CN109360161B - Multispectral image deblurring method based on gradient domain prior - Google Patents

Multispectral image deblurring method based on gradient domain prior Download PDF

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CN109360161B
CN109360161B CN201811053391.8A CN201811053391A CN109360161B CN 109360161 B CN109360161 B CN 109360161B CN 201811053391 A CN201811053391 A CN 201811053391A CN 109360161 B CN109360161 B CN 109360161B
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黄华
魏晓翔
张磊
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Beijing Institute of Technology BIT
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Abstract

The invention provides a gradient domain prior based multispectral image deblurring method, and belongs to the technical field of image processing. According to the similarity of images of adjacent channels, a Gaussian-like function is combined with a steeling kernel to calculate a reference image corresponding to each channel in a multispectral image; according to the similarity of the reference image and the target clear image on the gradient domain, taking the norm of the difference of the reference image and the target clear image on the gradient domain as the image prior of a deblurring formula; combining the image prior with a maximum posterior probability estimation method, establishing a multi-spectral image deblurring frame, and performing iterative solution to finally obtain a clear image. Compared with the existing method, the method fully considers the similarity of the adjacent channel images on the gradient domain, avoids the introduction of redundant image details, improves the deblurring quality of the multispectral image, and reduces the calculated amount in the deblurring process.

Description

Multispectral image deblurring method based on gradient domain prior
Technical Field
The invention relates to a multispectral image deblurring method, in particular to a multispectral image deblurring method based on gradient domain prior, and belongs to the technical field of image processing.
Background
With the development of multispectral imaging technology, more and more multispectral imaging technologies are applied to various industries, and the multispectral imaging technologies relate to various aspects of agriculture, remote sensing, microscopy, aerospace and the like. However, due to the weight-bearing limitations of the device itself, many lightweight multispectral imaging applications cannot be equipped with complex lens sets, and instead choose imaging systems that use simple lenses. The refractive index difference of a simple lens for light rays with different wavelengths is large, so that the light rays form dispersion circles with different sizes on an imaging plane, and images of all channels show defocusing blur with different degrees. These defocused blurs significantly reduce the imaging quality of the device on the one hand and also affect the image perception experience on the other hand. Therefore, there is a need for an efficient deblurring method for multispectral images that removes these defocus blurs with less computation.
For the problem of removing defocus blur of multispectral images, a large amount of basic research has been carried out by scholars at home and abroad. The commonly used multispectral defocus blur removing method is mainly divided into two types: a deblurring method based on single-channel images and a deblurring method based on multi-channel images.
The deblurring method based on the single-channel image is represented by a deblurring method based on outlier processing (Dong J, Pan J, Su Z, et al. blind image deblocking with outlier handling, iccv.2017). According to the method, an efficient data retention item is established according to the influence of outliers on a deblurring algorithm, and then a corresponding target clear image is obtained through calculation. However, this method does not take into account the correlation of contents between the multiple spectral band images when dealing with defocus blur of the multispectral image, resulting in poor deblurring effect and large computation amount.
The multi-channel image-based deblurring method is represented by a guide graph-based Multispectral deblurring method (s. -j.chen and h. -l.shen., Multispectral image out-of-focus deblurring using interaction, IEEE trans. image process., vol.24, No.11, pp.4433-4445,2015). The method mainly obtains a guide image corresponding to a target channel through Tikhonov regularization, and obtains a clear target image by using the guide image in combination with a maximum posterior probability estimation method. The method has low calculation amount, but because the image information of the edge channel is used when the guide image is solved, some redundant details are introduced in the deblurring process, so that the finally obtained clear image has low accuracy.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and effectively solve the problem of de-blurring and blurring of a multispectral image, and provides a new gradient domain prior-based multispectral image de-blurring method, which can improve the de-blurring quality of the multispectral image and reduce the computational complexity of de-blurring.
The main principle of the method is as follows:
and according to the correlation between adjacent frequency spectrums in the multispectral image, calculating by using a Gaussian-like function to obtain a reference image corresponding to the target spectrum segment. And establishing image prior according to the similarity of the reference image and the target clear image on the gradient domain. And (3) preprocessing and deblurring the blurred image by using image prior and combining maximum posterior probability estimation to finally obtain the deblurred sharp image.
