CN113610717A - Method for enhancing ultraviolet fluorescence image of skin disease - Google Patents

Method for enhancing ultraviolet fluorescence image of skin disease Download PDF

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CN113610717A
CN113610717A CN202110806197.8A CN202110806197A CN113610717A CN 113610717 A CN113610717 A CN 113610717A CN 202110806197 A CN202110806197 A CN 202110806197A CN 113610717 A CN113610717 A CN 113610717A
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CN113610717B (en
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魏明生
庄飞飞
张正军
孙红
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Jiangsu Normal University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20048—Transform domain processing
    • G06T2207/20064—Wavelet transform [DWT]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
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    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing
    • G06T2207/30088—Skin; Dermal

Abstract

A method for enhancement of ultraviolet fluorescence images of skin conditions, comprising: dividing an original fluorescence image into a low-frequency image and a high-frequency image by utilizing wavelet decomposition; processing the low-frequency image by adopting a pixel pair gray scale stretching algorithm, wherein the number of pixel pairs needing to be counted is greatly reduced; processing the high-frequency image by using a denoising method based on weighted TV regularization; and reconstructing the low-frequency enhanced signal and the high-frequency de-noised signal through wavelet inverse transformation. The algorithm of the invention combines the advantages of the enhancement algorithm and the denoising algorithm to the maximum extent, not only retains the singularity of the fluorescence image, improves the definition and the contrast of the fluorescence image, but also obviously weakens the noise, displays the detail information of the fluorescence image, has no over-enhancement phenomenon and has good visual effect.

Description

Method for enhancing ultraviolet fluorescence image of skin disease
Technical Field
The invention relates to the technical field of fluorescence image processing, in particular to a dermatosis ultraviolet fluorescence image enhancement algorithm based on pixel pair gray scale stretching and weighted TV regularization.
Background
After the skin is irradiated by ultraviolet light with specific wavelength, melanin and dermal collagen in the skin can absorb the ultraviolet light; then, blue light is emitted as fluorescence of the main color, and different skin lesions can generate fluorescence of different degrees and colors, thereby reflecting different degrees and kinds of skin diseases. The principle can be used for assisting doctors to accurately diagnose skin diseases such as pigment abnormality diseases, skin infection and the like.
The fluorescence radiated by the skin can be imaged under the irradiation of ultraviolet light through an ultraviolet fluorescence imaging technology, however, because the fluorescence signal belongs to a weak signal, the fluorescence image of the dermatosis obtained by the system has darker brightness and lower contrast, so that the details of the fluorescence image in a plurality of dark areas cannot be distinguished, and the misdiagnosis of a dermatologist is caused. Because the high-quality and high-precision fluorescent image is an important basis for doctors to diagnose the skin diseases, and meanwhile, along with the development of artificial intelligence and machine learning, the improvement of the imaging precision is beneficial to further intelligent analysis, and lays a foundation for the automatic identification of the skin diseases in the future. Therefore, it is necessary to perform enhancement of the fluorescence image.
Disclosure of Invention
The invention aims to provide a fluorescence image enhancement algorithm based on pixel pair gray scale stretching and weighting TV regularization, so as to effectively solve the problems of dark fluorescence image brightness, low contrast, detail loss and the like in the background technology, improve the diagnosis accuracy and efficiency of skin diseases, and realize early discovery and early treatment of pigment and infectious skin diseases.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a fluorescence image enhancement algorithm based on pixel-to-gray stretching and weighted TV regularization, comprising:
firstly, dividing an original fluorescence image into a low-frequency image and a high-frequency image by utilizing wavelet decomposition; secondly, processing the low-frequency image by using a pixel pair gray scale stretching algorithm, wherein the number of pixel pairs needing to be counted is greatly reduced; processing the high-frequency image by using a denoising method based on weighted TV regularization; and finally, reconstructing the low-frequency enhanced signal and the high-frequency de-noising signal through wavelet inverse transformation to obtain a processed fluorescent image with high definition and contrast.
The method comprises the following concrete implementation steps:
step 1: the low frequency sub-band and the high frequency sub-band of the original image are separated by wavelet transform. For an M × N two-dimensional image f (x, y), its two-dimensional Discrete Wavelet Transform (DWT) is defined as:
Figure BDA0003166465740000021
in the formula 1, j0As an initial scale parameter, the value of,
Figure BDA0003166465740000022
is a coefficient of the approximation that is,
Figure BDA0003166465740000023
represented by f (x, y) at j0An approximation of (d);
Figure BDA0003166465740000024
for detail coefficient, when j is more than or equal to j0When the temperature of the water is higher than the set temperature,
Figure BDA0003166465740000025
with three-directional details attached, H represents the horizontal direction, V represents the vertical direction, and D represents the diagonal direction.
