Image recovery apparatus and removing aberrations in an acquired image from imperfect imaging optics

1 . A computer implemented process for removing aberrations in an acquired image from imperfect imaging optics, the process comprising: acquiring an acquired image of an object with an imperfect imaging system that comprises an imperfect imaging optic, the acquire comprising a plurality of pixels; producing a prior that comprises an expectation of data for the object; determining a pixel-by-pixel uncertainty of the acquired image; determining a total transfer function h k of the acquired image from the prior and the acquire image; and determining a data vector d from the total transfer function h k and the acquired image to remove aberrations from the acquired image; wherein the total transfer function hk is provided by

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2 . The process of claim 1 , further comprising converting the acquired image to vector m j .

3 . The process of claim 1 , wherein the prior is set to zero if there is no expectation of data.

4 . The process of claim 1 , wherein the prior is provided by a Gaussian distribution function.

5 . The process of claim 1 , wherein the expectation comprises information about the object or information about the imperfect imaging system.

6 . The process of claim 1 , wherein determining the pixel-by-pixel uncertainty of the acquired image comprises accounting for photon shot noise of a digital imaging device of the imperfect imaging system that acquired the acquired image.

7 . The process of claim 6 , wherein accounting for the photon shot noise comprises obtaining the square root of the pixel values of the acquired image.

8 . The process of claim 6 , further comprising performing background subtraction on the acquired image prior to determining the pixel-by-pixel uncertainty of the acquired image.

9 . The process of claim 6 , wherein determining the pixel-by-pixel uncertainty of the acquired image comprises accounting for readout noise of the imperfect imaging system that acquired the acquired image.

10 . The process of claim 8 , further comprising, after performing background subtraction, replacing any negative values of the pixel values with a positive value.

11 . The process of claim 10 , wherein the positive value is the smallest positive number of all of the pixels.

12 . The process of claim 10 , wherein the positive value is obtained by averaging pixel values of neighboring pixels.

13 . The process of claim 1 , wherein determining the total transfer function h k comprises determining aberrations in the acquired image, the aberrations comprising attenuation y and phase shift B.

14 . The process of claim 1 , wherein the data vector d is an optimal reconstructed image.

15 . The process of claim 1 , wherein determining the data vector d comprises numerically solving linear equations with a conjugate gradient method.

16 . The process of claim 1 , further comprising estimating a Fourier pupil function of the imperfect imaging system.

17 . The process of claim 16 , wherein estimating the Fourier pupil function comprises determining a density correlation.

18 . The process of claim 16 , wherein estimating the Fourier pupil function comprises determining aberrations in the acquired image from a diffraction pattern in the acquired image.

19 . The process of claim 16 , wherein estimating the Fourier pupil function comprises determining a point spread function and obtaining even order aberrations from the point spread function.

20 . The process of claim 16 , further comprising producing a polynomial a plurality of loss coefficients as a result of estimating the Fourier pupil function of the imperfect imaging system.

21 . The process of claim 20 , further comprising quantifying the spatial structure of the object as the pixel-by-pixel uncertainty of the acquired image.

22 . A computer implemented process for removing aberrations in an acquired image from imperfect imaging optics, the process comprising: acquiring an acquired image of an object with an imperfect imaging system that comprises an imperfect imaging optic, the acquired image comprising a plurality of pixels; producing a prior that comprises an expectation of data for the object; determining a pixel-by-pixel uncertainty of the acquired image; determining a total transfer function h k of the acquired image from the prior and the acquired image; and determining a data vector d from the total transfer function h k and the acquired image to remove aberrations from the acquired image; wherein, in determining the total transfer function h k , the attenuation γ and the phase shift β are accounted for by the following forward transfer function h E

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23 . A computer implemented process for removing aberrations in an acquired image from imperfect imaging optics, the process comprising: acquiring an acquired image of an object with an imperfect imaging system that comprises an imperfect imaging optic, the acquired image comprising a plurality of pixels; producing a prior that comprises an expectation of data for the object; determining a pixel-by-pixel uncertainty of the acquired image; determining a total transfer function h k of the acquired image from the prior and the acquired image; and determining a data vector d from the total transfer function h k and the acquired image to remove aberrations from the acquired image; further comprising verifying a statistical likelihood of the data vector d based on the acquired image and the pixel-by-pixel uncertainty of the acquired image, wherein verifying the statistical likelihood of the data vector d comprises evaluating

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