CN114663304B - Sparse prior-based optical synthetic aperture system imaging enhancement method - Google Patents
Sparse prior-based optical synthetic aperture system imaging enhancement method Download PDFInfo
- Publication number
- CN114663304B CN114663304B CN202210257107.9A CN202210257107A CN114663304B CN 114663304 B CN114663304 B CN 114663304B CN 202210257107 A CN202210257107 A CN 202210257107A CN 114663304 B CN114663304 B CN 114663304B
- Authority
- CN
- China
- Prior art keywords
- image
- synthetic aperture
- aperture system
- imaging enhancement
- optical synthetic
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 45
- 230000003287 optical effect Effects 0.000 title claims abstract description 36
- 238000003384 imaging method Methods 0.000 title claims abstract description 33
- 108091006146 Channels Proteins 0.000 claims description 34
- 239000011159 matrix material Substances 0.000 claims description 14
- 238000004364 calculation method Methods 0.000 claims description 10
- 238000005070 sampling Methods 0.000 claims description 3
- 230000015556 catabolic process Effects 0.000 abstract description 5
- 238000006731 degradation reaction Methods 0.000 abstract description 5
- 230000000694 effects Effects 0.000 abstract description 4
- 238000001914 filtration Methods 0.000 description 4
- 238000004088 simulation Methods 0.000 description 4
- 238000002474 experimental method Methods 0.000 description 2
- 230000015572 biosynthetic process Effects 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 230000002708 enhancing effect Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000011148 porous material Substances 0.000 description 1
- 210000001747 pupil Anatomy 0.000 description 1
- 238000001228 spectrum Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000003786 synthesis reaction Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T5/00—Image enhancement or restoration
- G06T5/90—Dynamic range modification of images or parts thereof
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T5/00—Image enhancement or restoration
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Image Processing (AREA)
Abstract
The invention discloses an optical synthetic aperture system imaging enhancement method based on sparse prior. The method is used for solving the imaging degradation problem of the optical synthetic aperture system caused by the influence of an array structure and a common phase error. The method is characterized in that a dark channel and an image gradient prior are used as sparse prior to design an imaging enhancement model, the method comprises the steps of firstly calculating a point spread function under an array structure of a synthetic aperture system to serve as initial blur kernel input, then solving the sparse prior through a semi-quadratic splitting method, and estimating a final blur kernel and an image after imaging enhancement by the solution model. The invention utilizes the inherent priori theory of the synthetic aperture system, and has the advantages of wide application range, simple realization, good enhancement effect and the like.
Description
Technical Field
The invention relates to the technical field of image processing and optical engineering, in particular to the field of image restoration and enhancement of an optical synthetic aperture system, and particularly relates to an optical synthetic aperture system imaging enhancement method based on sparse prior.
Background
An optical synthetic aperture system uses small apertures that are easier to manufacture to achieve equivalent resolution in space to a single large aperture in a certain arrangement. The serious problem is that the image is degraded and blurred, and the reasons for the degradation are mainly reduced light passing area caused by an array structure and PSF dispersion caused by a common phase error. And thus needs to be addressed from the standpoint of imaging enhancement.
The wiener filtering method is commonly adopted as an imaging enhancement method aiming at a synthetic aperture system at present. Wiener filtering is based on the principle of least squares, and treats a digital image as a continuous signal with two-dimensional stability, and the central idea is to minimize the mean square error between a restored image and an image before degradation and maximize the similarity. Wiener filtering has good restoration effect on known PSF and noise types, but when the noise power spectrum cannot be estimated well, the restoration effect is poor, meanwhile, the phase error cannot be solved, and the restored image can generate ringing phenomenon.
