CN101364302A - A method for sharpening defocused blurred images - Google Patents

Abstract

The invention discloses a defocus blurred image sharpness processing method, which is implemented according to the following steps: firstly, the mean value and the variance of the edge width is calculated according to gradient information of an image; an initial parameter of a fuzzy model is obtained according to the statistical data; secondly, the blurred image is divided into concentric circles around the center of the image and is broken down into sub-images, wherein, the number of the concentric circles is k and the number of the sub-images is k+1; the corresponding blurred initial semidiameters are distributed to the sub-images; the optimal blurred semidiameter is found through an iterative mode, and the sharpness processing of all sub-images is performed by adopting a frequency domain inverse-filtering manner; finally, all the sub-images are added to synthesize the whole sharpness image. The defocus blurred image sharpness processing method overcomes the limitations in the existing circular disc function modeling recovery method based on the fixed semidiameter, and serves the purpose for restoring the sharp image.

Description

A method for sharpening defocused blurred images

technical field

The invention belongs to the technical field of digital image restoration, and relates to a method for clearing defocused blurred images.

Background technique

When taking a photo, sometimes the image will be blurred, which is mainly caused by the fact that the object to be photographed is not on the focal plane of the imaging system, which is called defocus blur. For some photos containing important information, which cannot be recognized due to defocus blur, if there is no chance to shoot again, or the cost of taking another shot is too high, you can use the defocus blur restoration and clearing technology to clear them . Most of the existing defocus blur restoration and clearing techniques are based on fixed-radius disk function modeling restoration methods, which have extremely limited ability to restore optical defocus blur generated in practice.

Contents of the invention

The purpose of the present invention is to provide a method for sharpening defocused blurred images, which overcomes the problem of limited recovery ability of blurred images in the prior art, and can restore defocused blurred images to clear images.

The technical solution adopted in the present invention is a method for clearing defocused blurred images, which is implemented according to the following steps,

Step 1: Establish a mathematical model for the defocused blurred image to be processed

A disc function is used to model the blurred image, namely:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& {\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ></span>{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, R _b is the blur radius, π is the circumference ratio, and (x, y) is a certain pixel point on the image;

Step 2: Pick an initial blur radius

Search for the blur radius of the defocused blurred image to be processed, first sharpen the captured defocused image, and generate the gradient map E _s and the direction map E _o ; the obtained gradient map E _s and the gradient direction map E _o , use the non-maximum value suppression technique to obtain the local gradient magnitude maximum point set E _n ; binarize E _n under a given threshold to obtain the contour map E _e , and then calculate the edge width, the obtained width Calculate the mean value M and variance D, and select M/2 as the initial blur radius R _b of the whole image;

Step 3: Division of sub-images

Substitute the variance D obtained in step 2 into the equation k=int[D-1] to obtain the parameter k of the number of sub-images, and then draw k concentric circles with the center of the image as a dot, and its radius is R _k = R ₁ +(k-1)·ΔR, where R ₁ is the radius of the innermost circle, and ΔR is the increment. The image is decomposed into a circular area, k-1 circular areas, and the remaining image areas are k+1 sub-images, denoted as g _s1 , g _s2 ...g _s(k+1) ;

Step 4: Sharpening of sub-images

With the variance obtained in step 2 and the k obtained in step 3, the step size of the disk radius is D/k, and the initial blur radius under the i-th sub-image is obtained. According to the blur radius, the sub-image is obtained according to equation (1). The disk function h _i (x, y) of the image, the sub-image g _si (x, y) is converted in the frequency domain, and then the corresponding disk function under each sub-image is converted in the frequency domain, and the noise and the original image are calculated The power spectrum S _nn (u, v) and S _ff (u, v); and then based on the inverse filter to restore image clarity, change the blur radius, that is, calculate R _i (0) and R _i (0)±ΔR _i , to This obtains three restored sub-images, calculates the Sobel sharpening detail energy map of the three restored images, and calculates the difference in variance of the three restored images, and then iterates in the direction of the small difference until the opportunity with the smallest variance difference is found , stop the iteration, select the image of the maximum energy mean value in the two energy maps when the iteration stops as the final result, set it as f _i *(x, y);

