low resolution images having lower resolution than the selected images as in [Equation vi] below; and
u 1=IMG i
u 2=IMG j
v 1=pixelBinning( u 1 ,m )
v 2=pixelBinning( u 2 ,m ) [Equation vi]
wherein the u1 and the u2 indicate the obtained images, the v1 and the v2 indicate the low resolution images, and the m indicates a factor applied in order to process the obtained images as the low resolution images, respectively;
calculate the variable from the low resolution images as in [Equation viii] by using a loss function defined as in [Equation vii] below; and
L
(
α
)
=
I
(
v
1
;
v
2
-
α
×
v
1
)
[
Equation
vii
]
=
arg
min
α
L
(
α
)
=
arg
min
α
I
(
v
1
;
v
2
-
α
×
v
1
)
[
Equation
viii
]
wherein the indicates the variable;
updating the update function by applying the variable as in [Equation ix] below;
[
X
1
(
k
+
1
)
X
2
(
k
+
1
)
⋮
X
N
(
k
+
1
)
]
=
[
1
-
γ
α
^
1
,
2
(
k
)
…
-
γ
α
^
1
,
N
(
k
)
-
γ
α
^
2
,
1
(
k
)
1
⋱
⋮
⋮
⋱
⋱
-
γ
α
^
N
-
1
,
N
(
k
)
-
γ
α
^
N
,
1
(
k
)
…
-
γ
α
^
N
,
N
-
1
(
k
)
1
]
[
X
1
(
k
)
X
2
(
k
)
⋮
X
N
(
k
)
]
[
Equation
ix
]
wherein the k indicates an iteration number, the γ indicates an update ratio, and the X i(k+1) indicates an i-th channel image after a k-th iteration.
9. The electronic device of claim 8 , wherein the processor is configured to obtain the plurality of images in different detection spectral ranges distinguished from one another, respectively.
10. The electronic device of claim 9 , wherein emission spectra of at least two of the fluorophores are overlapped in each of the detection spectral ranges.
11. The electronic device of claim 8 , wherein the processor is configured to:
iteratively perform selecting two images of the obtained images and updating the update function based on all the permutation combinations, and
obtain a plurality of new images updated from the obtained images by using the update function when the iteration is completed.
12. The electronic device of claim 8 , wherein the processor is configured to:
iteratively perform obtaining the plurality of new images updated from the obtained images by a predetermined number of times by using the update function, and
obtain the obtained images as the images of the fluorophores, respectively, when completing the iteration.
13. The electronic device of claim 8 , wherein the processor is configured to:
iteratively perform obtaining the plurality of new images updated from the obtained images until the mutual information between the obtained images is equal to or smaller than a reference value by using the update function, and
obtain the obtained images as the images of the fluorophores, respectively, when completing the iteration.
14. The electronic device of claim 8 , wherein the images of the respective fluorophores are obtained as in [Equation x] by imposing positive number restrictions on a solution obtained through the iterative operation;
X i,k =max( X i,k ,0) [Equation x].
15. A non-transitory computer-readable storage medium for storing one or more programs for executing a method, the method comprising:
obtaining a plurality of images with respect to a plurality of fluorophores labeled on different biomolecules, respectively; and
unmixing images of the fluorophores from the obtained images, respectively, while simultaneously minimizing mutual information shared between the obtained images based on all permutation combinations ( N P 2 ) of the obtained images;
wherein the unmixing of the images of the respective fluorophores comprises:
selecting two images of the obtained images based on one of all the permutation combinations ( N P 2 );
updating an update function wherein updating of the update function comprises processing the selected images as low-resolution images having lower resolution than the selected images as in [Equation i] below; and
u 1=IMG i
u 2=IMG j
v 1=pixelBinning( u 1 ,m )
v 2=pixelBinning( u 2 ,m ) [Equation i]
wherein the u1 and the u2 indicate the obtained images, the v1 and the v2 indicate the low-resolution images, and the m indicates a factor applied in order to process the obtained images as the low-resolution images, respectively;
calculating the variable from the low-resolution images as in [Equation iii] by using a loss function defined as in [Equation ii] below; and
L
(
α
)
=
I
(
v
1
;
v
2
-
α
×
v
1
)
[
Equation
ii
]
α
i
,
j
^
=
arg
min
α
L
(
α
)
=
arg
min
α
I
(
v
1
;
v
2
-
α
×
v
1
)
[
Equation
iii
]
wherein the indicates the variable;
updating the update function by applying the variable as in [Equation iv] below;
[
X
1
(
k
+
1
)
X
2
(
k
+
1
)
⋮
X
N
(
k
+
1
)
]
=
[
1
-
γ
α
^
1
,
2
(
k
)
…
-
γ
α
^
1
,
N
(
k
)
-
γ
α
^
2
,
1
(
k
)
1
⋱
⋮
⋮
⋱
⋱
-
γ
α
^
N
-
1
,
N
(
k
)
-
γ
α
^
N
,
1
(
k
)
…
-
γ
α
^
N
,
N
-
1
(
k
)
1
]
[
X
1
(
k
)
X
2
(
k
)
⋮
X
N
(
k
)
]
[
Equation
iv
]
wherein the k indicates an iteration number, the γ indicates an update ratio, and the X i(k+1) indicates an i-th channel image after a k-th iteration; and
obtaining a plurality of new images updated from the obtained images by using the update function, and X i(k+1) obtained in a previous step is used as an input image IMG i .
16. The non-transitory computer-readable storage medium of claim 15 , wherein the images of the respective fluorophores are obtained as in [Equation v] by imposing positive number restrictions on a solution obtained through the iterative operation;
X i,k =max( X i,k ,0) [Equation v].