In order to achieve the purpose, the invention adopts the following technical scheme:
a multispectral image deblurring method based on gradient domain prior comprises the following steps:
step one, calculating a fuzzy core corresponding to each channel of the multispectral image.
For multispectral image to be processed { B1B2...BNThe original image is processed by a fuzzy kernel estimation method based on a normalized cross-correlation matching algorithm (refer to S. -J.Chen and H. -L.Shen, Multispectral image out-of-focus decoding using inter channel correlation, IEEE trans.image processing, vol.24, No.11, pp.4433-4445, 2015), and a fuzzy kernel { G corresponding to each channel is obtained1G2...GN}. Wherein N is a positive integer.
Meanwhile, a calculation model of the reference image is established, and the reference image is calculated.
Setting multispectral image { B1B2...BNThe corresponding sharp image sequence is { L }1L2...LNAnd calculating to obtain a reference image corresponding to the target spectrum band by using a Gaussian-like function according to the similarity of the images of the adjacent channels:
Figure BDA0001795146630000031
wherein R isiFor the reference image, H is the preset window size, v (i, j) represents the weight function, and the clear image L is determinedjThe weight of (c). In finding the reference image, there may be portions where the sharp image is unknown, and therefore, the choice of the sharp image is constrained using a constraint function δ (j), if LjIf unknown, the value of delta (j) is 0, otherwise the value of delta (j) is 1.
In equation (1), the weight function v (i, j) determines the quality of the reference picture, which is of the form:
Figure BDA0001795146630000032
wherein, the functions delta (m) and delta (j) are constraint functions.
Figure BDA0001795146630000033
Is a steeling kernel regression model of the form:
Figure BDA0001795146630000034
Figure BDA0001795146630000035
wherein MSE (B)i,Lj) Representing the original image BiAnd a sharp image LjMean square error between, MSE (B)i,Lm) Representing the original image BiAnd a sharp image LmMean square error between. Beta is a scale operator for controlling the weight.
And step two, establishing image prior on the gradient domain according to the reference image.
Since the reference image and the target sharp image have great similarity in the gradient domain, the gradient similarity of the reference image and the target sharp image is used as an image prior, which is specifically as follows:
Figure BDA0001795146630000036
wherein,
Figure BDA0001795146630000037
represents a gradient operator, LiAnd RiAnd respectively obtaining the target clear image and the reference image calculated in the step one.
And step three, establishing a deblurring process formula based on image prior, and iteratively solving a fuzzy core to obtain a target clear image.
And (3) establishing a deblurring process formula by utilizing a maximum posterior probability estimation method and combining the image prior obtained in the step two, wherein the formula is expressed as follows:
Figure BDA0001795146630000041
wherein L represents a clear image of the target, B represents an original image of the target,
Figure BDA0001795146630000042
representing a gradient operator, representing convolution operation, k representing a fuzzy kernel to be obtained through calculation, and G representing the fuzzy kernel obtained through calculation in the step one; the parameters λ and η are used to control the specific gravity of the second term and the third term in equation (6), respectively, the values of which are selected according to the mean square error between the images, or are manually specified.
In view of the difficulty in directly solving equation (6), the method can be further decomposed into two sub-problems for solving, as follows:
Figure BDA0001795146630000043
Figure BDA0001795146630000044
finally, iterative solution of the fuzzy kernel k on the frequency domain by using an alternative iteration methodiClear with the target image LiIs estimated value of
Figure BDA0001795146630000045
And
Figure BDA0001795146630000046
and finally obtaining a clear target image.
Advantageous effects
(1) The traditional deblurring method based on the single-channel image treats each channel image in the multispectral image as an independent image to be processed, and does not consider the internal relation among channels in the multispectral image, so that the deblurred image has information loss. Meanwhile, the methods generally use formulas such as 1-norm or 0-norm which are difficult to solve, so that the calculation complexity is high. The method of the invention considers the content correlation between adjacent spectral images in the multispectral image, and improves the quality and efficiency of deblurring the multispectral image by combining the 2-norm which is easy to solve.
(2) The existing de-blurring method based on the multi-channel image has a good effect when processing images with small blurring degree. However, when processing an image with a large degree of blur, because the image information of the current channel is relatively seriously lost, information of other channels is introduced to perform completion, and at this time, a problem of information redundancy occurs, that is, information which should not appear in the current channel appears. This situation can greatly reduce the quality of the deblurring. The invention restricts the value of the method to be taken only in a small window through the Gaussian-like function, thereby avoiding the situation of inconsistent contents.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a comparison of the reference image and the original image.
