Machine learning assisted super resolution microscopy

1. A method of providing super-resolved images of a photon emitting particle, comprising:

providing a machine-learning (ML) platform, wherein the ML platform is configured to receive pixel-based sparse autocorrelation data and generate a predicted super-resolved image of a photon emitting particle;

receiving photons from the photon emitting particle by two or more photon detectors, each generating an electrical pulse associated with receiving an incident photon thereon;

generating sparse autocorrelation data from the two or more photon detectors for each pixel within an image area; and

inputting the pixel-based sparse autocorrelation data to the ML platform, thereby generating a predicted super-resolved image of the imaging area, wherein the resolution of the super-resolved image is improved by √n as compared to a classical optical microscope limited by Abbe diffraction limit.

2. The method of claim 1 , wherein n is 2.

3. The method of claim 2 , wherein processing speed of generating the super-resolved image is improved by at least 12 times as compared to a non-ML arrangement.

4. The method of claim 1 , wherein the ML platform is a convolutional neural network (CNN).

5. The method of claim 1 , training of the ML platform, comprising:

providing the pixel-based generated sparse autocorrelation data from the two or more photon detectors to the ML platform in training;

generate a predicted super-resolved image for all pixels within the imaging area;

compare the predicted super-resolved image for all pixels with a super-resolved image generated experimentally from a full dataset, thereby generating an error signal; and

minimizing the error signal by altering characteristics of the ML platform.

6. The method of claim 5 , wherein the experimentally generated super-resolved image is based on:

G (n) ( x,y )˜ Ñ ( x,y ) n Σ i=1 i=i max c i X i ,

where Ñ(x, y) is the average number of detected photons from a given point (x,y) of the imaging area,

X i is a function of the product g (i 1 ) (x, y, 0)g (i 2 ) (x, y, 0) . . . g (i l ) (x, y, 0), and

i max is the number of ordered combinations, fulfilling the condition Σ k=1 l j k =n.

7. The method of claim 6 , wherein if n=2 (2 detectors) G (2) (x,y) is expressed by:

G (2) ( x,y )˜ Ñ ( x,y ) 2 (1− g (2) ( x,y, 0)).

8. The method of claim 7 , wherein the 2 nd order autocorrelation function is expressed by Levenberg-Marquardt (LM) fitting:

g

(

2

)

(

τ

)

=

1

-

a

1

⁢

e

-

τ

t

1

+

a

2

⁢

e

-

τ

t

2

where, a j , t j , j=1,2 are the fitting parameters related to internal dynamics of the photon emitters.

9. The method of claim 8 , wherein the ML platform is a convolutional neural network.

10. The method of claim 6 , wherein the error minimization is based on gradient descent.

11. A system for generating super-resolved images of a photon emitting particle, comprising:

a platform configured to receive a particle for which a super-resolved image to be generated;

a light source configured to illuminate the particle;

two or more photon detectors configured to receive photons emanating from the particle, each photon detector generating an electrical pulse associated with receiving an incident photon emanating from the particle thereon; and

a computer system having a processor and non-transient memory with software thereon configured to:

provide a machine-learning (ML) platform, the ML platform is configured to receive pixel-based sparse autocorrelation data associated with the two or more detectors and generate a predicted super-resolved image of the photon emitting particle;

generate sparse autocorrelation data from the two or more photon detectors for each pixel within an image area; and

input the pixel-based sparse autocorrelation data to the ML platform, thereby generating a predicted super-resolved image of the imaging area, wherein the resolution of the super-resolved image is improved by √n as compared to a classical optical microscope limited by Abbe's diffraction limit.

12. The system of claim 11 , wherein n is 2.

13. The system of claim 12 , wherein processing speed of generating the super-resolved image is improved by at least 12 times as compared to a non-ML arrangement.

14. The system of claim 11 , wherein the ML platform is a convolutional neural network (CNN).

15. The system of claim 11 , training of the ML platform, comprising:

providing the pixel-based generated sparse autocorrelation data from the two or more photon detectors to the ML platform in training;

generate a predicted super-resolved image for all pixels within the imaging area;

compare the predicted super-resolved image for all pixels with a super-resolved image generated experimentally from a full dataset, thereby generating an error signal; and

minimizing the error signal by altering characteristics of the ML platform.

16. The system of claim 15 , wherein the experimentally generated super-resolved image is based on:

G (n) ( x,y )˜ Ñ ( x,y ) n Σ i=1 i=i max c i X i ,

where Ñ(x, y) is the average number of detected photons from a given point (x,y) of the imaging area,

X i is a function of the product g (i 1 ) (x, y, 0)g (i 2 ) (x, y, 0) . . . g (i l ) (x, y, 0, and

i max is the number of ordered combinations, fulfilling the condition Σ k=1 l j k =n.

17. The system of claim 16 , wherein if n=2 (2 detectors) G (2) (x,y) is expressed by:

G (2) ( x,y )˜ Ñ ( x,y ) 2 (1− g (2) ( x,y, 0)).

18. The system of claim 17 , wherein the 2 nd order autocorrelation function is expressed by Levenberg-Marquardt (LM) fitting:

g

(

2

)

(

τ

)

=

1

-

a

1

⁢

e

-

τ

t

1

+

a

2

⁢

e

-

τ

t

2

where, a j , t j , j=1,2 are the fitting parameters related to internal dynamics of the photon emitters.

19. The system of claim 18 , wherein the ML platform is a convolutional neural network.

20. The system of claim 16 , wherein the error minimization is based on gradient descent.