CN114663304A - A Sparse Prior-Based Imaging Enhancement Method for Optical Synthetic Aperture Systems - Google Patents

Abstract

The invention discloses an imaging enhancement method of optical synthetic aperture system based on sparse prior. It is used to solve the imaging degradation problem of optical synthetic aperture system due to the influence of array structure and common phase error. The characteristics of the method are that the dark channel and the image gradient prior are used as the sparse prior to design the imaging enhancement model. The method flow is to first calculate the point spread function under the synthetic aperture system array structure as the initial blur kernel input, and then use the semi-quadratic splitting method. The sparse prior is solved, and the solution model estimates the final blur kernel and the image after imaging enhancement. The invention utilizes the inherent a priori theory of the synthetic aperture system, and has the advantages of wide application range, simple implementation, good enhancement effect and the like.

Description

A Sparse Prior-Based Imaging Enhancement Method for Optical Synthetic Aperture Systems

technical field

The invention relates to the technical fields of image processing and optical engineering, in particular to the field of image restoration and enhancement of optical synthetic aperture systems, and in particular to a sparse prior-based imaging enhancement method of optical synthetic aperture systems.

Background technique

Optical synthetic aperture systems use smaller, easier-to-manufacture apertures arranged in space to achieve resolution equivalent to a single large aperture. The serious problem it faces is the degradation and blurring of the image, which is mainly caused by the reduction of the light transmission area caused by the array structure and the PSF dispersion caused by the common phase error. Therefore, it needs to be solved from the perspective of imaging enhancement.

At present, the commonly used imaging enhancement method for synthetic aperture system is the Wiener filter method. Wiener filtering is based on the principle of least squares, and regards the digital image as a two-dimensional stable continuous signal. Wiener filtering has a good recovery effect on known PSF and noise types, but when the noise power spectrum cannot be well estimated, the recovery effect is poor, and the phase error cannot be resolved, and the recovered image will produce ringing.

SUMMARY OF THE INVENTION

In view of the above-mentioned problems existing in the current technology, the present invention proposes an optical synthetic aperture system imaging enhancement method based on sparse prior. The histogram of , it can be found that the dark channel value of the clear image is close to 0 value, while the dark channel value of the blurred image is rising. Therefore, the dark channel can be used as the inherent prior for image enhancement of the synthetic aperture system. Combined with the image gradient prior, for a specific optical synthetic aperture system, only the point spread function under a fixed array structure needs to be considered, and the imaging effect of the system can be improved. to enhance.

The technical scheme adopted by the method of the present invention is: a sparse prior-based optical synthetic aperture system imaging enhancement method, comprising the following steps:

Step 1: Calculate the system PSF function of the optical synthetic aperture under the fixed array structure.

Step 2: Propose a model for optical synthetic aperture imaging enhancement:

为保真项，其中B表示输入的模糊图像矩阵，其m*n*3大小，k表示模糊核矩阵，其p*p大小，I表示估计的清晰图像矩阵，其m*n*3大小，

表示卷积的过程，该项使用L2范数约束，用来约束清晰图像与模糊核卷积后的值与模糊图像损失最小；第二项

用来正则化模糊核的解，该项使用L2范数约束；第三项

为梯度约束项，

表示图像的梯度矩阵，该项使用L0范数约束；第四项

为暗通道约束项，D(I)表示图像I的暗通道值矩阵，该项使用L0范数约束，α、β和λ为权重参数。Among them, the first

is the fidelity term, where B represents the input blurred image matrix with the size of m*n*3, k represents the blur kernel matrix with the size of p*p, and I represents the estimated clear image matrix with the size of m*n*3,

Represents the process of convolution. This item uses the L2 norm constraint to constrain the value of the clear image and the blur kernel convolved with the blurred image to minimize the loss; the second item

Used to regularize the solution of the fuzzy kernel, this term uses the L2 norm constraint; the third term

is the gradient constraint term,

Represents the gradient matrix of the image, which uses the L0 norm constraint; the fourth term

is the dark channel constraint term, D(I) represents the dark channel value matrix of the image I, this term uses the L0 norm constraint, and α, β and λ are the weight parameters.