Step 5. Obtain the whole clear image

Add f _i *(x, y),

sharpen image $f(x,\mathrm{the\; y})=\underset{i=1}{\overset{k+1}{\mathrm{\&Sigma;}}}{f}_i*(x,\mathrm{the\; y}).$

The clearing processing method of the defocused blurred image of the present invention overcomes the limitations of the existing method of modeling and restoration based on the fixed-radius disc function, and uses the basic imaging principle of the defocused blurred image to construct a degenerated blurred model disc with a variable radius function to achieve the purpose of recovering a clear image.

Description of drawings

Figure 1 is a schematic diagram of the defocusing principle, where a is the arrangement relationship between the camera and the shooting scene, and b is the schematic diagram of the defocusing principle;

Fig. 2 is a schematic diagram of sub-image decomposition in the method of the present invention, wherein a is the division of concentric circles, and b is the area range of the kth sub-image.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

The present invention proposes a recovery method under variable-radius disc function, which is based on the basic imaging principle of defocused blurred images, constructs degenerated blur model disc functions with different radii, decomposes the blurred image into multiple sub-images, and calculates each sub-image The image is respectively searched for the best blur radius through an iterative method, and the frequency domain inverse filtering method is used to inverse filter the defocused blurred sub-image, so as to achieve the purpose of recovering a clear image.

The clearing processing method of the defocused blurred image of the present invention is implemented according to the following steps:

Step 1: Establish a mathematical model based on the degradation principle of defocused blurred images

Figure 1a is a schematic diagram of the relative positions of the digital imaging equipment and the shooting target, which is an ideal shooting state. As shown in Figure 1b, defocus blur occurs when the image point is not projected onto the imaging plate (CCD plane) inside the camera. Two of the four dotted lines in Figure 1b represent the path of the light cone emitted from different positions of the target. The image point, that is, the apex of the light cone does not fall on the imaging plate of the camera, so what is received on the imaging plate will be the horizontal direction of the light cone. A section is a piece of light spots, and the image is formed by superimposing these light spots, so it forms a blur effect. The shape and radius of the approximately circular spot received by the imaging plate of the camera will change due to the relative position to the center of the lens (that is, the center position of the image). The change rule is that the closer the spot is to the center of the image, the closer the spot is to a circle shape, the smaller the radius of the spot; the farther away from the center of the image, the increasing the radius of the spot.

Therefore, defocus can be approximated as a uniformly distributed circular spot expanded from a point, and the radius increases as it moves away from the center of the image, then it can be simplified as a disc function to model the blurred image, namely :

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}& {\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ></span>{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, R _b is the blur radius, π is the circumference ratio, and (x, y) is a certain pixel point on the image.

Step 2: Selection of initial blur radius

From the mathematical model of defocus blur obtained in step 1, it can be seen that the blur radius R _b is a parameter to determine the degree of blur. Therefore, according to the following method, the blur radius is first searched for the entire image, and the specific steps for obtaining it are as follows:

2.1. Image gradient information extraction

The captured defocused image is sharpened to generate the gradient map E _s and the gradient direction map E _o , the sharpening uses the Sobel operator, and the calculation equation of the gradient is:

$\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

g表示散焦图像。in,

g represents a defocused image.

Then the gradient map E _s is E _s =[S(i, j)].

Gradient direction angle, calculated according to the following formula:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; tg</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

The obtained θ _M is divided into 90° according to five ranges of 90°～67.5°, 67.5°～22.5°, 22.5°～-22.5°, -22.5°～-67.5°, -67.5°～-90°, 45°, 0°, -45°, -90° five directions to form the gradient pattern E _o .