Figure BDA0003166465740000026
And
Figure BDA0003166465740000027
respectively, a scale function and a wavelet function, wherein the two functions can be divided in two dimensions;
step 2: after the low-frequency component and the high-frequency component of the image are separated by utilizing wavelet transformation, the main body energy of the image is in the low-frequency component, and the low-frequency component is enhanced by using a pixel pair gray scale stretching algorithm, so that the aim of enhancing the local contrast of the image is fulfilled, and the main body display effect of the image can be effectively improved;
first, defining the non-weight gray scale stretch coefficient g between pixel elements p and qpq：
Figure BDA0003166465740000028
In the formula 2, IPIs the gray value of the picture element p, IqIs the gray value of the picture element q, deltagHas a value of
Figure BDA0003166465740000029
ImaxIs the maximum value, δ, of the grey values in the original imageg-Is 1, deltadThe value of (2). d (p, q) is the Euclidean distance between the pixel p and the pixel q.
Second, the sharpness weight θ is introducedpWith the aim of reducing image noise interference, thetapThe formula of (1) is:
Figure BDA00031664657400000210
in equation 3, the gray value of the pixel r is the same as the gray value of the pixel p, d (p, r) is the Euclidean distance between the two pixels, δθIs equal to 1. ThetapRepresenting the probability that the picture element p is a non-noise point.
Then, theta is adjustedpAnd thetaqMultiply and square again, then sum with gpqMultiplying to obtain the gray scale stretch coefficient c with definition weightpq：
Figure BDA00031664657400000211
Finally, setting the gray scale transformation function as T, wherein T is a global transformation function, and converting the gray scale value I of the collected imagepIs mapped into
Figure BDA00031664657400000212
In order for T to enhance the local contrast of the fluorescence image, T needs to have the following features: i T (I)p)-T(Iq) I and cpqAnd (4) in proportion. But in the fluorescent imageThe number of pixel pairs is too large, the equation set of T is an overdetermined equation set, and an approximate solution needs to be searched.
Defining a picture element P and a set of picture elements { q | I | having a grey difference x from itq＝Ip+ x cumulative gray scale stretch coefficient Cp(x) Comprises the following steps:
Figure BDA0003166465740000031
let x >0, in order to guarantee monotonicity of T, make it satisfy:
Figure BDA0003166465740000032
in equation 6, α is a normalized constant. H (I)p) Is as follows, it represents the first order difference of the transformation function T.
H(Ip)＝T(Ip)-T(Ip-1) (7)
Combining equations 5 and 6, we derive:
H(Ip+x)＝α×Cp(x) (8)
the above equation shows that for each pixel p in the input image, a system of linear equations can be obtained:
H＝αCp (9)
in formula 9
H＝[H(1),H(2),...,H(255)]T (10)
Cp＝[Cp(-Ip),...,Cp(-1),Cp(1),...,Cp(255-Ip)]T (11)
Defining a weighted cost function J (H) as:
Figure BDA0003166465740000033
w in formula 12pIs a diagonal matrix, the value of the ith diagonal element is 2/(1+ exp (| I-I)p|)). The matrix H is subjected to polarization calculation by J (H) and polarization is takenThe value point can obtain the optimal solution H*The method comprises the following steps:
Figure BDA0003166465740000034
alpha to H*The sum of all elements of (a) is 255. Then, in combination with equation 7, the equation for T can be derived as:
Figure BDA0003166465740000041
t (0) in the above formula is 0. Although T is a global transformation function, T can be derived from the gray scale stretch coefficient, so that it is locally adaptive.
And step 3: designing a denoising optimization framework consisting of data fidelity and weighted TV regularization, wherein the framework is based on two weights: the intensity mean to variance ratio and the directionality of the edges, and then the framework is optimized using the Douglas-Rachford segmentation method.
The high-frequency image contains detail information such as edges of the image and noise, and the characteristics of the fluorescence image in which the noise level is closely related to the average intensity are considered. The ratio of the intensity mean and variance is to control the degree of smoothing, and the directionality of the edges is to preserve the details of the image.