Disclosure of Invention
In view of the above-mentioned problems in the prior art, the present invention proposes an optical synthetic aperture system imaging enhancement method based on sparse prior, as shown in fig. 2, by imaging the histograms of the dark channel values of the simulated clear image and the blur image of 445 optical synthetic aperture systems, it can be found that the dark channel value of the clear image is close to 0 value, and the dark channel value of the blur image is increased. Therefore, a dark channel can be used as an inherent priori for image enhancement of the synthetic aperture system, and the imaging effect of the system can be enhanced by considering only a point spread function under a fixed array structure aiming at a specific optical synthetic aperture system in combination with an image gradient priori.
The technical scheme adopted by the method is as follows: an optical synthetic aperture system imaging enhancement method based on sparse prior comprises the following steps:
step one: the system PSF function of the optical synthetic aperture under a fixed array structure is calculated.
Step two: a model for optical synthetic aperture imaging enhancement is proposed:
wherein the first itemIs a fidelity term, wherein B represents an input blurred image matrix, m x n x 3 size, k represents a blurred kernel matrix, wherein p is p, I represents the estimated sharp image matrix, m is n is 3, and +.>Representing a convolution process, the term using an L2 norm constraint to constrain a minimum of a value and a blurred image loss after convolution of a sharp image and a blur kernel; second item->A solution to regularize the fuzzy kernel, the term using an L2 norm constraint; third item->For gradient constraint term->Representing a gradient matrix of the image, the term using an L0 norm constraint; fourth item->For the dark channel constraint term, D (I) represents the dark channel value matrix of image I, which uses the L0 norm constraint, α, β, and λ as weight parameters.
Step three: image dark channel and gradient are directed to optical synthesis in the form of L0 normThe pore diameter imaging enhancement model is used as regularization term sparse constraint. The dark channel is expressed as the minimum value of three channels within the area 3*3 of each pixel of the acquired RGB image, and is calculated as followsWherein x and y represent the positions of the image pixels, respectively, and P (x) is a neighborhood centered on x; c is the color channel of the set { r, g, b }, D (I) (x) represents the dark channel value of image I at x pixels, +.>Any pixel representing image I is set to the minimum of the three RGB channels within its neighborhood P (x). The gradient represents the change rate of the pixel point in the horizontal direction and the vertical direction, and the calculation mode is as follows: />gx and gy represent the rates of change in the horizontal and vertical directions, respectively, and the calculation interval is 2 pixels.
Step four: inputting the blurred image acquired by the synthetic aperture system and taking the PSF function calculated in the step one as an initial blur kernel.
Step five: the image is downsampled in the form of a pyramid. In the down sampling process, firstly, the acquired synthetic aperture system image is calculated according to the input fuzzy kernel size KemelSize, and the layer number num_scales of the pyramid are calculated:and in the first iteration process, the image is reduced to the minimum value according to the layer number proportion, and the later iteration is up-sampled according to the layer number proportion of the image pyramid according to the result of the last layer.
Step six: and solving an objective function of the model by adopting a semi-quadratic splitting method. The size of the blur kernel is calculated from the initial blur kernel size KernelSize and the number of layers of the image pyramid i=num_scales as follows:each fuzzy kernel estimate is the result of the previous calculation.
The invention provides an imaging enhancement method based on a sparse prior of a gradient and a dark channel, and compared with the prior art, the imaging enhancement method has the following advantages and innovations:
1. using an inherent prior: the dark channel and the gradient prior have the characteristics of simplicity and high efficiency, and the method can obtain a final clear image through repeated iterative estimation by only inputting a point spread function under an array structure as an initial value of fuzzy kernel estimation.
2. Compared with the existing image enhancement method requiring strict optical system prior, the method has better generalization capability, and can initialize the blur kernel into a zero matrix under the condition of not requiring parameters of an optical system, and perform blind restoration on the blur image imaged by the system.
3. The invention can effectively solve the problems of noise generated by system imaging and image degradation caused by common phase errors.
Drawings
Fig. 1 is a flowchart of an optical synthetic aperture system imaging enhancement method based on sparse priors.
