System and method for solving inverse imaging problems
There is provided a computer-implemented method for solving inverse imaging problems to compensate for distortions in an image. The method comprises: minimizing a cost objective function containing a data fitting term and one or more image prior terms to each of the plurality of channels, the one or more image prior terms comprising cross-channel information for a plurality of channels derived from the image.
1. A method for solving inverse imaging problems in an image, the image comprising information on a plurality of channels, the method comprising:
minimizing a cost objective function containing a data fitting term and one or more image prior terms to each of the plurality of channels, the one or more image prior terms comprising cross-channel information for the plurality of channels derived from the image; and
solving each channel iteratively while holding other channels fixed by:
jointly inverse imaging the image into corresponding channel information associated with each channel, said jointly inverse imaging comprising:
decomposing the image into image components corresponding to respective channels;
reconstructing the image by iteratively minimizing the cost objective function in one channel of the plurality of channels while maintaining the image components in a remaining one or more channels of the plurality of channels, wherein said minimizing the cost objective function comprises a comparison of image components in said one channel to image components in said remaining one or more channels and adjusting said image components accordingly; and
outputting a reconstructed image.
2. The method of claim 1 , wherein each channel comprises information from a range of electromagnetic frequencies.
3. The method of claim 1 , wherein the image comprises information on a plurality of color channels.
4. The method of claim 1 , wherein an image is divided into possibly overlapping tiles, and an inverse imaging sub-problem is solved independently in said tile.
5. The method of claim 1 , further comprising repeating a minimization on each of the remaining one or more channels by maintaining the image components in other channels of said plurality of channels.
6. The method of claim 1 , further comprising performing a calibration comprising:
obtaining a calibration image of a target;
generating a reference image for the target;
comparing the calibration image to the reference image to determine a point spread function (PSF) value for each of a plurality of image tiles; and
using the determined PSF values in the solution of inverse imaging problems.
7. The method of claim 6 , further comprising at least one of comparing and averaging adjacent PSF values to reduce noise.
8. The method of claim 6 , wherein the reference image is obtained synthetically or by obtaining another image with the camera using a different configuration.
9. The method of claim 6 , wherein the joint inverse imaging further comprises utilizing information from a particular channel in the image to correct remaining ones of the plurality of channels in the image.
10. The method of claim 1 , wherein the objective cost function is convex.
11. The method of claim 1 , further comprising at least one of the following: chromatic aberrations, geometric aberrations, spatially varying aberrations, and compensating for motion blur due to movement of an imaging device.
12. The method of claim 1 , wherein aberrations are introduced due to a lens of an imaging device capturing the image.
13. The method of claim 1 , wherein the cost objective function includes at least one of: an effect of a color filter array (CFA), and an effect of a down-sampled image sensor resolution.
14. The method of claim 1 , wherein the reconstructed image corresponds to a global minimum of the cost objective function.
15. The method of claim 1 , wherein the image prior terms include a term for cross-channel information for dark intensity regions.
16. The method of claim 1 , wherein the channels comprise color information representing light wavelengths in the visible range.
17. The method of claim 1 , wherein the channels represent at least one of: electromagnetic radiation in the visible range, and electromagnetic radiation in the non-visible range.
18. The method of claim 1 , wherein the image comprises values between A and B.
19. The method of claim 18 , wherein the image has been offset by +α to include values between A+α and B+α.
20. The method of claim 18 , wherein a resultant improved image has been negatively offset by the addition of −α, to contain values between A and B.
21. The method of claim 1 , wherein the image is captured using an imaging device comprising one or more lens elements.
22. A non-transitory computer readable medium comprising computer executable instructions for solving inverse imaging problems to compensate for distortions in an image, the image comprising information on a plurality of channels, comprising computer executable instructions for:
minimizing a cost objective function containing a data fitting term and one or more image prior terms to each of the plurality of channels, the one or more image prior terms comprising cross-channel information for the plurality of channels derived from the image; and
solving each channel iteratively while holding other channels fixed by:
jointly inverse imaging the image into corresponding channel information associated with each channel, said jointly inverse imaging comprising:
decomposing the image into image components corresponding to respective channels;
reconstructing the image by iteratively minimizing the cost objective function in one channel of the plurality of channels while maintaining the image components in a remaining one or more channels of the plurality of channels, wherein said minimizing the cost objective function comprises a comparison of image components in said one channel to image components in said remaining one or more channels and adjusting said image components accordingly; and
outputting a reconstructed image.
23. The non-transitory computer readable medium of claim 22 , wherein the image comprises information on a plurality of color channels.
24. An electronic device comprising a processor and memory, the memory computer executable instructions for solving inverse imaging problems to compensate for distortions in an image, the image comprising information on a plurality of channels, comprising computer executable instructions for:
minimizing a cost objective function containing a data fitting term and one or more image prior terms to each of the plurality of channels, the one or more image prior terms comprising cross-channel information for the plurality of channels derived from the image; and
solving each channel iteratively while holding other channels fixed by:
jointly inverse imaging the image into corresponding channel information associated with each channel, said jointly inverse imaging comprising:
decomposing the image into image components corresponding to respective channels;
reconstructing the image by iteratively minimizing the cost objective function in one channel of the plurality of channels while maintaining the image components in a remaining one or more channels of the plurality of channels, wherein said minimizing the cost objective function comprises a comparison of image components in said one channel to image components in said remaining one or more channels and adjusting said image components accordingly; and
outputting a reconstructed image.
25. The electronic device of claim 24 , wherein the image comprises information on a plurality of color channels.
26. The computer readable medium of claim 22 , wherein an image is divided into possibly overlapping tiles, and an inverse imaging sub-problem is solved independently in said tile.
27. The computer readable medium of claim 22 , further comprising instructions for repeating a minimization on each of the remaining one or more channels by maintaining the image components in other channels of said plurality of channels.
28. The computer readable medium of claim 22 , further comprising instructions for performing a calibration comprising:
obtaining a calibration image of a target;
generating a reference image for the target;
comparing the calibration image to the reference image to determine a point spread function (PSF) value for each of a plurality of image tiles; and
using the determined PSF values in the solution of inverse imaging problems.
29. The electronic device of claim 24 , wherein an image is divided into possibly overlapping tiles, and an inverse imaging sub-problem is solved independently in said tile.
30. The electronic device of claim 24 , further comprising instructions for repeating a minimization on each of the remaining one or more channels by maintaining the image components in other channels of said plurality of channels.
31. The electronic device of claim 24 , further comprising instructions for performing a calibration comprising:
obtaining a calibration image of a target;
generating a reference image for the target;
comparing the calibration image to the reference image to determine a point spread function (PSF) value for each of a plurality of image tiles; and
using the determined PSF values in the solution of inverse imaging problems.