CN106780338B - Rapid super-resolution reconstruction method based on anisotropy - Google Patents
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Abstract
The invention discloses a quick super-resolution reconstruction method based on anisotropy, which comprises the following steps: performing motion compensation and up-sampling on all the acquired original images to obtain an image after the high-resolution image is blurred, and using the image as a reference image; improving a reconstruction model based on an L1 norm least square method to obtain an optimized reconstruction model; introducing an anisotropic regularization term, and constructing an adaptive parameter based on the regularization term to obtain an anisotropic-based adaptive reconstruction model; and taking the obtained reference image as an iteration initial value, bringing the reference image into the constructed adaptive reconstruction model to start iteration, calculating the peak signal-to-noise ratio of each reconstructed image, and stopping iteration when the peak signal-to-noise ratio of the iteration result is lower than that of the previous time to complete image reconstruction. The method removes the redundant process in the reconstruction model, reduces the calculated amount in the reconstruction process, and simultaneously improves the speed and the quality of the image super-resolution reconstruction.
Description
Technical Field
The invention belongs to the technical field of optical image reconstruction, and particularly relates to a quick super-resolution reconstruction method based on anisotropy.
Background
Image super-resolution reconstruction techniques are techniques that utilize a set of low-quality, low-resolution images or motion sequences to produce a single high-quality, high-resolution image. The image with high pixel density on the unit scale is called a high-resolution image, and the high-resolution image has more image details and more information. The resolution is an important technical index for representing the image observation level, is limited by the number of detector arrays and the structure of the detectors, and the spatial sampling frequency of an imaging system cannot meet the sampling theorem, so that the frequency mixing phenomenon is easily generated, and the image is blurred.
There are generally two approaches to increasing the spatial resolution of an image. One is to improve physical characteristics of the imaging device such as reduction in pixel size, increase in chip area, and the like. However, this method has the inherent defects that the charge transfer rate is reduced due to the increase of the chip area, and the light receiving amount of a unit pixel is reduced due to the reduction of the pixel size, the influence of shot noise on an imaging unit is increased, and the quality of an imaged image is further reduced sharply. The other is to improve the focal length and aperture of the optical lens.
Super-resolution reconstruction techniques for single image restoration were first proposed by Harris and Goodman in the 60's of the 20 th century. In the early 80 s of the 20 th century, Tsai and Huang first proposed super-resolution reconstruction techniques based on sequence images. The super-resolution reconstruction of the image is a technology for reconstructing a high-resolution image by using a low-resolution image of the same scene of one frame or a plurality of frames containing complementary information by adopting a signal processing technology and a computer software method. The super-resolution reconstruction algorithm is divided into a frequency domain algorithm and a spatial domain algorithm. The frequency domain algorithm is an algorithm for realizing super-resolution restoration based on the translation characteristic of Fourier transform and the transformation relation between continuous Fourier transform and discrete Fourier transform. The theory is simple, the calculation amount is small, but the method has the defect that the method is only suitable for the global translational motion and the degradation model. The space domain algorithm comprises a non-uniform interpolation method, a back projection iteration method, a convex set projection method and a maximum posterior probability method. The interpolation method can interpolate a single low-resolution image into a composite image with higher density, but cannot provide additional information, lose high-frequency components and cannot recover, and interpolation errors cannot be avoided in the interpolation process; the convex set projection method degradation model has generality, prior knowledge is more conveniently merged, but the solution is not unique, the algorithm is seriously dependent on the selection of an initial value, and the iteration times are more; the maximum a posteriori probability method has the advantages of having a unique solution, but has slow convergence speed, overlarge operation amount and easy smoothing of image details.
The super-resolution reconstruction algorithm based on the regularization term is characterized in that the regularization energy functional is constructed according to a degradation model of a low-resolution image and the regularization term corresponding to the image model, the high-resolution image is obtained through the minimized energy functional, statistical assumption is not needed to be carried out on image noise, but image details are inhibited, and the image is too smooth. Farsiu et al propose a fast super-resolution image reconstruction method based on bilateral total variation regularization (Farsiu, Robinson, Elad, et a1.fast robust multiframe super-resolution [ J ]. IEEE Transactionson on image processing,2004,13(10): 1327-1344), which improves the image reconstruction speed, but easily causes a step effect in the presence of strong noise, and cannot protect the texture effect of an image. Soohwan et al propose a function of adaptive local multivariate linear regression (Soohwan, Woseok, Seungong, et al, Single image super resolution using a local adaptive multiple linear regression [ J ]. Journal of the optical society of America A,2015,32(12),2264 + 2275), which can overcome the limitation of spatial resolution of digital images, thereby achieving an algorithm for improving the resolution of images; the algorithm proposed by Kanaev et al for super-resolution reconstruction under complex motion takes into account the uncertainty of the motion of the target object (Kanaev, miller. multi-frame super-resolution algorithm for complex motion patterns [ J ]. OPTICS EXPRESS,2013,21(17) 19850-. The algorithms have advantages in improving the image reconstruction quality, but do not effectively improve the image reconstruction rate, and still appear to be delayed in acquiring information.