其中x和y分别表示图像像素的位置，P(x)是以x为中心的邻域；c为集合{r，g，b}的颜色通道，D(I)(x)表示图像I在x像素点的暗通道值，

表示图像I的任一像素点设置为在其邻域P(x)内RGB三通道中的最小值。梯度表示像素点在水平和垂直两个方向上的变化率，计算方式为：

gx和gy分别表示水平和垂直方向的变化率，计算区间为2个像素点。Step 3: Use the image dark channel and gradient in the form of L0 norm as regularization term sparse constraints in the model for optical synthetic aperture imaging enhancement. The dark channel is expressed as the minimum value of the three channels within the 3*3 range of each pixel point of the acquired RGB image, and is calculated as follows

where x and y represent the position of the image pixel respectively, P(x) is the neighborhood centered at x; c is the color channel of the set {r, g, b}, D(I)(x) represents the image I at x the dark channel value of the pixel,

Any pixel representing image I is set as the minimum value among the three RGB channels in its neighborhood P(x). The gradient represents the rate of change of a pixel in both horizontal and vertical directions, and is calculated as:

gx and gy represent the rate of change in the horizontal and vertical directions, respectively, and the calculation interval is 2 pixels.

Step 4: Input the blurred image collected by the synthetic aperture system and the PSF function calculated in step 1 as the initial blur kernel.

第一次迭代过程，将图像按层数比例缩小到最小值，之后的迭代按照上一层的结果按图像金字塔层数的比例向上采样。Step 5: Downsample the image in the form of a pyramid. The downsampling process first calculates the number of pyramid layers num_scales according to the input blur kernel size KemelSize of the collected synthetic aperture system image:

In the first iteration process, the image is scaled down to the minimum value according to the number of layers, and the subsequent iterations are up-sampled according to the result of the previous layer according to the ratio of the number of image pyramid layers.

每次模糊核的估计为上一层计算的结果。Step 6: Use the semi-quadratic splitting method to solve the objective function of the model. The size of the blur kernel is calculated according to the initial blur kernel size KernelSize and the number of layers i=num_scales of the image pyramid, as follows:

The estimation of each blur kernel is the result calculated by the previous layer.

The present invention proposes an imaging enhancement method using sparse prior based on gradients and dark channels. Compared with the existing technology, the present invention has the following advantages and innovations:

1. Using inherent priors: Dark channel and gradient priors are simple and efficient. The method only needs to input the point spread function under the array structure as the initial value of the fuzzy kernel estimation, and the final value can be obtained after multiple iterations of estimation. clear image.

2. Compared with the existing image enhancement methods that require strict optical system priors, the present invention has better generalization ability, and can initialize the blur kernel to a zero matrix without requiring the parameters of the optical system, so as to improve the image quality of the system. Blind restoration of blurred images.

3. The present invention can effectively solve the problem of image degradation caused by noise in system imaging and common phase error.

Description of drawings

FIG. 1 is a flowchart of an imaging enhancement method for an optical synthetic aperture system based on a sparse prior of the present invention.

FIG. 2 is a histogram of the dark channel values of the pixel points of the clear image and the blurred image for verifying the dark channel prior theory according to the present invention.

Fig. 3 is the simulation experiment result of the present invention.

FIG. 4 is the average PSNR and SSIM index results of the simulation experiment of the present invention.

Fig. 5 is the blind restoration result of the practical application of this method.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

The invention proposes an imaging enhancement method for a synthetic aperture optical system. First, the dark channel and the gradient are used as inherent prior constraints, and then the PSF function calculated under the array structure of the optical system is used as the initial blur kernel, and the solution is iteratively solved. The final estimated sharply restored image. The method can solve the image blur caused by image noise, common phase error and other factors, and restore the details of the image.