First, from a noise-contaminated high-frequency image R, taking into account the Poisson distribution of low-light noisePIn-process recovery of the original image SP. Thus, each MPThe discrete poisson probability of (a) is as follows:
Figure BDA0003166465740000042
the estimated image S should be most similar to the input image M. Thus, Bayesian law is used here as follows:
Figure BDA0003166465740000043
maximize P (M | S) P (S). In general, the data fidelity term is derived by maximizing the posterior probability density P (M | S). Then, the following results were obtained:
Figure BDA0003166465740000044
TV regularization was chosen as a prior distribution as follows:
Figure BDA0003166465740000045
where λ is the regularization parameter.
To improve computational efficiency, minimize-log (P (R | S) P (S)) is used instead of maximize P (R | S) P (S)
The following function is then minimized:
Figure BDA0003166465740000046
second, it is assumed that the noise is signal independent and has the same variance throughout the image. While in low light conditions the photon counting process is a major source of sensor noise corrupting the image. In this case, the statistics of the noise image are described by a multivalued poisson process, the amount of noise is controlled by the total number of photons: the higher the number of photons, the lower the noise will corrupt the image. Thus, the variation of noise is different in the bright and dark areas. To solve this problem, the degree of smoothing is controlled using the ratio of the intensity variance to the mean in the region as a weight. By deviation of the pixel intensities, a simple measure B can be obtainedpFor estimating the scale within the region, as follows:
Figure BDA0003166465740000051
in the formula, σpIs the mean absolute deviation, xpIs the average pixel intensity. Using the statistical data to obtainThe variance-mean weighting graph is as follows:
Vp＝Bp×xp (21)
in addition, edge directivity is used as another weight LpTo distinguish noise and edge details, as follows:
Figure BDA0003166465740000052
Figure BDA0003166465740000053
Figure BDA0003166465740000054
wherein g isp,qIs a weight function, and is obtained by:
Figure BDA0003166465740000055
Figure BDA0003166465740000056
depending on whether the gradients in W are uniform or not. L is generally smaller than it, even on edges, if it contains only noise. For complex patterns, noise-edge mapping is used to control the degree of smoothing of noise and edges, since the edges of local windows have a greater effect on the gradient direction than noise. In weighted TV optimization, V is usedPAnd LPA more efficient regularized denoising is formed. The objective function is expressed as:
Figure BDA0003166465740000057
the Alternating Direction Multiplier Method (ADMM) cannot be used to solve the minimum problem because it does not use quadratic data fidelity terms. Thus, the Douglas-Rachford fragmentation method was used to minimize (25) as follows:
Figure BDA0003166465740000061
ψ(S)＝S-IlogS，
Figure BDA0003166465740000062
and updating S and d for denoising the fluorescence image.
And 4, step 4: f (x, y) can be reconstructed using inverse wavelet transform to obtain the final enhancement result. The following formula:
Figure BDA0003166465740000063
compared with the prior art, the invention has the beneficial effects that:
the fluorescence image enhancement algorithm not only keeps the singularity of the fluorescence image, improves the definition and contrast of the fluorescence image, but also obviously weakens the noise. The detailed information of the fluorescence image is displayed, the phenomenon of over enhancement is not generated, and the visual effect is good. The method has relatively balanced enhancement effect on the fluorescence image.
Drawings
FIG. 1 is a general block diagram of an image enhancement algorithm
FIG. 2(a) is an original image of a leucoderma fluorescence image;
FIG. 2(b) is the effect of histogram equalization on the leucoderma fluorescence image;
FIG. 2(c) shows the effect of the present invention on the treatment of fluorescence images of vitiligo;
FIG. 3(a) is an original drawing of a hypopigmentation fluorescence image;
FIG. 3(b) is a graph illustrating the effect of histogram equalization on hypopigmented fluorescence images;
FIG. 3(c) is a graph showing the effect of the method of the present invention on the processing of hypopigmented fluorescence images;
FIG. 4(a) is an original drawing of a chloasma fluorescence image;
FIG. 4(b) is the effect of histogram equalization on the treatment of chloasma fluorescence image;
FIG. 4(c) shows the effect of the present invention on the treatment of chloasma fluorescence image.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings and the embodiments, and the described embodiments are only illustrative of the present invention and are not intended to limit the present invention.