Detailed Description
The following is a more detailed description of embodiments of the process of the present invention, taken in conjunction with the accompanying drawings.
A multispectral image deblurring method based on gradient domain prior comprises the following steps:
step one, calculating a fuzzy core corresponding to each channel of the multispectral image. Meanwhile, a calculation model of the reference image is established, and the reference image is calculated.
For multispectral image to be processed { B1B2...BNAnd (5) regarding an image corresponding to the middle spectrum as a clear image, and performing fuzzy processing on other images by using fuzzy cores with different sizes. Obtaining each channel by using a fuzzy kernel estimation method based on a normalized cross-correlation matching algorithm (refer to S. -J.Chen and H. -L.Shen, Multispectral image out-of-focus decoding using inter-channel correlation, IEEE trans. image Process., vol.24, No.11, pp.4433-4445, 2015)Corresponding fuzzy kernel { G1G2...GN}. Wherein N is a positive integer.
Meanwhile, a calculation model of the reference image is established, and the reference image is calculated.
Setting multispectral image { B1B2...BNThe corresponding sharp image sequence is { L }1L2...LNAnd calculating to obtain a reference image corresponding to the target spectrum band by using a Gaussian-like function according to the similarity of the images of the adjacent channels:
Figure BDA0001795146630000051
wherein R isiFor the reference image, H is the preset window size, v (i, j) represents the weight function, and the clear image L is determinedjThe weight of (c). In finding the reference image, there may be portions where the sharp image is unknown, and therefore, the choice of the sharp image is constrained using a constraint function δ (j), if LjIf unknown, the value of delta (j) is 0, otherwise the value of delta (j) is 1.
In equation (1), the weight function v (i, j) determines the quality of the reference picture, which is of the form:
Figure BDA0001795146630000061
wherein, the functions delta (m) and delta (j) are constraint functions.
Figure BDA0001795146630000062
Is a steeling kernel regression model of the form:
Figure BDA0001795146630000063
Figure BDA0001795146630000064
wherein MSE (B)i,Lj) Representing the original image BiAnd a sharp image LjMean square error between, MSE (B)i,Lm) Representing the original image BiAnd a sharp image LmMean square error between. Beta is a scale operator for controlling the weight. In this embodiment, β is set to 0.05, and the reference image effect obtained in this case is preferable.
Fig. 2 shows an example of a reference image, in fig. 2, the left image is a sharp image, the middle image is an obtained reference image, and the right image is an original blurred image.
And step two, establishing image prior on the gradient domain according to the reference image.
Since the reference image and the target sharp image have great similarity in the gradient domain, the gradient similarity of the reference image and the target sharp image is used as an image prior, which is specifically as follows:
Figure BDA0001795146630000065
wherein,
Figure BDA0001795146630000066
represents a gradient operator, LiAnd RiAnd respectively obtaining the target clear image and the reference image calculated in the step one.
And step three, establishing a deblurring process formula based on image prior, and iteratively solving a fuzzy core to obtain a target clear image.
And (3) establishing a deblurring process formula by utilizing a maximum posterior probability estimation method and combining the image prior obtained in the step two, wherein the formula is expressed as follows:
Figure BDA0001795146630000071
wherein L and B represent the target sharp image and the original image respectively,
Figure BDA0001795146630000072
representing a gradient operator, representing convolution operation, k representing a fuzzy kernel to be obtained through calculation, and G representing the fuzzy kernel obtained through calculation in the step one; the parameters λ and η are used to control the specific gravity of the second term and the third term in equation (6), respectively, the values of which are selected according to the mean square error between the images, or are manually specified.
In view of the difficulty in directly solving equation (6), the method can be further decomposed into two sub-problems for solving, as follows:
Figure BDA0001795146630000073
Figure BDA0001795146630000074
step four, iterative solution of the fuzzy kernel k on the frequency domain by using an alternative iteration methodiClear with the target image LiIs estimated value of
Figure BDA0001795146630000075
And
Figure BDA0001795146630000076
and finally obtaining a clear target image.