As shown in FIG. 1 , the present invention provides an optical synthetic aperture system imaging enhancement method based on L0 sparse prior, including the following steps:

Step 1: Calculate the system PSF function of the optical synthetic aperture under a fixed array structure. It is calculated as follows:

Among them, 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; λ is the center wavelength; z is the The distance between the exit pupil plane and the image plane of the system is the focal length of the synthetic aperture system; a _m and b _m are the positions of the center of the sub-apertures on the coordinate axis, respectively; PSF _sub (x, y) is the amplitude spread function of each sub-aperture of the system, Expressed as:

Among them, r ₀ is the field diaphragm diameter of the sub-aperture, and J ₁ is the first-order Bessel function;

Step 2: Propose a model for optical synthetic aperture imaging enhancement:

为保真项，其中B表示输入的模糊图像矩阵，其m*n*3大小，k表示模糊核矩阵，其p*p大小，I表示估计的清晰图像矩阵，其m*n*3大小，

表示卷积的过程，该项使用L2范数约束，用来约束清晰图像与模糊核卷积后的值与模糊图像损失最小；第二项

用来正则化模糊核的解，该项使用L2范数约束，可通过快速傅里叶变换求解；第三项

为梯度约束项，

表示图像的梯度，用来剔除较小的梯度，而保留梯度较大的细节，该项使用L0范数约束；第四项

为暗通道约束项，D(I)表示图像I的暗通道值矩阵(大小为m*n)，使得估计的清晰图像暗通道稀疏程度尽可能的高，该项使用L0范数约束，α、β和λ为权重参数，分别初始化为0.001、0.004和0.004。the first item

is the fidelity term, where B represents the input blurred image matrix with the size of m*n*3, k represents the blur kernel matrix with the size of p*p, and I represents the estimated clear image matrix with the size of m*n*3,

Represents the process of convolution. This item uses the L2 norm constraint to constrain the value of the clear image and the blur kernel convolved with the blurred image to minimize the loss; the second item

The solution used to regularize the fuzzy kernel, which uses the L2 norm constraint and can be solved by the fast Fourier transform; the third term

is the gradient constraint term,

Indicates the gradient of the image, which is used to eliminate smaller gradients and retain the details with larger gradients. This item uses the L0 norm constraint; the fourth item

is the dark channel constraint term, D(I) represents the dark channel value matrix of image I (size is m*n), so that the estimated clear image dark channel sparse degree is as high as possible, this term uses the L0 norm constraint, α, β and λ are weight parameters, which are initialized to 0.001, 0.004, and 0.004, respectively.

其中x和y分别表示图像像素的位置，P(x)是以x为中心的邻域，设置为3*3像素大小；c为集合{r，g，b}的颜色通道，D(l)(x)表示图像I在x像素点的暗通道值，

表示图像I的任一像素点设置为在其邻域P(x)内RGB三通道中的最小值。梯度表示像素点在水平和垂直两个方向上的变化率，计算方式为：

gX和gy分别表示水平和垂直方向的变化率，计算区间为2个像素点。Step 3: The image dark channel and gradient are sparsely constrained as regularization terms in the model in the form of L0 norm. The dark channel is expressed as the minimum value of the three channels within the 3*3 range of each pixel point of the RGB image of the acquired optical synthetic aperture system, and is calculated as follows

Where x and y represent the position of the image pixel respectively, P(x) is the neighborhood of x as the center, set to 3*3 pixel size; 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 as the minimum value among the three RGB channels in its neighborhood P(x). The gradient represents the rate of change of a pixel in both horizontal and vertical directions, and is calculated as:

gX and gy represent the rate of change in the horizontal and vertical directions, respectively, and the calculation interval is 2 pixels.

Step 4: Input the blurred image collected by the synthetic aperture system and the PSF function calculated in step 1 as the initial blur kernel.

第一次迭代过程，将图像按层数比例缩小到最小值，之后的迭代过程按照上一层的结果按图像金字塔层数的比例向上采样。Step 5: Downsample the image in the form of a pyramid. The downsampling process first calculates the number of pyramid layers num_scales according to the input blur kernel size KemelSize=35*35 of the collected synthetic aperture system image:

In the first iterative process, the image is reduced to the minimum value according to the number of layers, and the subsequent iterative process is up-sampled according to the result of the previous layer according to the proportion of the number of image pyramid layers.

每次模糊核的估计为上一层计算的结果。Step 6: Use the semi-quadratic splitting method to solve the objective function of the model. The size of the blur kernel is calculated according to the initial blur kernel size KemelSize and the number of layers i=num_scales of the image pyramid, as follows:

The estimation of each blur kernel is the result calculated by the previous layer.