The invention provides a fluorescent image enhancement algorithm based on pixel pair gray scale stretching and weighted TV regularization, the overall block diagram of the algorithm is shown in figure 1, firstly, an original fluorescent image is divided into a low-frequency image and a high-frequency image by utilizing wavelet decomposition; secondly, processing the low-frequency image by using a pixel pair gray scale stretching algorithm, wherein the number of pixel pairs needing to be counted is greatly reduced; processing the high-frequency image by using a denoising method based on weighted TV regularization; and finally, reconstructing the low-frequency enhanced signal and the high-frequency de-noising signal through wavelet inverse transformation to obtain a processed fluorescent image with high definition and contrast. The original (low-light) fluorescence image is enhanced by using fig. 2(a), fig. 3(a) and fig. 4(a), and the specific implementation steps are as follows:
step 1: the low frequency sub-band and the high frequency sub-band of the original image are separated by wavelet transform. For an M × N two-dimensional image f (x, y), its two-dimensional Discrete Wavelet Transform (DWT) is defined as:
Figure BDA0003166465740000071
in the formula 1, j0As an initial scale parameter, the value of,
Figure BDA0003166465740000072
is a coefficient of the approximation that is,
Figure BDA0003166465740000073
represented by f (x, y) at j0An approximation of (d);
Figure BDA0003166465740000074
for detail coefficient, when j is more than or equal to j0When the temperature of the water is higher than the set temperature,
Figure BDA0003166465740000075
with three-directional details attached, H represents the horizontal direction, V represents the vertical direction, and D represents the diagonal direction.
Figure BDA0003166465740000076
And
Figure BDA0003166465740000077
respectively, a scale function and a wavelet function, both of which are two-dimensionally separable.
Step 2: after the low-frequency component and the high-frequency component of the image are separated by utilizing wavelet transformation, the main body energy of the image is in the low-frequency component, and the low-frequency component is enhanced by using a pixel pair gray scale stretching algorithm, so that the aim of enhancing the local contrast of the image is fulfilled, and the main body display effect of the image can be effectively improved.
First, defining the non-weight gray scale stretch coefficient g between pixel elements p and qpq：
Figure BDA0003166465740000078
In the formula 2, IPIs the gray value of the picture element p, IqIs the gray value of the picture element q, deltagHas a value of
Figure BDA0003166465740000079
ImaxIs the maximum value, δ, of the grey values in the original imageg-Is 1, deltadThe value of (2). d (p, q) is the Euclidean distance between the pixel p and the pixel q.
Second, the sharpness weight θ is introducedpWith the aim of reducing image noise interference, thetapThe formula of (1) is:
Figure BDA00031664657400000710
in equation 3, the gray value of the pixel r is the same as the gray value of the pixel p, d (p, r) is the Euclidean distance between the two pixels, δθIs equal to 1. ThetapRepresenting the probability that the picture element p is a non-noise point.
Then, theta is adjustedpAnd thetaqMultiply and square again, then sum with gpqMultiplying to obtain the gray scale stretch coefficient c with definition weightpq：
Figure BDA0003166465740000081
Finally, setting the gray scale transformation function as T, wherein T is a global transformation function, and converting the gray scale value I of the collected imagepIs mapped into
Figure BDA0003166465740000082
In order for T to enhance the local contrast of the fluorescence image, T needs to have the following features: i T (I)p)-T(Iq) I and cpqAnd (4) in proportion. However, the number of pixel pairs in the fluorescence image is too large, the equation set of T is an overdetermined equation set, and an approximate solution needs to be searched.
Defining a picture element P and a set of picture elements { q | I | having a grey difference x from itq＝Ip+ x cumulative gray scale stretch coefficient Cp(x) Comprises the following steps:
Figure BDA0003166465740000083
let x >0, in order to guarantee monotonicity of T, make it satisfy:
Figure BDA0003166465740000084
in equation 6, α is a normalized constant. H (I)p) Is as follows, it represents the first order difference of the transformation function T.