Disclosure of Invention
The invention aims to provide a quick super-resolution reconstruction method based on an anisotropic regularization term, so that the calculated amount in the reconstruction process is reduced, and the reconstruction quality of an image is improved on the basis of improving the reconstruction rate of the image.
The technical solution for realizing the purpose of the invention is as follows: a quick super-resolution reconstruction method based on anisotropy comprises the following steps:
step 2, improving the reconstruction model based on the L1 norm least square method to obtain the optimized reconstruction model;
step 3, introducing an anisotropic regularization term, and constructing an adaptive parameter based on the regularization term to obtain an anisotropic-based adaptive reconstruction model;
step 4, taking the reference image obtained in the step 1 as an iteration initial value
Will be provided with
And (4) starting iteration by substituting the self-adaptive reconstruction model constructed in the step (3), calculating the peak signal-to-noise ratio of the reconstructed image every time, and stopping iteration when the peak signal-to-noise ratio of the iteration result is lower than that of the previous time, so that the image reconstruction is finished.
Further, the high resolution image in step 1 is blurred
The method specifically comprises the following steps:
and respectively carrying out motion compensation and up-sampling on all the acquired original images, and then solving the average value of the pixels at the corresponding positions of each image to obtain the image after the high-resolution image is subjected to blur degradation.
Further, the reconstruction model after the optimization in step 2 is:
wherein,
is a maximum likelihood estimate of the original high resolution image X, H represents the blur matrix.
Further, step 3 introduces an anisotropic regularization term, constructs an adaptive parameter based on the regularization term, and obtains an anisotropic-based adaptive reconstruction model, specifically:
(1) anisotropy regularization term
Comprises the following steps:
in which Ψ(s)2)＝2μ2(1+s2/μ2)0.5Is a Charbonnier function, where μ is a fixed parameter, v1、v2Are two orthogonal vectors of the image structure tensor J, which is formulated as follows:
wherein, represents convolution operator, t represents vector transposition, GρIs a Gaussian kernel, ρ1、ρ2Respectively a neighborhood smooth scale and an image smooth scale;
(2) the adaptive regularization parameters β are:
wherein σ is 0.0000001;
(3) the final fast super-resolution reconstruction model based on anisotropy is as follows:
wherein,
represents the result value of the nth iteration, λ represents the gradient descent step size, and Ψ' represents the derivation of Ψ.
Further, step 4 takes the reference image obtained in step 1 as an iteration initial value
Will be provided with
And (3) carrying in the self-adaptive reconstruction model constructed in the step (3) to start iteration, calculating the peak signal-to-noise ratio of the reconstructed image at each time, stopping iteration when the peak signal-to-noise ratio of the iteration result is lower than that of the previous time, and completing image reconstruction, wherein the iteration conditions are as follows:
if(i＞＝2&&PSNR(i)＜PSNR(i-1))break；
wherein PSNR is the peak signal-to-noise ratio, X is the original high resolution image,
PSNR (i) is the peak signal-to-noise ratio of the ith iteration image for the super-resolution image formed by the nth iteration.
Compared with the prior art, the invention has the following remarkable advantages: (1) the iterative model is optimized and improved, redundant calculation is removed, the calculated amount is greatly reduced, and the reconstruction rate is improved; (2) an anisotropic regularization term with self-adaptive parameters is introduced, and the regularization term effectively protects the image edge details, so that the reconstruction quality of the image can be improved on the basis of improving the image reconstruction rate.
Drawings
FIG. 1 is a schematic flow chart of a fast super-resolution reconstruction algorithm based on anisotropy.
Fig. 2 is a lens graph which is a result graph reconstructed by different algorithms, wherein (a) is a TV regularization algorithm result graph, (b) is a conventional iterative algorithm + anisotropic smoothing term result graph, and (c) is a result graph reconstructed by the method.
