Airy-disk correction for deblurring an image
In one embodiment, a method includes accessing an image captured by an imaging system that includes an aperture and an optical sensor, wherein the imaging system blurs the image; and de-blurring the image by applying an Airy-disk correction that attributes at least part of the blurring in the image to a circular aperture rather than to a pinhole aperture.
1 . A method comprising:
accessing an image captured by an imaging system comprising an aperture and an optical sensor, wherein the imaging system blurs the image;
determining an Airy-disk correction that attributes at least part of the blurring in the image to a circular aperture rather than to a pinhole aperture, comprising:
determining an inverse kernel for the image, wherein the inverse kernel attributes blurring in the image to a pinhole aperture;
updating the inverse kernel to attribute blurring in the image to a circular aperture rather than to a pinhole aperture;
using the updated inverse kernel to determine the Airy-disk correction; and
generating a deblurred image by applying the determined Airy-disk correction to the accessed image.
2 . The method of claim 1 , wherein updating the inverse kernel comprises:
determining a Fourier-space representation H of a point-spread function for the imaging system that attributes blurring to a pinhole aperture;
determining a Fourier-space representation K of a point-spread function for the imaging system that attributes blurring to a circular aperture; and
determining a Fourier-space representation of de-blurred image based on: (1) convolving H and K, and (2) the accessed image captured by the imaging system.
3 . The method of claim 1 , further comprising:
converting the image to plurality of image channels, wherein one of the plurality of channels represents a luminance of the image; and
de-blurring the image by applying the Airy-disk correction only to the luminance channel.
4 . The method of claim 3 , further comprising:
one or more of:
determining whether a point-spread function (PSF) for each of a plurality of color channels are equivalent to each other; or
determining whether the PSF for each of the plurality of color channels are similar to each other and there are no significant artifacts or loss of image quality in the recovered image; and
in response to the one or more determinations, then de-blurring the image by applying the Airy-disk correction only to the luminance channel.
5 . The method of claim 4 , further comprising:
determining that the edges in an image corresponding to a first color channel align with the edges in an image corresponding to a second color channel; and
in response to the determination, then de-blurring the image by applying the Airy-disk correction only to the luminance channel.
6 . The method of claim 1 , wherein the imaging system is integrated into a client computing device.
7 . The method of claim 6 , wherein the client computing device comprises a smartphone.
8 . The method of claim 6 , wherein the imaging system is disposed behind a display of the client computing device.
9 . A system comprising one or more processors and a non-transitory computer readable storage media embodying instructions coupled to the one or more processors, the one or more processors operable to execute the instructions to:
access an image captured by an imaging system comprising an aperture and an optical sensor, wherein the imaging system blurs the image; and
determine an Airy-disk correction that attributes at least part of the blurring in the image to a circular aperture rather than to a pinhole aperture, comprising:
determining an inverse kernel for the image, wherein the inverse kernel attributes blurring in the image to a pinhole aperture;
updating the inverse kernel to attribute blurring in the image to a circular aperture rather than to a pinhole aperture;
using the updated inverse kernel to determine the Airy-disk correction; and
generate a deblurred image by applying the determined Airy-disk correction to the accessed image.
10 . The system of claim 9 , wherein updating the inverse kernel comprises:
determining a Fourier-space representation H of a point-spread function for the imaging system that attributes blurring to a pinhole aperture;
determining a Fourier-space representation K of a point-spread function for the imaging system that attributes blurring to a circular aperture; and
determining a Fourier-space representation of de-blurred image based on: (1) convolving H and K, and (2) the accessed image captured by the imaging system.
11 . The system of claim 9 , wherein the one or more processors are further operable to execute the instructions to:
convert the image to plurality of image channels, wherein one of the plurality of channels represents a luminance of the image; and
de-blur the image by applying the Airy-disk correction only to the luminance channel.
12 . The system of claim 11 , wherein the one or more processors are further operable to execute the instructions to:
one or more of:
determine whether a point-spread function (PSF) for each of a plurality of color channels are equivalent to each other; or
determine whether the PSF for each of the plurality of color channels are similar to each other and there are no significant artifacts or loss of image quality in the recovered image; and
in response to the one or more determinations, then de-blur the image by applying the Airy-disk correction only to the luminance channel.
13 . The system of claim 12 , wherein the one or more processors are further operable to execute the instructions to:
determine that the edges in an image corresponding to a first color channel align with the edges in an image corresponding to a second color channel; and
in response to the determination, then de-blur the image by applying the Airy-disk correction only to the luminance channel.
14 . The system of claim 9 , wherein the imaging system is integrated into a client computing device.
15 . The system of claim 14 , wherein the client computing device comprises a smartphone.
16 . The system of claim 14 , wherein the imaging system is disposed behind a display of the client computing device.
17 . One or more non-transitory computer readable storage media embodying instructions and coupled to one or more processors that are operable to execute the instructions to:
access an image captured by an imaging system comprising an aperture and an optical sensor, wherein the imaging system blurs the image; and
determine an Airy-disk correction that attributes at least part of the blurring in the image to a circular aperture rather than to a pinhole aperture, comprising:
determining an inverse kernel for the image, wherein the inverse kernel attributes blurring in the image to a pinhole aperture;
updating the inverse kernel to attribute blurring in the image to a circular aperture rather than to a pinhole aperture;
using the updated inverse kernel to determine the Airy-disk correction; and
generate a deblurred image by applying the determined Airy-disk correction to the accessed image.
18 . The media of claim 17 , wherein updating the inverse kernel comprises:
determining a Fourier-space representation H of a point-spread function for the imaging system that attributes blurring to a pinhole aperture;
determining a Fourier-space representation K of a point-spread function for the imaging system that attributes blurring to a circular aperture; and
determining a Fourier-space representation of de-blurred image based on: (1) convolving H and K, and (2) the accessed image captured by the imaging system.
19 . The media of claim 17 , wherein the imaging system is integrated into a client computing device.
20 . The media of claim 19 , wherein the imaging system is disposed behind a display of the client computing device.