Method and apparatus for multiplexed imaging of biomolecule through iterative unmixing of fluorophore signals
The present disclosure provides a method and apparatus for biomolecular multiplexed imaging through the iterative unmixing of fluorophores. According to the first embodiments of the present disclosure, although signals of two fluorophores are detected in the first fluorescent detection spectral range, the signals of the two images obtained from two detection spectral ranges can be unmixed through the iterative minimization of mutual information. Furthermore, the present disclosure provides a multi-color unmixing method and apparatus through the iterative minimization of mutual information. In the second embodiments of the present disclosure, a plurality of images of a plurality of fluorophores marking different biomolecules, respectively, for example, N fluorophores are obtained. Images, each containing the signals of single fluorophore can be obtained from the obtained images while minimizing the mutual information shared by images of each of pairs each consisting of two of the obtained images.
1. A method of an electronic device, comprising:
obtaining at least two images of at least two fluorophores marking different biomolecules, respectively; and
unmixing the at least two images into unmixed images, each of the unmixed images containing signals of a single fluorophore, while iteratively minimizing mutual information shared by the at least two images in the unmixed images,
wherein the obtaining of the at least two images of at least two fluorophores comprises obtaining two images of two fluorophores, and
wherein the unmixing of the two images comprises obtaining two unmixed images updated from the two images by applying variables for minimizing the mutual information calculated with respect to the two images, the iteration resulting in each of the unmixed images containing signals of a single fluorophore,
wherein the obtaining of the two updated unmixed images from the two images comprises processing the two images as low-resolution images having lower resolution than the two images, respectively, as in [Equation i] below;
v 1=pixelBinning( u 1, k )
v 2=pixelBinning( u 2, k ) [Equation i]
wherein the u1 and the u2 indicate the two images, respectively, the v1 and the v2 indicate the low-resolution images, respectively, and the k indicates a factor applied in order to process the two images as the low-resolution images, respectively,
calculating variables from the low-resolution images as in [Equation iii] below by using a loss function defined as in [Equation ii] below; and
L
1
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α
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=
I
(
v
1
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(
α
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v
2
;
v
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,
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β
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=
I
(
v
1
;
v
2
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β
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v
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[
Equation
ii
]
β
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=
arg
min
β
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2
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=
arg
min
β
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v
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v
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[
Equation
iii
]
wherein the {circumflex over (α)} and {circumflex over (β)} the indicate the variables, respectively,
obtaining the two updated unmixed images from the two images by applying the variables and an update ratio λ to the two images as in [Equation iv] below;
u 1← u 1−λ{circumflex over (α)} u 2
u 2← u 2−λ{circumflex over (β)} u 1 [Equation iv]
2. A method of an electronic device, comprising:
obtaining at least two images of at least two fluorophores marking different biomolecules, respectively; and
unmixing the at least two images into unmixed images, each of the unmixed images containing signals of a single fluorophore, while iteratively minimizing mutual information shared by the at least two images in the unmixed images,
wherein the obtaining of at least two images of at least two fluorophores comprises obtaining three or more images of three or more fluorophores, and
wherein the unmixing of the at least two images comprises unmixing the three or more images into the unmixed images, each of the unmixed images containing signals of a single fluorophore, while minimizing the mutual information shared by each pair of the three or more images, each pair consisting of two of the three of more images.
3. The method of claim 2 , wherein the unmixing of the three or more images comprises obtaining a plurality of unmixed images updated from the three or more images by applying variables for minimizing the mutual information calculated with respect to the each pair of the three or more images.
4. The method of claim 3 , wherein the obtaining of a plurality of unmixed images updated from the three or more images is configured to obtain the plurality of unmixed images updated from the three or more images at a predetermined update speed and is iterated by a predetermined number, and
when the iteration of the obtaining of the unmixed images updated from the three or more images is completed, each of the unmixed images containing signals of a single fluorophore.
5. The method of claim 4 , wherein the number is determined based on target accuracy and the update speed as in [Equation v] below:
(1−ζ) p <ε [Equation v]
wherein the p indicates the number, the c indicates the target accuracy, the indicates the update speed, and the update speed is a real number between 0 and 1.
6. The method of claim 3 , wherein the obtaining of a plurality of unmixed images updated from the three or more images comprises:
calculating the variables from each pair of the three or more images; and
updating one of the pairs of the three or more images by applying the variables to the one of the pairs of the three or more images.
7. 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 at least two images of at least two fluorophores marking different biomolecules, respectively, and
unmix the at least two images into unmixed images, each of the unmixed images containing signals of a single fluorophore, while iteratively minimizing mutual information shared by the at least two images in the unmixed images,
obtain three or more images of three or more fluorophores, and
unmix the three or more images into the unmixed images, each of the unmixed images containing the signals of a single fluorophore, while minimizing the mutual information shared by each pair of the three or more images.
8. The electronic device of claim 7 , wherein the processor is configured to perform an operation of obtaining a plurality of unmixed images updated from the three or more images by applying a variable for minimizing mutual information calculated with respect to each pair of the three or more images.
9. The electronic device of claim 8 , wherein the processor is configured to:
perform the operation at a predetermined update speed, and
iterate the operation by a predetermined number,
when the iteration of the operation is completed, images, each containing the signals of a single fluorophore, are obtained.
10. The electronic device of claim 9 , wherein the number is determined based on target accuracy and the update speed for each of the images of the respective fluorophores as in [Equation x] below:
(1−ζ) p <ε [Equation x]
wherein the p indicates the number, the c indicates the target accuracy, the ζ indicates the update speed, and the update speed is a real number between 0 and 1.
11. The electronic device of claim 8 , wherein the processor is configured to:
calculate the variables from each pair of the three or more images, and
update one of the pairs of the three or more images by applying the variables to the one of the pairs of the three or more images.