H(Ip)＝T(Ip)-T(Ip-1) (7)
Combining equations 5 and 6, we derive:
H(Ip+x)＝α×Cp(x) (8)
the above equation shows that for each pixel p in the input image, a system of linear equations can be obtained:
H＝αCp (9)
in formula 9
H＝[H(1),H(2),...,H(255)]T (10)
Cp＝[Cp(-Ip),...,Cp(-1),Cp(1),...,Cp(255-Ip)]T (11)
Defining a weighted cost function J (H) as:
Figure BDA0003166465740000085
w in formula 12pIs a diagonal matrix, the value of the ith diagonal element is 2/(1+ exp (| I-I)p|)). The optimal solution H can be obtained by calculating the deviation of the matrix H according to J (H) and taking the extreme point*The method comprises the following steps:
Figure BDA0003166465740000091
alpha to H*The sum of all elements of (a) is 255. Then, in combination with equation 7, the equation for T can be derived as:
Figure BDA0003166465740000092
t (0) in the above formula is 0. Although T is a global transformation function, T can be derived from the gray scale stretch coefficient, so that it is locally adaptive.
And step 3: the high-frequency image contains detail information such as edges of the image and noise, and the characteristics of the fluorescence image in which the noise level is closely related to the average intensity are considered. Therefore, a de-noising optimization framework consisting of data fidelity and weighted TV regularization is designed. This framework is based on two weights: the ratio of the intensity mean to the variance and the directionality of the edges. The ratio of the intensity mean and variance is to control the degree of smoothing, and the directionality of the edges is to preserve the details of the image. The framework was then optimized using the Douglas-Rachford segmentation method.
First, considering the poisson distribution of weak light noise, it is desirable to derive a noise-contaminated high-frequency image RPIn-process recovery of the original image SP. Thus, each MPThe discrete poisson probability of (a) is as follows:
Figure BDA0003166465740000093
the estimated image S should be most similar to the input image M. Thus, Bayesian law is used here as follows:
Figure BDA0003166465740000094
maximize P (M | S) P (S). In general, the data fidelity term is derived by maximizing the posterior probability density P (M | S). Then, the following results were obtained:
Figure BDA0003166465740000095
TV regularization was chosen as a prior distribution as follows:
Figure BDA0003166465740000096
where λ is the regularization parameter.
To improve computational efficiency, minimize-log (P (R | S) P (S)) is used instead of maximize P (R | S) P (S)
The following function is then minimized:
Figure BDA0003166465740000101
second, it is assumed that the noise is signal independent and has the same variance throughout the image. While in low light conditions the photon counting process is a major source of sensor noise corrupting the image. In this case, the statistics of the noise image are described by a multivalued poisson process, the amount of noise is controlled by the total number of photons: the higher the number of photons, the lower the noise will corrupt the image. Thus, the variation of noise is different in the bright and dark areas. To solve this problem, the degree of smoothing is controlled using the ratio of the intensity variance to the mean in the region as a weight. By deviation of the pixel intensities, a simple measure B can be obtainedpFor estimating the scale within the region, as follows:
Figure BDA0003166465740000102
in the formula, σpIs the mean absolute deviation, xpIs the average pixel intensity. Using the above statistical data, a variance-mean weighted graph is obtained as follows:
Vp＝Bp×xp (21)
in addition, edge directivity is used as another weight LpTo distinguish noise and edge details, as follows:
Figure BDA0003166465740000103
Figure BDA0003166465740000104
Figure BDA0003166465740000105
wherein g isp,qIs a weight function, and is obtained by:
Figure BDA0003166465740000106
Figure BDA0003166465740000107
depending on whether the gradients in W are uniform or not. L is generally smaller than it, even on edges, if it contains only noise. For complex patterns, noise-edge mapping is used to control the degree of smoothing of noise and edges, since the edges of local windows have a greater effect on the gradient direction than noise. In weighted TV optimization, V is usedPAnd LPA more efficient regularized denoising is formed. The objective function is expressed as:
Figure BDA0003166465740000108
the Alternating Direction Multiplier Method (ADMM) cannot be used to solve the minimum problem because it does not use quadratic data fidelity terms. Thus, the Douglas-Rachford fragmentation method was used to minimize (25) as follows:
Figure BDA0003166465740000111
ψ(S)＝S-IlogS，
Figure BDA0003166465740000112
and updating S and d for denoising the fluorescence image.
And 4, step 4: f (x, y) can be reconstructed using inverse wavelet transform to obtain the final enhancement result.
