Methods, systems, and computer readable media for generating and using unbinned image data
Disclosed herein are methods, systems, and computer-readable media for generating and using unbinned image data, characterized by (a) receiving image data corresponding to an image; (b) generating the unbinned image data by performing an unbinning operation on the received image data, wherein the unbinning operation is characterized by conditions of invertibility and smoothness; and (c) using the unbinned image data for either: (i) displaying a version of the image based on the unbinned image data; and/or (ii) performing image processing.
1 . A method for generating and using unbinned image data, the method comprising:
receiving image data corresponding to an image, wherein the image data comprises original pixel intensity values;
generating the unbinned image data by performing an unbinning operation on the original pixel intensity values, wherein the unbinning operation is characterized by conditions of invertibility and smoothness, wherein the condition of invertibility requires that the original pixel intensity values be recoverable by a binning operation after the unbinning operation is performed on the original pixel intensity values, and the unbinning is performed by replacing each original pixel intensity value with multiple pixel intensity values that are unequal yet have a mean value equal to such original pixel intensity value, and subjecting the multiple pixel intensity values to the condition of smoothness by minimizing a measure of irregularity of the multiple pixel intensity values without changing the mean value of the multiple pixel intensity values; and
using the unbinned image data for performing image processing.
2 . The method of claim 1 , wherein generating the unbinned image data by performing an unbinning operation on the original pixel intensity values includes:
defining an unbinned vector b*, wherein elements of the unbinned vector b* have values that are equal to the original pixel intensity values;
determining an unbinned vector {tilde over (b)} as a sum of the unbinned vector b* and a correction vector, wherein the correction vector comprises a product of a transposed bin-constrained derivative vector
d
B
T
and a vector of parameters a; and,
solving for the values of the parameters a, while imposing the condition of smoothness on the unbinned vector {tilde over (b)}.
3 . The method of claim 2 , wherein determining the unbinned vector {tilde over (b)} includes computing the sum using the following expression:
b
˜
=
b
*
+
d
B
T
a
.
4 . The method of claim 2 , wherein solving for the values of the parameters, a, includes using the following expression:
(
d
B
Δ
(
k
)
d
B
T
)
a
=
-
d
B
Δ
(
k
)
b
*
,
where Δ (k) is a Laplacian operator and k is a constant.
5 . The method of claim 4 , wherein k=1.
6 . The method of claim 1 , wherein the image data comprises multi-dimensional image data, and wherein performing the unbinning operation includes performing the unbinning operation for each dimension of the multi-dimensional image data.
7 . The method of claim 3 , comprising applying the condition of smoothness in computing the unbinned vector {tilde over (b)} by computing the derivative of each element in the unbinned vector {tilde over (b)} with respect to the vector of parameters a and minimizing a sum of squares of the derivatives.
8 . The method of claim 1 , further comprising using the unbinned image data to determine an optical property of an optical system.
9 . The method of claim 8 , wherein determining the optical property includes determining a point spread function of the optical system.
10 . A system for generating and using unbinned image data, the system comprising:
a computing platform including at least one processor and a memory;
an unbinned image data generator implemented by the at least one processor for performing an unbinning operation on image data corresponding to an image, wherein the image data comprises original pixel intensity values, and the unbinning operation is characterized by a condition of invertibility and a condition of smoothness, wherein the condition of invertibility requires that the original pixel intensity values be recoverable by a binning operation after the unbinning operation is performed on the original pixel intensity values, and the unbinning is performed by replacing each original pixel intensity value with multiple pixel intensity values that are unequal yet have a mean value equal to such original pixel intensity value, and subjecting the multiple pixel intensity values to the condition of smoothness by minimizing a measure of irregularity of the multiple pixel intensity values without changing the mean value of the multiple pixel intensity values; and,
a memory to receive the unbinned image data for performing image processing.
11 . The system of claim 10 , wherein the unbinned image data generator is configured to:
generate an unbinned vector b*, wherein elements of the unbinned vector b* have values that are equal to the original pixel intensity values;
determine an unbinned vector {tilde over (b)} as a sum of the unbinned vector b* and a correction vector, wherein the correction vector comprises a product of a transposed bin-constrained derivative vector
d
B
T
and a vector of parameters, a; and
solve for the values of the parameters a, while imposing the condition of smoothness on the unbinned vector {tilde over (b)}.
12 . The system of claim 11 , wherein the unbinned image data generator is configured to compute the sum using the following expression:
b
˜
=
b
*
+
d
B
T
a
.
13 . The system of claim 11 , wherein the unbinned image data generator solves for the values of the parameters a using the following expression:
(
d
B
Δ
(
k
)
d
B
T
)
a
=
-
d
B
Δ
(
k
)
b
*
,
where Δ (k) is a Laplacian operator and k is a constant.
14 . The system of claim 13 , where k=1.
15 . The system of claim 10 , wherein the image data comprises multi-dimensional image data and wherein the unbinned image data generator performs the unbinning operation for each dimension of the multi-dimensional image data.
16 . The system of claim 11 , comprising applying the condition of smoothness in computing the unbinned vector {tilde over (b)} by computing the derivative of each element in the unbinned vector {tilde over (b)} with respect to the vector of parameters a and minimizing a sum of squares of the derivatives.
17 . A non-transitory computer readable medium having stored thereon executable instructions that when executed by a processor of a computer control the computer to:
generate unbinned image data by performing an unbinning operation on image data corresponding to an image, wherein the image data comprises original pixel intensity values, and the unbinning operation is characterized by a condition of invertibility and a condition of smoothness, wherein the condition of invertibility requires that the original pixel intensity values be recoverable by a binning operation after the unbinning operation is performed on the original pixel intensity values, and the unbinning is performed by replacing each original pixel intensity value with multiple pixel intensity values that are unequal yet have a mean value equal to such original pixel intensity value, and subjecting the multiple pixel intensity values to the condition of smoothness includes minimizing a measure of irregularity of pixel intensity values in the unbinned image data without changing the mean value of the multiple pixel intensity values; and
store the unbinned image data for performing image processing.