CN112967202A - Denoising method for encrypted image with privacy protection by hyperbolic partial differential equation - Google Patents
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Abstract
The invention discloses a denoising method for an encrypted image with privacy protection by using hyperbolic partial differential equations, and relates to the technical field of image processing. The denoising method of the encrypted image with the privacy protection function comprises the following steps: step 1: inputting an original image sample to be processed; step 2: noise adding is carried out on the input original image sample to be processed, and a noise-containing image is obtained; step 3: establishing a denoising model according to the obtained noise-containing image, and judging the image characteristics; step 4: selecting a threshold, detecting the edge of the noise image, and calculating the gradient amplitude of the noise image; step 5: establishing a hyperbolic partial differential equation according to the background of the related problems and the data of image processing; step 6: and solving the partial differential equation to obtain a noise-removed image. According to the hyperbolic partial differential equation image denoising method, the hyperbolic partial differential equation and the algorithm thereof are combined to denoise the image, so that the denoising efficiency and precision of the image are effectively improved, the denoised image is encrypted, and privacy protection can be formed.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a denoising method of an encrypted image with a protection privacy by using a hyperbolic partial differential equation.
Background
Image denoising refers to a process of reducing noise in a digital image, and the digital image in reality is often influenced by noise interference of imaging equipment and external environment in the digitization and transmission processes and is called a noisy image or a noise image; noise is an important cause of image interference, and an image may have various noises in practical application, and these noises may be generated in transmission or quantization, etc., and can be divided into three forms according to the relation between noise and signal, wherein f (x, y) represents a given original image, g (x, y) represents an image signal, and n (x, y) represents noise;
the hyperbolic partial differential equation is an important partial differential equation for describing vibration or wave phenomenon, the solution of the hyperbolic partial differential equation can be decomposed into a form of multiplying vibration and vibration or multiplying an exponential function and an exponential function, the general energy is infinite, the hyperbolic partial differential equation is mainly used for describing vibration, wave phenomenon and corresponding motion process, a typical special example of the hyperbolic partial differential equation is a wave equation and a wave equation with n =1, the hyperbolic partial differential equation can be used for describing tiny transverse vibration of a string and is called a string vibration equation, and the most important property of the hyperbolic partial differential equation is the suitability of the Cauchy problem. Sometimes, people also use the equation as the basis for the definition of the hyperbolic equation, a characteristic polynomial of the hyperbolic equation can allow multiple real roots to appear, and whether the equation is hyperbolic or not is related to a low-order term of the equation;
the conventional image denoising method has the disadvantages of insufficient convenience in practical operation application, complex operation, low algorithm combination degree with a hyperbolic partial differential equation, influence on operation efficiency, insufficient privacy protection effect on images and certain limitation; therefore, a hyperbolic partial differential equation denoising method with privacy protection encryption image is provided.
Disclosure of Invention
The invention aims to provide a denoising method of an encrypted image with a protected privacy by a hyperbolic partial differential equation, so as to solve the problems in the background.
In order to solve the technical problems, the invention is realized by the following technical scheme:
the invention discloses a denoising method of a hyperbolical partial differential equation encrypted image with privacy protection, which comprises the following steps:
step 1: inputting an original image sample to be processed;
step 2: noise adding is carried out on the input original image sample to be processed, and a noise-containing image is obtained;
step 3: establishing a denoising model according to the obtained noise-containing image, and judging the image characteristics;
step 4: selecting a threshold, detecting the edge of the noise image, and calculating the gradient amplitude of the noise image;
step 5: establishing a hyperbolic partial differential equation according to the background of the related problems and the data of image processing;
step 6: solving the partial differential equation to obtain a de-noised image;
step 7: decomposing the coefficient of the image by using a hyperbolic partial differential equation algorithm again, establishing a verification model, and performing a numerical experiment;
step 8: according to the experimental simulation result, if the image verification is successful, entering Step9, and if the image verification is unsuccessful, entering Step4 again until the image verification is completed;
step 9: encrypting the image to form privacy protection;
step 10: and outputting the denoised image.
Preferably, the Step2 adds noise to the input original image sample to be processed, and performs gray scale conversion if necessary.
Preferably, the adding sources of the image noise in Step2 comprise image acquisition, image transmission and image compression, and the noise types of the image comprise salt-pepper noise and Gaussian noise.
Preferably, the noise component in Step2 includes additive noise, which is independent of the input image signal, such as channel noise and noise generated when the camera of the photoconductive camera tube scans the image, and the additive noise is typically gaussian noise; multiplicative noise, which is related to image signals, noise when flying spot scanners scan images, correlated noise in television images, and grain noise in film; quantization noise, which is irrelevant to the input image signal, is generated by reflecting quantization error in the quantization process to the receiving end.
Preferably, when Step4 detects the edges of the noise image and calculates the gradient amplitude of the noise image, a weight function is selected and a suitable second order differential operator is constructed.
Preferably, the hyperbolic partial differential equation is solved in Step6, and the hyperbolic equation is determined according to coefficient characteristics of the partial differential equation and is decomposed into a form of multiplying vibration by vibration or multiplying an exponential function by the exponential function.