Fig. 2 is a histogram of dark channel values for pixel points of a clear image and a blur image for verifying a dark channel prior theory according to the present invention.
FIG. 3 shows the results of the simulation experiment of the present invention.
Fig. 4 shows the average PSNR and SSIM index results of the simulation experiment of the present invention.
Fig. 5 shows the blind restoration result of the practical application of the method.
Detailed Description
The invention is further described below with reference to the drawings and detailed description.
The invention provides an imaging enhancement method for a synthetic aperture optical system, which comprises the steps of firstly restricting a dark channel and a gradient as inherent priori, then taking a PSF function calculated under an array structure of the optical system as an initial fuzzy core, and solving a final estimated clear restored image through iteration. The method can solve the problem of image blurring caused by image noise, common phase errors and other factors, and restore the detail part of the image.
As shown in fig. 1, the invention provides an optical synthetic aperture system imaging enhancement method based on L0 sparse prior, which comprises the following steps:
step 1: the system PSF function of the optical synthetic aperture under a fixed array structure is calculated. The calculation method is as follows:
wherein PSF (x, y) is the PSF function of the system; x and y represent the position of the coordinate plane; n represents the number of sub-apertures of the synthetic aperture system; n and m represent any two sub-apertures; lambda is the center wavelength; z is the distance between the system exit pupil plane and the image plane, i.e. the focal length of the synthetic aperture system; a, a m And b m Respectively the positions of the circle centers of the sub-apertures on the coordinate axes; PSF (Power System factor) sub (x, y) is the amplitude spread function of each sub-aperture of the system, expressed as:
wherein r is 0 Field stop diameter, J, of sub-aperture 1 Is a first order Bessel function;
step 2: a model for optical synthetic aperture imaging enhancement is presented:
first itemIs a fidelity term, wherein B represents an input blurred image matrix, m x n x 3 size, k represents a blurred kernel matrix, wherein p is p, I represents the estimated sharp image matrix, m is n is 3, and +.>Representing a convolution process, the term using an L2 norm constraint to constrain a minimum of a value and a blurred image loss after convolution of a sharp image and a blur kernel; second item->A solution to regularize the blur kernel, the term being solvable by a fast fourier transform using an L2 norm constraint; third item->For gradient constraint term->Representing the gradient of the image to cull smaller gradients while preserving the details of larger gradients, the term using the L0 norm constraint; fourth item->For the dark channel constraint term, D (I) represents a matrix of dark channel values (of size m x n) for image I such that the estimated sharp image dark channel sparseness is as high as possible, using the L0 norm constraint, α, β, and λ as weight parameters initialized to 0.001, 0.004, and 0.004, respectively.
Step 3: the image dark channels and gradients are sparsely constrained in the model in the form of L0 norms as regularization terms. The dark channel is expressed as the minimum value of three channels within each pixel area 3*3 of the RGB image of the acquired optical synthetic aperture system, and is calculated as followsWherein x and y respectively represent the positions of image pixels, and P (x) is a neighborhood centered on x and is set to 3*3 pixels; c is the color channel of the set { r, g, b }, D (l) (x) represents the dark channel value of image I at x pixels, +.>Any pixel representing image I is set to the minimum of the three RGB channels within its neighborhood P (x). The gradient represents the change rate of the pixel point in the horizontal direction and the vertical direction, and the calculation mode is as follows: />gX and gy represent the rates of change in the horizontal and vertical directions, respectively, and the calculation interval is 2 pixels.
Step 4: inputting the blurred image acquired by the synthetic aperture system and taking the PSF function calculated in the step one as an initial blur kernel.
Step 5: the image is downsampled in the form of a pyramid. In the downsampling process, firstly, the acquired synthetic aperture system image is calculated according to the input blur kernel size KemelSize=35×35, and the layer number num_scales of the pyramid is calculated:and in the first iteration process, the image is reduced to the minimum value according to the layer number proportion, and then the iteration process is used for up-sampling according to the layer number proportion of the image pyramid according to the result of the last layer.