2.2. Use the non-maximum suppression technique to obtain the local gradient magnitude maximum point set E _n

For the gradient map E _s obtained in step 2.1, and the gradient direction map E _o , for each pixel g(x, y), according to the direction d _k indicated in the gradient direction map E _o , check the adjacent two pixels. If E _s (x, y) is greater than the gradient strength of two adjacent pixels, then set _En (x, y)=E _s (x, y), otherwise set _En (x, y)=0. The finally obtained matrix E _n (x, y) is the local gradient magnitude maximum point set.

2.3 Calculation of edge width

For the local gradient magnitude maximum point set E _n , perform binarization under a given threshold to obtain the contour map E _e . Afterwards, for any point P in E _n , according to the direction indicated by the gradient pattern E _o , search for the point in E _e along the positive and negative directions of the point. Assume that the first points in E _e searched along the positive and negative directions are P ₁ and P ₂ respectively, if both P ₁ and P ₂ satisfy: ‖PP ₁ ‖≤d and ‖PP ₂ ‖≤d (where d is given A given threshold, that is, the longest distance to search), then take the distance between _P1 and _P2 as the corresponding edge width, otherwise skip this point. Calculate the obtained width value to obtain the mean value M and the variance D. Select M/2 as the initial blur radius R _b of the whole image.

Step 3: Division of sub-images

Considering that during imaging, the degree of blurring of defocus is different in the whole image, so the present invention decomposes the original image into multiple sub-images.

The decomposition method is as follows: as shown in Figure 2a, draw k concentric circles with the center of the image as the dot, and the radius is R _k =R ₁ +(k-1)·ΔR. Where R ₁ is the radius of the innermost circle, and ΔR is the increment. Then the image can be decomposed into a circular area, k-1 circular areas, and k+1 sub-images in the remaining image area, denoted as g _s1 , g _s2 ... g _s(k+1) , the kth The range of the sub-map is shown in the shaded part in Fig. 2b.

Step 4: Sharpening of sub-images

From the variance obtained in step 2, the step size of the disk radius can be obtained as D/k, then the initial blur radius under the i-th sub-image can be defined as:

R _bi (0)=R _b +(i-1)·D/k (i=1, 2, 3 . . . , k+1).

4.1. According to the blur radius, the disk function h _i (x, y) of the sub-image can be obtained according to equation (1)

4.2. Use the discrete two-dimensional Fourier transform (DFT) to complete the frequency domain conversion of the blurred image sub-image g _si (x, y), namely:

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; the\; si</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;j</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ux</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; vy</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Wherein, G _i (u, v), i=1, 2, 3...k+1 is the frequency domain transformation of the sub-image.

4.3. Perform frequency domain transformation on the corresponding disc function under each sub-image. Right now:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;j</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ux</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; vy</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Wherein, h _i (u, v) is the disc function corresponding to the sub-image, and H _i (u, v) is the system function after frequency domain transformation.

4.4. Calculate noise and power spectrum S _nn (u, v) and S _ff (u, v) of the original image

The local variance of the pixel set near each pixel is directly calculated from the blurred image, and the maximum value of the local variance is selected as the variance of the image. At the same time, a flat area is found on the image, and its local variance is used as the noise variance. However, it is often difficult to find a flat area manually, so the local variance of the image can be calculated using the following formula, and the variance of the image boundary is not taken into account. The ratio of the maximum value and the minimum value of the local variance is used as an estimate of the image signal-to-noise ratio, namely:

${{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; yL</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; P</span>}}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Q</span>}}{\overset{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Among them, μ _y is the local mean, calculated as follows:

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; P</span>}}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Q</span>}}{\overset{\mathrm{<span\; class="notranslate">\; Q</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

The size of the window used for variance calculation is P=Q=2 (ie 5×5 window).