FIG. 3 is a result graph of the acer graph reconstructed by different algorithms, wherein (a) is a result graph of a TV regularization algorithm, (b) is a result graph of a traditional iterative algorithm plus an anisotropic smoothing term, and (c) is a result graph of the method reconstructed.
Detailed Description
The method comprises the steps of firstly, reading all low-resolution images by utilizing a computer to program, carrying out motion compensation and up-sampling on the low-resolution images to obtain an image after the high-resolution image is subjected to fuzzy degradation as a reference image, and then carrying out optimization improvement on a traditional reconstruction model to remove a redundancy process; and introducing an anisotropic regularization term with self-adaptive parameters to obtain a final reconstruction model. And reading the low resolution to be reconstructed, carrying out bicubic interpolation to obtain a first super-resolution image, bringing the first super-resolution image into a reconstruction model, and carrying out iterative computation. And taking the peak signal-to-noise ratio as a standard, and when the peak signal-to-noise ratio of the reconstructed image at a certain time is lower than that of the image at the last time, the image reconstruction is considered to be completed. The flow diagram is shown in fig. 1, and the specific implementation steps are as follows:
reading all original low-resolution images by using Matlab software, respectively performing motion compensation and upsampling on all the acquired original images, and then calculating the average value of pixels at corresponding positions of each image to obtain an image after the high-resolution image is subjected to fuzzy degradation, wherein the image is used as a reference image.
Step 2, improving the reconstruction model based on the L1 norm least square method to obtain the optimized reconstruction model, which is as follows:
wherein,
is a maximum likelihood estimate of the original high resolution image X, H represents the blur matrix.
Step 3, introducing an anisotropic regularization term, and constructing an adaptive parameter based on the regularization term to obtain an anisotropic-based adaptive reconstruction model, specifically:
(1) introducing an anisotropic regularization term, and designing an adaptive parameter based on the regularization term to obtain an anisotropic-based adaptive fast super-resolution reconstruction model. Wherein the anisotropic regularization term
Comprises the following steps:
in which Ψ(s)2)＝2μ2(1+s2/μ2)0.5Is a Charbonnier function, where μ is a fixed parameter, v1、v2Are two orthogonal vectors of the image structure tensor J, which is formulated as follows:
wherein, represents convolution operator, t represents vector transposition, GρIs a Gaussian kernel, ρ1、ρ2Respectively a neighborhood smooth scale and an image smooth scale;
(2) the adaptive regularization parameters β are:
where σ is a very small parameter, avoiding a denominator of 0, where σ takes 0.0000001.
(3) By using a fastest descent method, the final fast super-resolution reconstruction model based on anisotropy is as follows:
wherein,
represents the result value of the nth iteration, λ represents the gradient descent step size, and Ψ' represents the derivation of Ψ.
Step 4, taking the reference image obtained in the step 1 as an iteration initial value
Will be provided with
And (4) starting iteration by substituting the self-adaptive reconstruction model constructed in the step (3), calculating the peak signal-to-noise ratio of the reconstructed image every time, and stopping iteration when the peak signal-to-noise ratio of the iteration result is lower than that of the previous time, so that the image reconstruction is finished. Wherein the iteration condition is as follows:
if(i＞＝2&&PSNR(i)＜PSNR(i-1))break；
wherein PSNR is the peak signal-to-noise ratio, X is the original high resolution image,
PSNR (i) is the peak signal-to-noise ratio of the ith iteration image for the super-resolution image formed by the nth iteration.
It can be seen from the above steps that the iterative process in the reconstruction model is optimized, a large number of redundant processes are removed, and meanwhile, an anisotropic regularization term with adaptive parameters is introduced, and the regularization term can reduce smoothness in the data constraint direction, but not in the image edge direction, and the image is filled to realize the orthogonalization of the image, so that the two orthogonal terms of the image data have optimal complementarity, and finally, the reconstruction quality of the image can be improved on the basis of ensuring the improvement of the image reconstruction rate.
Example 1
To test the effectiveness of the fast super-resolution reconstruction method based on anisotropy, the present invention used 512 × 512 and 640 × 480 grayscale images as test images in the test, respectively, and the experimental platform was Intel Core i5-2430M @3.0GHz, Matlab R2015 b. Fig. 2(a) and fig. 3(a) are reconstructed images by a TV regularization method, fig. 2(b) and fig. 3(b) are reconstructed images by a conventional iterative algorithm, and fig. 2(c) and fig. 3(c) are reconstructed images by the method.