Preferably, the technique for encrypting the image in Step9 includes aliasing and diffusion, where the aliasing is performed by disturbing the original positions of the pixel values in the two-dimensional matrix; the diffusion is to process the matrix by a small change of a pixel value in the original image to cause a large change of the pixel value in the whole image, so as to achieve the final encryption purpose.
Preferably, the Step10 outputs the denoised image, and the operation is based on a computer and a computer memory, and the computer is electrically connected with the computer memory.
The invention has the following beneficial effects:
the hyperbolic partial differential equation denoising method with the privacy protection function has the advantages that technical support is carried out on image denoising through the hyperbolic partial differential equation and the algorithm thereof, and denoising efficiency and denoising precision of the image are effectively improved.
According to the hyperbolic partial differential equation denoising method for protecting the privacy encrypted image, disclosed by the invention, the denoising image is encrypted, so that privacy protection can be formed, and the safety is enhanced.
The hyperbolic partial differential equation has the advantages that the privacy protection encrypted image denoising method can better keep the edge state after image processing, and the image visual effect is improved.
The hyperbolic partial differential equation has the advantages of simple operation process, high operation efficiency, low operation cost, convenience in maintenance and higher popularization value.
Of course, it is not necessary for any product in which the invention is practiced to achieve all of the above-described advantages at the same time.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is an operation flow chart of a denoising method of a hyperbolic partial differential equation encrypted image with privacy protection provided by the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Please refer to fig. 1: the invention relates to a hyperbolic partial differential equation privacy-protecting encrypted image denoising method, which comprises the following steps:
step 1: inputting an original image sample to be processed;
step 2: noise adding is carried out on the input original image sample to be processed, and a noise-containing image is obtained;
step 3: establishing a denoising model according to the obtained noise-containing image, and judging the image characteristics;
step 4: selecting a threshold, detecting the edge of the noise image, and calculating the gradient amplitude of the noise image;
step 5: establishing a hyperbolic partial differential equation according to the background of the related problems and the data of image processing;
step 6: solving the partial differential equation to obtain a de-noised image;
step 7: decomposing the coefficient of the image by using a hyperbolic partial differential equation algorithm again, establishing a verification model, and performing a numerical experiment;
step 8: according to the experimental simulation result, if the image verification is successful, entering Step9, and if the image verification is unsuccessful, entering Step4 again until the image verification is completed;
step 9: encrypting the image to form privacy protection;
step 10: and outputting the denoised image.
In Step2, noise addition is performed on the input original image sample to be processed, and gradation conversion is performed if necessary.
The adding sources of the image noise in Step2 comprise image acquisition, image transmission and image compression, and the noise types of the image comprise salt and pepper noise and Gaussian noise.
The noise component in Step2 includes additive noise, which is independent of the input image signal, such as channel noise and noise generated when the camera of the photoconductive camera tube scans the image, and the additive noise is typically gaussian noise; multiplicative noise, which is related to image signals, noise when flying spot scanners scan images, correlated noise in television images, and grain noise in film; quantization noise, which is irrelevant to the input image signal, is generated by reflecting quantization error in the quantization process to the receiving end.
When Step4 detects the edges of the noise image and calculates the gradient amplitude of the noise image, a weight function needs to be selected and a suitable second-order differential operator is constructed.
In Step6, a hyperbolic partial differential equation is solved, and the hyperbolic equation is determined according to coefficient characteristics of the partial differential equation and is decomposed into a form of multiplying vibration by vibration or multiplying an exponential function by the exponential function.
The image encryption technology in Step9 includes confusion and diffusion, wherein the confusion is achieved by disturbing the original position of a pixel value in a two-dimensional matrix; the diffusion is to process the matrix by a small change of a pixel value in the original image to cause a large change of the pixel value in the whole image, so as to achieve the final encryption purpose.
The denoised image is output in Step10, the operation is based on a computer and a computer memory, and the computer is electrically connected with the computer memory.