4.5. Image clarity restoration based on inverse filtering

Calculate each complex conjugate function according to the sub-image function H _i (u, v) in the previous step The present invention selects the Wiener filter for inverse filtering processing, thereby realizing clearing, and the frequency domain expression of each sub-image clearing image is recorded as F _i (u, v), namely:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; *</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>}{{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; nn</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; ff</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

The two-dimensional discrete Fourier inverse transform is performed on each sub-image F _i (u, v) in the frequency domain to restore the original image f _i (x, y) of each sub-image.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; N</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;j</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ux</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; vy</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

4.6. Change the blur radius, that is, calculate R _bi (0) and R _bi (0)±ΔR _i (ΔR _i is recommended to be 1 pixel), and obtain respective restored sub-images according to steps 4.1 to 4.5.

4.7. Calculate the Sobel sharpened detail energy maps of the three recovered images obtained in step 4.6. The energy map acquisition method adopts equation (2).

4.8. Calculate the difference in the variance of the three restored images obtained in step 4.6, and then iterate in the direction of the small difference until the timing with the smallest variance difference is found, stop the iteration, and select the maximum energy mean value in the two energy graphs when the iteration stops The image of is the final result, set f _i *(x, y). So far, the sharpening restoration processing of all sub-images is completed.

Step 5: Obtain the whole sharpened image

Add f _i *(x, y),

$f(x,\mathrm{the\; y})=\underset{i=1}{\overset{k+1}{\mathrm{\&Sigma;}}}{f}_i*(x,\mathrm{the\; y}),$ That is, a clear image is obtained.

Claims (4)

1. A method for sharpening a defocused blurred image, which is implemented according to the following steps,

step 1: establishing mathematical model for defocusing blurred image to be processed

Modeling of blurred images using a disk function, namely:

<math> <mrow> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mfenced open='{' close='' separators=','> <mtable> <mtr> <mtd> <mfrac> <mn>1</mn> <mrow> <mi>&pi;</mi> <msup> <msub> <mi>R</mi> <mi>b</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> </mtd> <mtd> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>&le;</mo> <msup> <msub> <mi>R</mi> <mi>b</mi> </msub> <mn>2</mn> </msup> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>></mo> <msup> <msub> <mi>R</mi> <mi>b</mi> </msub> <mn>2</mn> </msup> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow></math>

wherein R is_bThe fuzzy radius is adopted, pi is the circumference ratio, and (x, y) is a certain pixel point on the image;

step 2; selecting an initial blur radius

The method comprises the steps of searching a blur radius of a defocus blur integral image to be processed, firstly sharpening the shot defocus image to generate a gradient image E_sSum pattern E_o(ii) a For the obtained gradient map E_sAnd gradient directional diagram E_oObtaining local gradient amplitude maximum value point set E by using non-maximum value inhibition technology_n(ii) a To E_nCarrying out binarization under a given threshold value to obtain a contour map E_eThen, the edge width is obtained, the obtained width value is calculated to obtain a mean value M and a variance D, and M/2 is selected as the initial fuzzy radius R of the whole graph_b；

And step 3: division of sub-images

Substituting the variance D obtained in step 2 into the equation k ═ int [ D-1-]Obtaining a parameter k of the sub-graph division number, drawing k concentric circles with the center of the image as a circular point and the radius of the concentric circles as R_k＝R₁+ (k-1). DELTA.R, wherein R₁Dividing the image into k +1 sub-images of a circular region, k-1 circular ring regions and the rest image region, and recording as g_s1、g_s2...g_s(k+1)；