Step 6: and solving an objective function of the model by adopting a semi-quadratic splitting method. The size of the blur kernel is calculated from the initial blur kernel size KemelSize and the number of layers of the image pyramid i=num_scales as follows:each fuzzy kernel estimate is the result of the previous calculation.
By carrying out image simulation degradation on an optical synthetic aperture system, the method and a wiener filtering method are subjected to a comparison experiment, the synthetic aperture system with the sub-aperture diameter D of 200mm and the circumscribed circle diameter D of 500mm under a Golay-3 array structure is subjected to simulation imaging, the imaging enhancement result is shown in figure 3, and the two objective index results of peak signal to noise ratio (PSNR) and Structural Similarity (SSIM) are shown in figure 4. Meanwhile, engineering practical experiments are carried out on the method of the invention, and the result is shown in figure 5. The above experimental results can prove that the present invention is effective for enhancing an optical synthetic aperture imaging system.
It should be understood that the foregoing description of the preferred embodiments is not intended to limit the scope of the invention, but rather to limit the scope of the claims, and that those skilled in the art can make substitutions or modifications without departing from the scope of the invention as set forth in the appended claims.
Claims (5)
1. An optical synthetic aperture system imaging enhancement method based on sparse prior is characterized by comprising the following steps of: comprises the following steps:
step one: calculating a system PSF function of the optical synthetic aperture under a fixed array structure;
step two: a model for optical synthetic aperture imaging enhancement is proposed;
step three: sparse constraint is carried out on dark channels and gradients of the image in the form of L0 norms as regularization terms in a model for optical synthetic aperture imaging enhancement;
step four: inputting a blur image acquired by a synthetic aperture system and taking the PSF function calculated in the first step as an initial blur kernel;
step five: downsampling the image in the form of a pyramid;
step six: solving an objective function of the model by adopting a semi-quadratic splitting method;
in the second and third steps, the model for optical synthetic aperture imaging enhancement is as follows:
wherein the first itemIs a fidelity term, wherein B represents an input fuzzy image matrix, m is equal to n is equal to 3, and k represents fuzzy nuclear momentAn array of p x p size; i represents an estimated sharp image matrix, whose m x n x 3 size; />Representing a convolution process, which uses an L2 norm to constrain the minimum loss of the blurred image and the value of the convolved sharp image and the blur kernel; second item->A solution to regularize the fuzzy kernel, the term using an L2 norm constraint; third item->For gradient constraint term->Representing a gradient matrix of the image, the term using an L0 norm constraint; fourth term D (I) I 0 For the dark channel constraint term, D (I) represents the dark channel value matrix of image I, which uses the L0 norm constraint, α, β, and λ as weight parameters.
2. The sparse prior-based optical synthetic aperture system imaging enhancement method of claim 1, wherein: the dark channel is expressed as the minimum value of three channels within each pixel area 3*3 of the RGB image of the acquired optical synthetic aperture system, and is calculated as followsWherein x and y represent the positions of the image pixels, respectively; p (x) is a neighborhood centered on x; c is the color channel of the set { r, g, b }, D (I) (x) represents the dark channel value of image I at x pixels, +.>Any pixel x representing image I is set to the minimum of the three RGB channels within its neighborhood P (x).
3. The sparse prior-based optical synthetic aperture system imaging enhancement method of claim 1 or 2, wherein: the gradient represents the change rate of the pixel point in the horizontal direction and the vertical direction, and the calculation mode is as follows:gx and gy represent the rates of change in the horizontal and vertical directions, respectively, and the calculation interval is 2 pixels.