Solving and using an alternate iteration mode, firstly, solving the two sub-problems in the step three on a frequency domain to obtain:
Figure BDA0001795146630000077
and
Figure BDA0001795146630000078
wherein,
Figure BDA0001795146630000079
and
Figure BDA00017951466300000710
respectively representing the two-dimensional discrete fourier transform and the conjugate of the fourier transform,
Figure BDA00017951466300000711
representing the inverse of the fourier transform.
Figure BDA0001795146630000081
A discrete fourier transform representing a gradient operator, of the form:
Figure BDA0001795146630000082
wherein,
Figure BDA0001795146630000083
and
Figure BDA0001795146630000084
representing the gradient operator in the horizontal and vertical directions, respectively, i.e.
Figure BDA0001795146630000085
Figure BDA0001795146630000086
T represents a transpose operation.
In the solution, since all the clear images are unknown at the beginning, a preprocessing process is required to obtain the clear images used as intermediate results. The pretreatment process is as follows:
firstly, an image corresponding to a channel in the middle of a spectrum segment in a multispectral image is used as a clear image, namely the image corresponding to the channel is clear enough, deblurring processing is not needed, and the channel is defined as s.
Then, the channel s expands towards two sides, and deblurring calculation is carried out on all the channels according to the sequence of the s-1s-2.. 1 'or the s +1s +2.. N', so that each channel can be guaranteed to have an available clear image for subsequent iterative calculation. In actual practice, with reference to fig. 1, both the preprocessing process and the deblurring process follow the following operations:
firstly, the fuzzy kernel G obtained in the step oneiK substituted in equation (8)iTo obtain the first iteration estimation value of the clear image
Figure BDA0001795146630000087
Then, will
Figure BDA0001795146630000088
L substituted into equation (7)iCalculating to obtain the first iteration estimated value of the fuzzy core
Figure BDA0001795146630000089
The above process completes the first iteration of the calculation.
In the second iteration, the calculation result of the first iteration is processed
Figure BDA00017951466300000810
And
Figure BDA00017951466300000811
k substituted into equation (8) respectivelyiAnd L of formula (7)iCalculating to obtain the calculation result of the second iteration
Figure BDA00017951466300000812
And
Figure BDA00017951466300000813
the subsequent iteration process is the same as the second iteration process, and the calculation result of the previous iteration is used as the input of the current iteration calculation for calculation. And if the calculation result is converged or the iteration number reaches the upper limit, stopping the iteration. Wherein, convergence refers to the calculation result of the previous iteration and the calculation result of the current iterationAre identical.
Both the pre-processing and the deblurring process follow the iterative process described above. The upper limits of the number of iterations for both can be set to 3 and 10, respectively.
The quality of the clear image obtained by solving is higher, and compared with the existing optimal method, the peak signal-to-noise ratio is improved by 2 to 3 decibels in a frequency spectrum with a larger fuzzy degree.

Claims (4)

1. A multispectral image deblurring method based on gradient domain prior is characterized by comprising the following steps:
step one, calculating a fuzzy core corresponding to each channel of the multispectral image;
for multispectral image to be processed { B1 B2 ... BNObtaining a fuzzy kernel { G corresponding to each channel by using a fuzzy kernel estimation method1 G2 ... GNWhere N is a positive integer;
meanwhile, a calculation model of the reference image is established, and the reference image is calculated:
setting multispectral image { B1 B2 ... BNThe corresponding sharp image sequence is { L }1 L2 ... LNAnd calculating to obtain a reference image corresponding to the target spectrum band by using a Gaussian-like function according to the similarity of the images of the adjacent channels:
Figure FDA0002985680950000011
wherein R isiFor the reference image, H is the preset window size, v (i, j) represents the weight function, and the clear image L is determinedjThe weight of (c); using a constraint function delta (j) to constrain the selection of a sharp image if LjIf not, the value of delta (j) is 0, otherwise, the value of delta (j) is 1;
in equation (1), the weight function v (i, j) determines the quality of the reference picture, which is of the form:
Figure FDA0002985680950000012
wherein, the functions delta (m) and delta (j) are constraint functions;
Figure FDA0002985680950000013
is a steeling kernel regression model of the form:
Figure FDA0002985680950000014
Figure FDA0002985680950000015
wherein MSE (B)i,Lj) Representing the original image BiAnd a sharp image LjMean square error between, MSE (B)i,Lm) Representing the original image BiAnd a sharp image LmThe mean square error between the two, beta is a scale operator for controlling the weight;