Through the image simulation degradation of the optical synthetic aperture system, this method is compared with the Wiener filtering method. The synthetic aperture system under the Golay-3 array structure with the sub-aperture diameter d of 200mm and the circumscribed circle diameter D of 500mm is simulated. The results of imaging and imaging enhancement are shown in Figure 3, and the results of two objective indicators, Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM), are shown in Figure 4. At the same time, a practical engineering experiment is carried out on the method of the present invention, and the result is shown in FIG. 5 . The above experimental results can prove that the present invention is effective for enhancing the optical synthetic aperture imaging system.

It should be understood that the above description of the preferred embodiments is relatively detailed, and therefore should not be considered as a limitation on the scope of the patent protection of the present invention. In the case of the protection scope, substitutions or deformations can also be made, which all fall within the protection scope of the present invention, and the claimed protection scope of the present invention shall be subject to the appended claims.

Claims (6)

1. an optical synthetic aperture system imaging enhancement method based on sparse prior, is characterized in that: comprise the following steps: Step 1: Calculate the system PSF function of the optical synthetic aperture under the fixed array structure; Step 2: Propose a model for optical synthetic aperture imaging enhancement; Step 3: The dark channel and gradient of the image are sparsely constrained in the form of L0 norm in the model for optical synthetic aperture imaging enhancement as a regularization term; Step 4: Input the blurred image collected by the synthetic aperture system and the PSF function calculated in step 1 as the initial blur kernel; Step 5: downsample the image in the form of a pyramid; Step 6: Use the semi-quadratic splitting method to solve the objective function of the model. 2. according to the optical synthetic aperture system imaging enhancement method based on sparse prior according to claim 1, it is characterized in that: in step 2 and step 3, the model for optical synthetic aperture imaging enhancement is as follows:

Among them, the first

is the fidelity item, where B represents the input blurred image matrix, whose size is m*n*3, k represents the blur kernel matrix, whose size is p*p; I represents the estimated clear image matrix, whose size is m*n*3;

Indicates the process of convolution. This item uses the L2 norm to constrain the value of the convolution between the clear image and the blur kernel and the blurred image with the least loss; the second item

Used to regularize the solution of the fuzzy kernel, this term uses the L2 norm constraint; the third term

is the gradient constraint term,

Represents the gradient matrix of the image, which uses the L0 norm constraint; the fourth item ||D(I)|| ₀ is the dark channel constraint item, D(I) represents the dark channel value matrix of the image I, and this item uses the L0 norm Number constraints, α, β and λ are weight parameters. 3. The optical synthetic aperture system imaging enhancement method based on sparse prior according to claim 1 or 2 is characterized in that: the dark channel is represented as each pixel field of the RGB image of the obtained optical synthetic aperture system 3*3 The minimum value of the three channels in the range, calculated as follows

where x and y represent the position of the image pixel respectively; P(x) is the neighborhood centered at x; c is the color channel of the set {r, g, b}, D(I)(x) represents the image I at x the dark channel value of the pixel,

Any pixel x representing the image I is set to the minimum value among the three RGB channels in its neighborhood P(x). 4. The optical synthetic aperture system imaging enhancement method based on sparse prior according to claim 1 or 3, characterized in that: the gradient represents the rate of change of the pixel in both horizontal and vertical directions, and the calculation method is:

gx and gy represent the rate of change in the horizontal and vertical directions, respectively, and the calculation interval is 2 pixels. 5. The optical synthetic aperture system imaging enhancement method based on sparse prior according to claim 1, is characterized in that: in step 5, the process of downsampling will first collect the synthetic aperture system image according to the input blur kernel size KernelSize , calculate the level num_scales of the pyramid:

In the first iterative process, the image is reduced to the minimum value according to the number of layers, and the subsequent iterative process is up-sampled according to the result of the previous layer according to the proportion of the number of image pyramid layers. 6. according to the optical synthetic aperture system imaging enhancement method based on sparse prior according to claim 1 or 6, it is characterized in that: the size of blur kernel is calculated according to the layer number i of initial blur kernel size KernelSize and image pyramid as follows :

The estimation of each blur kernel is the result calculated by the previous layer.

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