Method and system for restoring a motion-blurred image
View Patent ↗Embodiments of the present invention disclose a method and system for restoring a motion-blurred image. The method comprises determining parameters for a one-dimensional Optical Transfer Function (OTF) for the motion-blurred image in Fourier space; determining a signal-to-noise ratio for the motion-blurred image in the Fourier space; and correcting for motion blur based on the parameters of the OTF. Determining the parameters comprises calculating a function Φ(p,q) which is based on the square of the modulus of the Fourier transform |G(p,q)| 2 of the motion-blurred image. The parameters include the absolute value of the one-dimensional OTF, and the phase and sign of the OTF.
1. A method for correcting for motion blur in a motion-blurred image, the method comprising:
determining parameters for a one-dimensional Optical Transfer Function (OTF) for the motion-blurred image in Fourier space by calculating a function Φ(p,q), wherein the function is based on the square of the modulus of the Fourier transform G (p,q) 2 of the motion-blurred image;
determining a signal-to-noise ratio for the motion-blurred image in the Fourier space;
segmenting the motion-blurred image into blocks, each block comprising a plurality of windows, each window comprising a plurality of picture elements, wherein calculating the function Φ(p,q) includes calculating
Φ
k
(
p
,
q
)
=
∑
i
=
1
A
G
i
(
p
,
q
)
2
for each block k, where A is the number of windows in the kth block; and
correcting for motion blur based on the parameters.
2. The method of claim 1 , further comprising identifying and removing noise on the function Φ k (p,q) to form a function Φ k (noiseless) (p,q).
3. The method of claim 1 , wherein identifying the noise on the function Φ k (p,q)is based on a radial profile of ln(Φ k (p,q)).
4. The method of claim 3 , further comprising determining a direction of blur for each block.
5. The method of claim 4 , wherein determining the direction of blur comprises projecting ln└Φ k (noiseless) (p,q)┘ onto a diameter of a circle in a plurality directions, determining a width for the projection in each direction, determining a ratio of the widths in the different directions, and selecting the direction of blur as the direction with a minimum ratio of the widths.
6. The method of claim 5 , wherein the ratio of the widths has to be above a minimum threshold.
7. The method of claim 4 , wherein calculating the function Φ(p,q) comprises averaging the functions Φ k (p,q) over the blocks, taking into account the direction of blur.
8. The method of claim 7 , wherein determining parameters for the one-dimensional Optical Transfer Function (OTF) comprises determining the absolute value of the one-dimensional OTF based on the function ln└ k (noiseless) (p,q)┘.
9. The method of claim 8 , wherein determining parameters for the one-dimensional Optical Transfer Function (OTF) comprises determining a phase of the one-dimensional OTF based on the absolute value.
10. The method of claim 9 , wherein determining parameters for the one-dimensional Optical Transfer Function (OTF) comprises determining a sign for the phase of the one-dimensional OTF.
11. The method of claim 1 , wherein each window is square and sufficiently large to include individual elements of the motion-blurred image in their entirety.
12. The method of claims 11 , wherein for each window, components of each pixel are multiplied by a function that equals 1 at the center of the window and decreases to 0 at edges of the window.
13. A computer-readable medium having stored thereon a sequence of instructions which, when executed by a computer, causes the computer to perform a method for restoring a motion-blurred image, comprising
determining parameters for a one-dimensional Optical Transfer Function (OTF) for the motion-blurred image in Fourier space by calculating a function Φ(p,q), wherein the function is based on the square of the modulus of the Fourier transform |G (p,q) | 2 of the motion-blurred image;
determining a signal-to-noise ratio for the motion-blurred image in the Fourier space;
segmenting the motion-blurred image into blocks, each block comprising a plurality of windows, each window comprising a plurality of picture elements, wherein calculating the function Φ(p,q) includes calculating
Φ
k
(
p
,
q
)
=
∑
i
=
1
A
G
i
(
p
,
q
)
2
for each block k, where A is the number of windows in the kth block; and
correcting for motion blur based on the parameters.
14. The computer-readable medium of claim 13 , wherein the method further comprises identifying and removing noise on the function Φ k (p,q) to form a function Φ k (noiseless) (p,q).
15. The computer-readable medium of claim 14 , wherein identifying the noise on the function Φ k (p,q) is based on a radial profile of ln(Φ k (p,q))
16. The computer-readable medium of claim 13 , wherein calculating the function Φ(p,q) comprises averaging the functions Φ k (p,q) over the blocks, taking into account a direction of blur for each block.