In the invention, the noise model has different processing algorithms for different noises, and for the input image v (x) with noises, the additive noise can be expressed by an equation: v (x) = u (x) + η (x), x ∈ Ω, where u (x) is the original image without noise, x is the pixel set, η (x) is the additive noise term representing the influence of noise, Ω is the pixel set, i.e. the whole image, and it can be seen from this formula that the noise is directly superimposed on the original image, and this noise can be salt-pepper noise, gaussian noise, theoretically, if the noise can be accurately obtained, the original image can be restored by subtracting the noise from the input image, but the reality is always very bone-feeling, and unless the way of noise generation is explicitly known, the noise is difficult to be separately solved; in engineering, the noise in an image is often approximately represented by gaussian noise N (μ, σ 2), where μ =0, σ 2 is the variance of the noise, σ 2 is larger, the noise is larger, an effective way to remove gaussian noise is to average the image, and the averaging result of N identical images reduces the variance of gaussian noise to one N times of the original variance, and the denoising algorithms with better effect are designed based on this idea;
in the invention, the Gaussian low-pass filter is a linear smoothing filter with a transfer function being a Gaussian function, and the Gaussian function is a normally distributed density function, so the Gaussian low-pass filter is very effective for removing noise which obeys normal distribution;
in the scheme, the image denoising is distributed according to the noise density, and comprises Gaussian noise: the noise follows Gaussian distribution, that is, the number of noise points with certain intensity is the largest, the number of noise points with the farther distance from the intensity is smaller, and the rule follows the Gaussian distribution. Gaussian noise is an additive noise, i.e. the noise is directly added to the original image and can therefore be filtered out with a linear filter; salt and pepper noise (impulse noise): the salt and pepper is scattered on the image, so that the name is that the noise with many white spots or black spots appears on the image, such as snowflake noise in a television. The salt and pepper noise can be regarded as logic noise, the filtering result by a linear filter is not good, and a good result can be obtained by filtering by a median filter; uniform noise: refers to noise whose power spectral density (the distribution of signal power in the frequency domain) is constant over the entire frequency domain. Random noise with all frequencies having the same energy density is called white noise; rayleigh noise: the noise distribution is Rayleigh distribution; exponential noise: the noise distribution is exponential distribution; gamma noise: the noise distribution is Rayleigh distribution;
in the scheme, image information which can be recognized by naked eyes is reconstructed into a noise-like image by image encryption, the encrypted image does not contain any useful information of an original image, common confusion methods comprise sequencing, cyclic shift, Arnold transformation, magic square transformation and the like, the purpose of changing the pixel position is achieved by using different principles, the common diffusion method is XOR operation, namely the image is changed into a one-dimensional array, and the XOR operation is sequentially carried out on the pixel values in the array according to the sequence from left to right.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims (8)
1. The hyperbolic partial differential equation denoising method for the encrypted image with the privacy protection function is characterized by comprising the following steps: the denoising method of the encrypted image with the privacy protection function comprises the following steps:
step 1: inputting an original image sample to be processed;
step 2: noise adding is carried out on the input original image sample to be processed, and a noise-containing image is obtained;
step 3: establishing a denoising model according to the obtained noise-containing image, and judging the image characteristics;
step 4: selecting a threshold, detecting the edge of the noise image, and calculating the gradient amplitude of the noise image;
step 5: establishing a hyperbolic partial differential equation according to the background of the related problems and the data of image processing;
step 6: solving the partial differential equation to obtain a de-noised image;
step 7: decomposing the coefficient of the image by using a hyperbolic partial differential equation algorithm again, establishing a verification model, and performing a numerical experiment;
step 8: according to the experimental simulation result, if the image verification is successful, entering Step9, and if the image verification is unsuccessful, entering Step4 again until the image verification is completed;
step 9: encrypting the image to form privacy protection;
step 10: and outputting the denoised image.
2. The hyperbolic partial differential equation denoising method with privacy-preserving encryption image according to claim 1, wherein Step2 is implemented by adding noise to the input original image sample to be processed and performing gray-scale conversion if necessary.
3. The hyperbolic partial differential equation denoising method with privacy-preserving encryption according to claim 1, wherein the additional sources of image noise in Step2 comprise image acquisition, image transmission and image compression, and the noise types of the image comprise salt-pepper noise and gaussian noise.
4. The hyperbolic partial differential equation denoising method with privacy-preserving encryption image denoising method according to claim 1, wherein the noise component in Step2 includes additive noise, which is independent of the input image signal, such as channel noise and noise generated when the camera of the photoconductive camera tube scans the image, and the typical additive noise is gaussian noise; multiplicative noise, which is related to image signals, noise when flying spot scanners scan images, correlated noise in television images, and grain noise in film; quantization noise, which is irrelevant to the input image signal, is generated by reflecting quantization error in the quantization process to the receiving end.
5. The hyperbolic partial differential equation denoising method with privacy protection encryption image according to claim 1, wherein Step4 is to select a weight function and construct a suitable second order differential operator when detecting the noise image edge and calculating the gradient amplitude of the noise image.
6. The hyperbolic partial differential equation denoising method with privacy protecting encryption image protection function as claimed in claim 1, wherein the hyperbolic partial differential equation is solved in Step6, and the hyperbolic equation is determined according to coefficient characteristics of the hyperbolic partial differential equation and is decomposed into a form of multiplication of vibration and vibration or multiplication of exponential function and exponential function.
7. The hyperbolic partial differential equation denoising method with privacy protection encryption, according to claim 1, wherein the image encryption technology in Step9 includes aliasing and diffusion, and the aliasing is achieved by disturbing the original positions of pixel values in a two-dimensional matrix; the diffusion is to process the matrix by a small change of a pixel value in the original image to cause a large change of the pixel value in the whole image, so as to achieve the final encryption purpose.
8. The hyperbolic partial differential equation denoising method with privacy-preserving encryption image as claimed in claim 1, wherein the Step10 outputs the denoised image, and the operation is based on a computer and a computer memory, and the computer is electrically connected with the computer memory.
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