4. The sparse prior-based optical synthetic aperture system imaging enhancement method of claim 1, wherein: in the fifth step, the downsampling process firstly calculates the number of layers num_scales of the pyramid according to the input blur kernel size KernelSize of the acquired synthetic aperture system image:and in the first iteration process, the image is reduced to the minimum value according to the layer number proportion, and then the iteration process is used for up-sampling according to the layer number proportion of the image pyramid according to the result of the last layer.
5. The sparse prior-based optical synthetic aperture system imaging enhancement method of claim 1 or 4, wherein: the size of the blur kernel is calculated according to the initial blur kernel size KernelSize and the number of layers i of the image pyramid as follows:each blur kernel estimation is the result of the previous calculation.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210257107.9A CN114663304B (en) | 2022-03-16 | 2022-03-16 | Sparse prior-based optical synthetic aperture system imaging enhancement method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210257107.9A CN114663304B (en) | 2022-03-16 | 2022-03-16 | Sparse prior-based optical synthetic aperture system imaging enhancement method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114663304A CN114663304A (en) | 2022-06-24 |
| CN114663304B true CN114663304B (en) | 2023-09-19 |
Family
ID=82028792
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210257107.9A Active CN114663304B (en) | 2022-03-16 | 2022-03-16 | Sparse prior-based optical synthetic aperture system imaging enhancement method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114663304B (en) |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105023245A (en) * | 2015-05-05 | 2015-11-04 | 苏州大学 | Image smoothing method under strength and gradient sparsity constraint |
| CN105824030A (en) * | 2016-03-10 | 2016-08-03 | 中国科学院光电技术研究所 | Sparse optical synthetic aperture imaging method based on sub-aperture shutter modulation phase difference method |
| CN109633646A (en) * | 2019-01-21 | 2019-04-16 | 中国人民解放军陆军工程大学 | Bistatic ISAR imaging method based on weighted L1 norm constraint |
| CN109767404A (en) * | 2019-01-25 | 2019-05-17 | 重庆电子工程职业学院 | Infrared image deblurring method under a kind of salt-pepper noise |
| CN109919871A (en) * | 2019-03-05 | 2019-06-21 | 重庆大学 | Fuzzy core estimation method based on image and fuzzy core mixed constraints |
| CN113538374A (en) * | 2021-07-15 | 2021-10-22 | 中国科学院上海技术物理研究所 | Infrared image blur correction method for high-speed moving object |
| CN113689336A (en) * | 2021-08-25 | 2021-11-23 | 华北电力大学（保定） | Power equipment infrared image non-blind super-resolution method |
| CN113963349A (en) * | 2021-08-17 | 2022-01-21 | 大连理工大学 | Method for extracting individual space-time feature vector and tested classification |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9307208B2 (en) * | 2014-03-07 | 2016-04-05 | The University Of British Columbia | System and method for solving inverse imaging problems |
| US20190365355A1 (en) * | 2017-01-18 | 2019-12-05 | Technion Research & Development Foundation Ltd. | Sparsity-based ultrasound super-resolution imaging |
-
2022
- 2022-03-16 CN CN202210257107.9A patent/CN114663304B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105023245A (en) * | 2015-05-05 | 2015-11-04 | 苏州大学 | Image smoothing method under strength and gradient sparsity constraint |
| CN105824030A (en) * | 2016-03-10 | 2016-08-03 | 中国科学院光电技术研究所 | Sparse optical synthetic aperture imaging method based on sub-aperture shutter modulation phase difference method |
| CN109633646A (en) * | 2019-01-21 | 2019-04-16 | 中国人民解放军陆军工程大学 | Bistatic ISAR imaging method based on weighted L1 norm constraint |
| CN109767404A (en) * | 2019-01-25 | 2019-05-17 | 重庆电子工程职业学院 | Infrared image deblurring method under a kind of salt-pepper noise |