step two, establishing image prior on a gradient domain according to a reference image;
using the gradient similarity between the reference image and the target sharp image as an image prior, specifically as follows:
Figure FDA0002985680950000021
wherein,
Figure FDA0002985680950000022
represents a gradient operator, LiAnd RiRespectively obtaining a target clear image and a reference image obtained by calculation in the step one;
establishing a deblurring process formula based on image prior, and iteratively solving a fuzzy core to obtain a target clear image;
and (3) establishing a deblurring process formula by utilizing a maximum posterior probability estimation method and combining the image prior obtained in the step two, wherein the formula is expressed as follows:
Figure FDA0002985680950000023
wherein L represents a clear image of the target, B represents an original image of the target,
Figure FDA0002985680950000024
representing a gradient operator, representing convolution operation, k representing a fuzzy kernel to be obtained through calculation, and G representing the fuzzy kernel obtained through calculation in the step one; the parameters lambda and eta are respectively used for controlling the proportion of a second term and a third term in the formula (6), and the values of the parameters lambda and eta are selected according to the mean square error between the images or directly and manually specified;
here, the solving equation (6) is decomposed into two subproblems for solving, as follows:
Figure FDA0002985680950000025
Figure FDA0002985680950000026
finally, iterative solution of the fuzzy kernel k on the frequency domain by using an alternative iteration methodiClear with the target image LiIs estimated value of
Figure FDA0002985680950000027
And
Figure FDA0002985680950000028
and finally obtaining a clear target image.
2. The method as claimed in claim 1, wherein in the first step, the scale operator β for controlling the weight is set to 0.05.
3. The method according to claim 1, wherein in step three, the fuzzy kernel k is solved iteratively in the frequency domain by using an alternating iteration methodiClear with the target image LiIs estimated value of
Figure FDA0002985680950000031
And
Figure FDA0002985680950000032
the method comprises the following steps:
firstly, solving the two sub-problems in the step three on the frequency domain to obtain:
Figure FDA0002985680950000033
and
Figure FDA0002985680950000034
wherein,
Figure FDA0002985680950000035
and
Figure FDA0002985680950000036
respectively representing the two-dimensional discrete fourier transform and the conjugate of the fourier transform,
Figure FDA0002985680950000037
represents the inverse of the fourier transform;
Figure FDA0002985680950000038
a discrete fourier transform representing a gradient operator, of the form:
Figure FDA0002985680950000039
wherein,
Figure FDA00029856809500000310
and
Figure FDA00029856809500000311
representing the gradient operator in the horizontal and vertical directions, respectively, i.e.
Figure FDA00029856809500000312
Figure FDA00029856809500000313
T represents a transpose operation;
in the solution, since all the sharp images are unknown at the beginning, a preprocessing process is required to obtain the sharp image used as an intermediate result, and the preprocessing process is as follows:
firstly, taking an image corresponding to a channel in the middle of a spectrum segment in a multispectral image as a clear image, namely, the image corresponding to the channel is sufficiently clear, and the channel is defined as s without deblurring treatment;
then, the channel s expands towards two sides, and the deblurring calculation is carried out on all the channels according to the sequence of the s-1s-2.
4. The method according to claim 3, wherein the preprocessing process and the deblurring process both follow the following operations:
firstly, the fuzzy kernel G obtained in the step oneiK substituted in equation (8)iTo obtain the first iteration estimation value of the clear image
Figure FDA00029856809500000314
Then, will
Figure FDA00029856809500000315
L substituted into equation (7)iCalculating to obtain the first iteration estimated value of the fuzzy core
Figure FDA00029856809500000316
The above process completes the first iteration of the calculation;
in the second iteration, the calculation result of the first iteration is processed
Figure FDA0002985680950000041
And
Figure FDA0002985680950000042
k substituted into equation (8) respectivelyiAnd L of formula (7)iCalculating to obtain the calculation result of the second iteration
Figure FDA0002985680950000043
And
Figure FDA0002985680950000044
the subsequent iteration process is the same as the second iteration process, and the calculation result of the previous iteration is used as the input of the current iteration calculation for calculation; and if the calculation result converges or the iteration frequency reaches the upper limit, stopping the iteration, wherein the convergence means that the calculation result of the previous iteration is completely the same as the calculation result of the current iteration.
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