The following formula:
Figure BDA0003166465740000113
in order to verify the effectiveness of the fluorescence image enhancement algorithm provided by the invention, enhancement experiments are carried out on the fluorescence images of the skin diseases, and the fluorescence images are compared with the traditional image enhancement algorithm. Fig. 2(a) is an original image of a vitiligo fluorescence image, fig. 2(b) is a processing effect of a histogram equalization method on the vitiligo fluorescence image, and fig. 2(c) is a processing effect of the method of the present invention on the vitiligo fluorescence image; FIG. 3(a) is an original drawing of a hypopigmented fluorescence image, FIG. 3(b) is a processing effect of a histogram equalization method on the hypopigmented fluorescence image, and FIG. 3(c) is a processing effect of the method of the present invention on the hypopigmented fluorescence image; fig. 4(a) is an original drawing of a chloasma fluorescence image, fig. 4(b) is a processing effect of the histogram equalization method on the chloasma fluorescence image, and fig. 4(c) is a processing effect of the method of the present invention on the chloasma fluorescence image. As can be seen from the figure, the original image is a weak fluorescence image, and the overall brightness of the fluorescence image is improved after histogram equalization, but excessive enhancement may occur. The fluorescence image enhancement algorithm not only improves the definition and the contrast of the fluorescence image, but also obviously weakens the noise and displays the detail information of the fluorescence image.
For objective evaluation of the method of the present invention, the mean gradient, entropy and standard deviation of the fluorescence image before and after enhancement were calculated as shown in tables 1-3.
TABLE 1 average gradient contrast of two algorithms enhancement results
Figure BDA0003166465740000114
TABLE 2 information entropy comparison of two algorithms enhancement results
Figure BDA0003166465740000115
TABLE 3 two algorithms enhance the standard deviation comparison of the results
Figure BDA0003166465740000121
The experimental result shows that the average gradient, the information entropy and the standard deviation can be improved by the traditional enhancement algorithm, but compared with the algorithm in the invention, the effect is not obvious enough. The enhancement algorithm provided by the invention increases the average gradient by nearly 2.29 times, so that the image is clearer, the standard deviation is increased by 0.43 time, and the contrast of the fluorescence image is obviously improved. The information entropy is improved by 0.1 time, and the details in the image can be displayed.
While the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are illustrative only and not restrictive, and various modifications which do not depart from the spirit of the present invention and which are intended to be covered by the claims of the present invention may be made by those skilled in the art.

Claims (6)

1. An enhancement method for ultraviolet fluorescence images of skin diseases, which is characterized by comprising the following steps:
s1: dividing an original fluorescence image into a low-frequency image and a high-frequency image by utilizing wavelet decomposition;
s2: processing the low-frequency image by using a pixel pair gray level stretching algorithm, and greatly reducing the number of pixel pairs needing to be counted; processing the high-frequency image by using a denoising method based on weighted TV regularization;
s3: reconstructing the low-frequency enhanced signal and the high-frequency de-noising signal through wavelet inverse transformation to obtain a processed fluorescent image with high definition and high contrast.
2. The method according to claim 1, wherein the step S1 includes:
for an M × N two-dimensional image f (x, y), its two-dimensional Discrete Wavelet Transform (DWT) is defined as:
Figure FDA0003166465730000011
in the formula 1, j0As an initial scale parameter, the value of,
Figure FDA0003166465730000012
is a coefficient of the approximation that is,
Figure FDA0003166465730000013
represented by f (x, y) at j0An approximation of (d);
Figure FDA0003166465730000014
for detail coefficient, when j is more than or equal to j0When the temperature of the water is higher than the set temperature,
Figure FDA0003166465730000015
with the details of three directions attached, H represents the horizontal direction, V represents the vertical direction, D represents the diagonal direction,
Figure FDA0003166465730000016
and
Figure FDA0003166465730000017
respectively, a scale function and a wavelet function, both of which are two-dimensionally separable.
3. The method according to claim 1, wherein the step S2 includes:
s21: after low-frequency components and high-frequency components of the image are separated by utilizing wavelet transformation, the main energy of the image is in the low-frequency components, and the low-frequency components are enhanced by using a pixel pair gray scale stretching algorithm;
s22: constructing a denoising optimization framework consisting of data fidelity and weighted TV regularization, wherein the framework is based on two weights: the intensity mean to variance ratio and the directionality of the edges, and then the framework is optimized using the Douglas-Rachford segmentation method.