| CN109919871A (en) * | 2019-03-05 | 2019-06-21 | 重庆大学 | Fuzzy core estimation method based on image and fuzzy core mixed constraints |
| CN113538374A (en) * | 2021-07-15 | 2021-10-22 | 中国科学院上海技术物理研究所 | Infrared image blur correction method for high-speed moving object |
| CN113963349A (en) * | 2021-08-17 | 2022-01-21 | 大连理工大学 | Method for extracting individual space-time feature vector and tested classification |
| CN113689336A (en) * | 2021-08-25 | 2021-11-23 | 华北电力大学（保定） | Power equipment infrared image non-blind super-resolution method |
Non-Patent Citations (6)
| Title |
|---|
| Bin Fan等.Effective Spectral Unmixing via Robust Representation and Learning-based Sparsity.《Computer Vision and Pattern Recognition》.2017,1-13. * |
| Zongyong Cui等.Target recognition in synthetic aperture radar images via non-negative matrix factorisation.《ET Radar, Sonar & Navigation》.2015,第9卷(第9期),1376-1385. * |
| 廖斌等.基于多分辨率正则化LR的图像盲复原.《福建电脑》.2015,(第9期),16-17+31. * |
| 李霄.基于稀疏约束的图像盲复原方法研究.《中国优秀硕士学位论文全文数据库 (信息科技辑)》.2017,(第3期),I138-4611. * |
| 郑天宇等.基于增强拉东变换及稀疏先验的模糊星斑复原.《光学精密工程》.2018,(第6期),189-198. * |
| 高敬坤.阵列三维成像及雷达增强成像技术研究.《中国博士学位论文全文数据库 (信息科技辑)》.2021,(第1期),I136-295. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114663304A (en) | 2022-06-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110675347B (en) | Image blind restoration method based on group sparse representation | |
| CN107025632B (en) | Image super-resolution reconstruction method and system | |
| US20080253678A1 (en) | Denoise method on image pyramid | |
| CN104091312B (en) | A kind of simple lens formation method according to image spectrum information extraction fuzzy core priori | |
| CA2577735A1 (en) | Extended depth of field using a multi-focal length lens with a controlled range of spherical aberration and centrally obscured aperture | |
| CN109447930B (en) | Wavelet domain light field full-focusing image generation algorithm | |
| CN113538374B (en) | Infrared image blurring correction method for high-speed moving object | |
| CN114647079B (en) | Monolithic broadband diffraction calculation imaging method | |
| CN108629741B (en) | Fuzzy kernel estimation method based on L0 and L1 regular terms | |
| CN115345791A (en) | Infrared image deblurring algorithm based on attention mechanism residual error network model | |
| CN112330549A (en) | Blind deconvolution network-based blurred image blind restoration method and system | |
| CN107220945B (en) | Restoration method of multiple degraded extremely blurred image | |
| Huang et al. | Light-field reconstruction and depth estimation from focal stack images using convolutional neural networks | |
| CN114663304B (en) | Sparse prior-based optical synthetic aperture system imaging enhancement method | |
| CN112488920A (en) | Image regularization super-resolution reconstruction method based on Gaussian-like fuzzy kernel | |
| CN113379647A (en) | Multi-feature image restoration method for optimizing PSF estimation | |
| CN112784747A (en) | Multi-scale eigen decomposition method for hyperspectral remote sensing image | |
| KR102617023B1 (en) | System and method for improving light field spatial resolution | |
| CN116029924A (en) | Image processing method of infrared system by single-chip diffraction | |
| CN115937302A (en) | Hyperspectral image sub-pixel positioning method combined with edge preservation | |
| Wang et al. | Optical satellite image MTF compensation for remote-sensing data production | |
| Su et al. | Atmospheric turbulence degraded image restoration using a modified dilated convolutional network | |
| Deepak et al. | Analysis of Single Image Super-Resolution Techniques: An Evolutionary Study | |
| CN114359103A (en) | Hyperspectral image defogging method and device, computer product and storage medium | |
| CN108681988B (en) | Robust image resolution enhancement method based on multiple images |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |