Method and apparatus for the restoration of degraded multi-channel images
View Patent ↗An imager and method for operating the imager. The imager comprises a pixel array for producing an image signal and an image processor configured to restore images degraded by inter-channel degradations and intra-channel degradations in all channels of the image simultaneously by diagonalizing an image degradation matrix and componentizing the diagonalized image degradation matrix and multi-channel image.
1. An apparatus for restoring a degraded digital image, said apparatus comprising:
an image processor configured to perform the steps of:
transforming an image degradation matrix into a circulant matrix;
applying a frequency transformation to the circulant matrix and a data vector to obtain a frequency domain solution for the restored image;
componentizing the frequency domain solution to produce a plurality of frequency domain components; and
processing each frequency domain component individually, wherein the frequency domain solution is componentized and represented by {circumflex over (F)} k =(Ω k * T Ω k +λQ k * T Q k ) −1 Ω k * T G k where Λ H is a block diagonal matrix having on its diagonal multi-channel frequency response matrices, G is the data vector after the frequency transformation, Ω k represents a matrix in the diagonal the frequency transformed degradation matrix, λ is a scalar and Q k is an entry in a matrix Q containing a predetermined constraint kernel.
2. The apparatus of claim 1 , wherein the image processor is further configured to perform the step of:
transforming the frequency domain solution to a spatial domain solution.
3. The apparatus of claim 1 , wherein the frequency transformation has the following form:
S
=
[
(
W
S
1
⊗
W
S
2
)
(
0
,
0
)
*
I
P
(
W
S
1
⊗
W
S
2
)
(
0
,
1
)
*
I
P
⋯
⋯
(
W
S
1
⊗
W
S
2
)
(
0
,
L
-
1
)
*
I
P
(
W
S
1
⊗
W
S
2
)
(
1
,
0
)
*
I
P
(
W
S
1
⊗
W
S
2
)
(
1
,
1
)
*
I
P
⋱
⋱
⋮
⋮
⋮
⋱
⋱
⋮
⋱
⋱
⋱
⋱
⋮
⋮
⋱
⋱
⋱
⋮
(
W
S
1
⊗
W
S
2
)
(
L
-
1
,
0
)
*
I
P
(
W
S
1
⊗
W
S
2
)
(
L
-
1
,
1
)
*
I
P
⋯
⋯
(
W
S
1
⊗
W
S
2
)
(
L
-
1
,
L
-
1
)
*
I
P
]
where S is the frequency transformation, W j has as columns the basis functions of a Discrete Fourier Transform (DFT), symbolizes the Kronecker product operation, I p is a P×P identity matrix, P is a number of channels, N is a number of pixels in the digital image, and N is derived by multiplying a number of rows N1 in the image by the number of columns N2 in the image, a degrading kernel size for each channel is equal to M×M, L is the size in pixels of the degraded digital image after a two dimensional (2D) convolution, L=S1×S2, S1=N1+M−1 and S2=N2+M−1.
4. The apparatus of claim 1 , wherein the frequency transformation is applied to the circulant matrix such that SHcS −1 =Λ H , wherein S is the frequency transformation, Hc is the circulant matrix and Λ H is a block diagonal matrix having on its diagonal multi-channel frequency response matrices.
5. The apparatus of claim 1 , wherein the frequency domain solution is derived from a linear minimum mean square error criteria.
6. The apparatus of claim 5 , wherein the image processor is further configured to perform the steps of:
constructing a noise correlation matrix and a signal correlation matrix; and
applying the frequency transformation to the noise correlation matrix and the signal correlation matrix to obtain a frequency transformed noise matrix and a frequency transformed signal matrix.
7. An apparatus for restoring a degraded digital image, said apparatus comprising:
an image processor configured to perform the steps of:
transforming an image degradation matrix into a circulant matrix;
applying a frequency transformation to the circulant matrix and a data vector to obtain a frequency domain solution for the restored image;
componentizing the frequency domain solution to produce a plurality of frequency domain components;
processing each frequency domain component individually, wherein the frequency domain solution is derived from a linear minimum mean square error criteria;
constructing a noise correlation matrix and a signal correlation matrix; and
applying the frequency transformation to the noise correlation matrix and the signal correlation matrix to obtain a frequency transformed noise matrix and a frequency transformed signal matrix, where the frequency domain solution has the form {circumflex over (F)}=Λ f Λ H * T [Λ H Λ f Λ H * T +Λ n ] −1 G, where Λ f is the frequency transformed signal matrix, Λ n is the frequency transformed noise matrix, Λ H is the frequency transformed degradation matrix and G is the frequency transformed data vector.