4. The method according to claim 3, wherein the step S21 includes:
first, defining the non-weight gray scale stretch coefficient g between pixel elements p and qpq：
Figure FDA0003166465730000018
In the formula 2, IPIs the gray value of the picture element p, IqIs the gray value of the picture element q, deltagHas a value of
Figure FDA0003166465730000019
ImaxIs the maximum value, δ, of the grey values in the original imageg-Is 1, deltadThe value of (A) is 2; d (p, q) is the Euclidean distance between the pixel p and the pixel q;
second, the sharpness weight θ is introducedpReduction of image noise interference, thetapThe formula of (1) is:
Figure FDA0003166465730000021
in equation 3, the gray value of the pixel r is the same as the gray value of the pixel p, d (p, r) is the Euclidean distance between the two pixels, δθIs equal to 1; thetapRepresenting the probability of non-noise points of the pixel p;
then, theta is adjustedpAnd thetaqMultiply and square again, then sum with gpqMultiplying to obtain the gray scale stretch coefficient c with definition weightpq：
Figure FDA0003166465730000022
Finally, setting the gray scale transformation function as T, wherein T is a global transformation function, and converting the gray scale value I of the collected imagepMapping to T(Ip)；
Defining a picture element P and a set of picture elements { q | I | having a grey difference x from itq＝Ip+ x cumulative gray scale stretch coefficient Cp(x) Comprises the following steps:
Figure FDA0003166465730000023
let x >0, in order to guarantee monotonicity of T, make it satisfy:
Figure FDA0003166465730000024
in formula 6, α is a normalized constant; h (I)p) Is given below, which represents the first difference of the transformation function T;
H(Ip)＝T(Ip)-T(Ip-1) (7)
combining equations 5 and 6, we derive:
H(Ip+x)＝α×Cp(x) (8)
the above equation shows that for each pixel p in the input image, a system of linear equations can be obtained:
H＝αCp (9)
in formula 9
H＝[H(1),H(2),...,H(255)]T (10)
Cp＝[Cp(-Ip),...,Cp(-1),Cp(1),...,Cp(255-Ip)]T (11)
Defining a weighted cost function J (H) as:
Figure FDA0003166465730000031
w in formula 12pIs a diagonal matrix, the value of the ith diagonal element is 2/(1+ exp (| I-I)p|); the optimal solution H can be obtained by calculating the deviation of the matrix H according to J (H) and taking the extreme point*The method comprises the following steps:
Figure FDA0003166465730000032
alpha to H*The sum of all elements of (a) is 255; then, in combination with equation 7, the equation for T can be derived as:
Figure FDA0003166465730000033
wherein T (0) ═ 0.
5. The method according to claim 3, wherein the step S22 comprises:
first, from a noise-contaminated high-frequency image R, taking into account the Poisson distribution of low-light noisePIn-process recovery of the original image SP(ii) a Thus, each MPThe discrete poisson probability of (a) is as follows:
Figure FDA0003166465730000034
using bayes' law as follows:
Figure FDA0003166465730000035
maximizing P (M | S) P (S) yields:
Figure FDA0003166465730000036
TV regularization was chosen as a prior distribution as follows:
Figure FDA0003166465730000037
wherein λ is a regularization parameter;
using minimize-log (P (R | S) P (S)) instead of maximize P (R | S) P (S), then minimize the following function:
Figure FDA0003166465730000041
using the ratio of the intensity variance and the mean value in the region as a weight to control the smoothness degree; by deviation of the pixel intensity, a simple measure B is obtainedpFor estimating the scale within the region, as follows:
Figure FDA0003166465730000042
in the formula, σpIs the mean absolute deviation, xpIs the average pixel intensity; using the above statistical data, a variance-mean weighted graph is obtained as follows:
Vp＝Bp×xp (21)
in addition, edge directivity is used as another weight LpTo distinguish noise and edge details, as follows:
Figure FDA0003166465730000043
Figure FDA0003166465730000044
Figure FDA0003166465730000045
wherein g isp,qIs a weight function, and is obtained by:
Figure FDA0003166465730000046
using noise-edge mapping to control the degree of smoothing of noise and edges; in weighted TV optimization, V is usedPAnd LPForming more effective regularized denoising; the objective function is expressed as:
Figure FDA0003166465730000047
the Douglas-Rachford fragmentation method was used to minimize (25) as follows:
Figure FDA0003166465730000048
ψ(S)＝S-IlogS，
Figure FDA0003166465730000049
and updating S and d for denoising the fluorescence image.
6. The method according to claim 5, wherein the step S3 includes:
reconstructing f (x, y) using an inverse wavelet transform to obtain the final enhancement result, as follows:
Figure FDA0003166465730000051
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