And 4, step 4: sharpening processing of sub-images

Obtaining the step length of the disc radius as D/k by using the variance obtained in the step 2 and the k obtained in the step 3, obtaining the initial fuzzy radius under the ith sub-image, and obtaining the disc function h of the sub-image according to the fuzzy radius and the equation (1)_i(x, y), sub-image g_si(x, y) performing frequency domain conversion, performing frequency domain conversion on the corresponding disc function under each sub-image, and calculating the power spectrum S of the noise and the original image_nn(u, v) and S_ff(u, v); then, based on inverse filtering, the image sharpness is restored, the fuzzy radius is changed, namely R is calculated_i(0) And R_i(0)±ΔR_iObtaining three recovery sub-images, calculating Sobel sharpening energy-saving graphs of the three recovery images, calculating the variance difference of the three recovery images, then iterating according to the direction with small variance until the time with the minimum variance difference is found, stopping iterating, selecting the image with the maximum energy mean value in the two energy graphs when iterating is stopped as a final result, and setting the final result as f_i ^*(x，y)；

Step 5, obtaining the whole clear image

Will f is_i ^*(x, y) are added to each other,

the clear image is obtained <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>*</mo> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow></math>

2. A sharpening process according to claim 1, wherein said selecting an initial blur radius takes the following specific steps:

2.1 image gradient information extraction

Sharpening the shot defocused image to generate a gradient image E_sAnd gradient pattern E_oThe Sobel operator is adopted for sharpening, and the gradient calculation equation is as follows:

$S(i,j)=\sqrt{d_x^2+d_y^2}---\left(2\right)$

wherein,

，

g denotes defocused image, gradient map E_sIs E_s＝[S(i，j)]，

The gradient direction angle is calculated according to the following formula:

<math> <mrow> <msub> <mi>&theta;</mi> <mi>M</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>tg</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>d</mi> <mi>y</mi> </msub> <msub> <mi>d</mi> <mi>x</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow></math>

to obtain theta_MThe gradient directional diagram E is formed according to five directions of 90 degrees to 67.5 degrees, 67.5 degrees to 22.5 degrees, 22.5 degrees to-67.5 degrees, 67.5 degrees to-90 degrees, divided into 90 degrees, 45 degrees, 0 degrees, 45 degrees and-90 degrees₀；

2.2, obtaining a local gradient amplitude maximum value point set En by using a non-maximum value inhibition technology

For the gradient map E obtained in step 2.1_sAnd gradient pattern E_oFor each pixel g (x, y), according to the gradient direction diagram E_oDirection d indicated in_kChecking two adjacent pixels in both forward and reverse directions, if E_s(x, y) is greater than the gradient strength of two adjacent pixels, let E_n(x，y)＝E_s(x, y), otherwise let E_n(x, y) is 0, resulting in matrix E_n(x, y) is the local gradient amplitude maximum point set;

2.3 determination of edge width

For local gradient amplitude maximum value point set E_nBinary at a given thresholdTransforming to obtain a contour map E_eThen to E_nAccording to a gradient pattern E_oThe indicated direction, search E in the positive and negative directions of the point_eA point in (E) is searched in the positive and negative directions_eRespectively, is P₁、P₂If P is₁And P₂All satisfy: P-P | |₁D and P-P are less than or equal to | |₂If | is ≦ d, where d is the given threshold, i.e., the longest distance searched, then P is added₁And P₂The distance between them, otherwise skipping this point,

calculating the obtained width value to obtain a mean value M and a variance D, and selecting an initial fuzzy radius R with M/2 as the whole image_b。

3. The processing method according to claim 1, characterized in that the sharpening of the sub-image in step 4 is carried out according to the following specific steps,

obtaining the step size of the disc radius as D/k from the variance obtained in step 2 of claim 1 and k obtained in step 3, and obtaining the initial blur radius under the ith sub-image as:

R_bi(0)＝R_b+(i-1)·D/k (i＝1，2，3...，k+1)

4.1 obtaining the disk function h of the subimage according to the equation (1) based on the blur radius_i(x，y)；

4.2 sub-image g of the image to be blurred_si(x, y) performing frequency domain conversion by using discrete two-dimensional Fourier transform respectively, namely:

<math> <mrow> <msub> <mi>G</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>g</mi> <mi>si</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>[</mo> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>&pi;j</mi> </mrow> <mi>N</mi> </mfrac> <mrow> <mo>(</mo> <mi>ux</mi> <mo>+</mo> <mi>vy</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow></math>

wherein G is_i(u, v), i ═ 1, 2, 3.. k +1 is the frequency domain transform of the sub-images;

4.3, carrying out frequency domain transformation on the corresponding disc function under each sub-image, namely:

<math> <mrow> <msub> <mi>H</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>h</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>[</mo> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>&pi;j</mi> </mrow> <mi>N</mi> </mfrac> <mrow> <mo>(</mo> <mi>ux</mi> <mo>+</mo> <mi>vy</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow></math>

wherein h is_i(u, v) is the corresponding disk function for the subimage, H_i(u, v) a system function after frequency domain transformation;

4.4 calculating the Power Spectrum S of the noise and the original image_nn(u, v) and S_ff(u，v)；

Calculating the local variance of a pixel set near each pixel directly from a blurred image, selecting the maximum value in the local variances as the variance of the image, simultaneously finding a flat area on the image, using the local variance as the noise variance, calculating the local variance of the image by using an equation (6), and using the ratio of the maximum value and the minimum value of the local variance as the estimation of the signal-to-noise ratio of the image, namely:

<math> <mrow> <msub> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mi>yL</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mrow> <mo>(</mo> <mn>2</mn> <mi>P</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mi>Q</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mo>-</mo> <mi>P</mi> </mrow> <mi>P</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mo>-</mo> <mi>Q</mi> </mrow> <mi>Q</mi> </munderover> <msup> <mrow> <mo>[</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mi>k</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&mu;</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow></math>

μ in equation (6)_yIs the local mean, calculated as:

<math> <mrow> <msub> <mi>&mu;</mi> <mi>y</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mrow> <mo>(</mo> <mn>2</mn> <mi>P</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mi>Q</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mo>-</mo> <mi>P</mi> </mrow> <mi>P</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mo>-</mo> <mi>Q</mi> </mrow> <mi>Q</mi> </munderover> <mi>y</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mi>k</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mi>l</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow></math>

the size of the window used for variance calculation is P ═ Q ═ 2;

4.5 inverse filter based image sharpness restoration

Subimage function H according to step 4.3_i(u, v) calculating respective complex conjugate functionsPerforming inverse filtering with a filter to realize sharpening, wherein the frequency domain expression of each sub-image sharpened image is recorded as F_i(u, v), namely:

$F_i(u,v)=\frac{{H^{*}}_i(u,v)G_i(u,v)}{{\left|H_i(u,v)\right|}^2+S_{\mathrm{nn}}(u,v)/S_{\mathrm{ff}}(u,v)}---\left(8\right)$

for each sub-image F in the frequency domain_i(u, v) performing inverse discrete Fourier transform to recover the original image f of each sub-image_i(x，y)，

<math> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mi>N</mi> <mn>2</mn> </msup> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>F</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>[</mo> <mfrac> <mrow> <mn>2</mn> <mi>&pi;j</mi> </mrow> <mi>N</mi> </mfrac> <mrow> <mo>(</mo> <mi>ux</mi> <mo>+</mo> <mi>vy</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow></math>

4.6 changing the blur radius, i.e. calculating R_i(0) And R_i(0)±ΔR_iObtaining three recovery sub-images according to the steps 4.1 to 4.5;

4.7, calculating a Sobel sharpened detailed energy-saving map of the three recovered images obtained in the step 4.6, wherein the energy map acquisition method adopts an equation (2);

4.8, calculating the variance difference of the three recovery images obtained in the step 4.6, then iterating according to the direction with small variance until the time with the minimum variance difference is found, stopping iterating, selecting the image with the maximum energy mean value in the two energy graphs when iterating is stopped as a final result, and setting the final result as f_i ^*(x，y)。

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