The advantages of the method in the aspect of image reconstruction quality are illustrated by observing fig. 2 and fig. 3, and the image reconstructed by using the method has better quality than the image reconstructed by using total variation regularization. For example, the cap edge and hair in Lena are more intuitive as shown in fig. 2(b), (c) and more blurred in (a); the same effect is also obtained by the character pattern in fig. 3. From the peak snr of each image, the three images in fig. 2 correspond to values of 23.25, 25.50, and 26.32, respectively; the corresponding values in fig. 3 are 22.5, 24.60, 25.35, respectively. The anisotropic smoothing term can have good capability of protecting edges in a complex motion mode, and the regularization parameters are adjusted in time along with the iterative process, so that a higher-quality image can be obtained.
TABLE 1 comparison of conventional Algorithm with the reconstructed results of the Algorithm herein
In the aspect of reconstructed image quality, according to the data provided in table 1, the peak signal-to-noise ratio of the reconstructed image is slightly higher than that of the conventional iterative algorithm, the iteration frequency is about half of that of the conventional iterative algorithm, and the reconstruction time is only one tenth or even lower than that of the conventional iterative algorithm, which shows that the method can obtain a high-quality image with less time consumption.
Claims (4)
1. A quick super-resolution reconstruction method based on anisotropy is characterized by comprising the following steps:
step 1, performing motion compensation and up-sampling on all collected original images to obtain a high scoreImage after resolution image blurring
As a reference figure;
step 2, improving the reconstruction model based on the L1 norm least square method to obtain the optimized reconstruction model;
step 3, introducing an anisotropic regularization term, and constructing an adaptive parameter based on the regularization term to obtain an anisotropic-based adaptive reconstruction model;
step 4, taking the reference image obtained in the step 1 as an iteration initial value
Will be provided with
Carrying in the self-adaptive reconstruction model constructed in the step 3 to start iteration, calculating the peak signal-to-noise ratio of the reconstructed image at each time, and stopping iteration when the peak signal-to-noise ratio of the iteration result is lower than that of the previous time to complete image reconstruction;
step 3, introducing an anisotropic regularization term, and constructing an adaptive parameter based on the regularization term to obtain an anisotropic-based adaptive reconstruction model, specifically:
(1) anisotropy regularization term
Comprises the following steps:
in which Ψ(s)2)＝2μ2(1+s2/μ2)0.5Is a Charbonnier function, where μ is a fixed parameter, v1、v2Are two orthogonal vectors of the image structure tensor J, which is formulated as follows:
wherein, represents convolution operator, t represents vector transposition, GρIs a Gaussian kernel, ρ1、ρ2Respectively a neighborhood smooth scale and an image smooth scale;
(2) the adaptive regularization parameters β are:
wherein σ is 0.0000001;
(3) the final fast super-resolution reconstruction model based on anisotropy is as follows:
wherein,
represents the result value of the nth iteration, λ represents the gradient descent step size, and Ψ' represents the derivation of Ψ.
2. The method for fast super-resolution reconstruction based on anisotropy according to claim 1, characterized in that the blurred image of the high resolution image in step 1
The method specifically comprises the following steps:
and respectively carrying out motion compensation and up-sampling on all the acquired original images, and then solving the average value of the pixels at the corresponding positions of each image to obtain the image after the high-resolution image is subjected to blur degradation.
3. The anisotropic-based fast super-resolution reconstruction method according to claim 1, wherein the optimized reconstruction model in step 2 is:
wherein,
is a maximum likelihood estimate of the original high resolution image X, H represents the blur matrix.
4. The method for reconstructing fast super-resolution images based on anisotropy as claimed in claim 1, wherein step 4 is implemented by using the reference map obtained in step 1 as an initial iteration value
Will be provided with
And (3) carrying in the self-adaptive reconstruction model constructed in the step (3) to start iteration, calculating the peak signal-to-noise ratio of the reconstructed image at each time, stopping iteration when the peak signal-to-noise ratio of the iteration result is lower than that of the previous time, and completing image reconstruction, wherein the iteration conditions are as follows:
if(i＞＝2&&PSNR(i)＜PSNR(i-1))break；
wherein PSNR is the peak signal-to-noise ratio, X is the original high resolution image,
PSNR (i) is the peak signal-to-noise ratio of the ith iteration image for the super-resolution image formed by the nth iteration.
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| CN108830796B (en) * | 2018-06-20 | 2021-02-02 | 重庆大学 | Hyperspectral image super-resolution reconstruction method based on spectral-spatial combination and gradient domain loss |
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