A method for smoothing and denoising a noisy image

Abstract

The application discloses a noise image smoothing denoising method and relates to the technical field of computer digital image processing. The method comprises the following steps: in a Bayesian probability framework, a Gaussian probability model is used to model noise, and a gradient l0 norm and an l1 norm are used to model a clear image; three regularization constraint coefficients are introduced, the three models in the step 1) are weighted and summed, and a noise image restoration problem model is constructed; a quadratic penalty function method is used for solving, two auxiliary variables corresponding to horizontal and vertical gradients of the clear image are introduced, a penalty coefficient is introduced, and the noise image restoration problem model is converted. In a Bayesian maximum posterior estimation framework, the clear image is modeled by introducing the l0 norm and the l1 norm of the image gradient, the regularization constraint condition is formed, and an optimal estimation problem is comprehensively constructed, and an iterative optimization algorithm is designed, so that the noise can be effectively suppressed, and the significant edges can be sharpened and enhanced, thereby generating a high-quality restored image.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of computer digital image processing, and particularly relates to a noise image smoothing and denoising method. BACKGROUND

[0002] In the fields of daily photography, optical remote sensing, medical imaging, laser communication, etc., due to the influence of background light, instrument noise, atmospheric turbulence, etc., unnecessary signals are often introduced in the process of image shooting and transmission, thereby affecting the image quality and causing interference in subsequent image processing, and affecting the use value. Therefore, image denoising is the basis and premise of image processing, and is an important research direction in the field of image processing.

[0003] Traditional image denoising algorithms are to perform weighted average operation in a local area, such as mean filtering, median filtering, bilateral filtering, etc. The mean filtering and median filtering method is simple and fast in operation, but it will damage the image details. The bilateral filtering can better preserve the detail information for images with non-concentrated noise, but the operation speed is slow, and it cannot effectively remove the shadows in the image.

[0004] In mathematics, image blurring can be described by the convolution operation of a clear image and a point spread function, and the inverse process, i.e. the image restoration process, is called deconvolution. By taking an image block as a unit to find the similar area of the noise image and the convolved image, the significant edge detail information in the image can be effectively protected. However, the deconvolution process is a typical ill-posed process, that is, a little energy noise in the image will be amplified and propagated to the restored image in the opposite direction, so that the restored result deviates far from the real clear image.

[0005] Therefore, the present application proposes a regularization condition for constraining noise, and a method for solving the deconvolution after adding the regularization condition. It can effectively suppress noise and sharpen and enhance the significant edges, thereby producing a high-quality restored image, and has strong practical value. SUMMARY

[0006] The purpose of the present application is to provide a noise image smoothing and denoising method to solve the technical problems proposed in the background art.

[0007] The present application is realized by the following technical scheme: a noise image smoothing and denoising method, comprising the following steps:

[0008] Step 1), in the Bayesian probability framework, a Gaussian probability model is used to model the noise, and a gradient l0 norm and a l1 norm are used to model the clear image;

[0009] Step 2), three regularization constraint coefficients are introduced, the three models in step 1) are weighted and summed, and a noise image restoration problem model is constructed.

[0010] Step 3), using the twice penalty function method to solve, introducing two auxiliary variables corresponding to the horizontal gradient and vertical gradient of the clear image respectively, and introducing a penalty coefficient, the noise image restoration problem model is converted;

[0011] Step 4), the model in step 3) is decomposed into two optimal estimation problems about the clear image and auxiliary variables;

[0012] Step 5), the initial value of the clear image is initialized by the noise image, and the initial value and the maximum value of the penalty coefficient are set;

[0013] Step 6), fixing the estimated value of the clear image, the optimal estimation problem about the auxiliary variable is solved to obtain the estimated value of the auxiliary variable, and the auxiliary variable value is updated;

[0014] Step 7), fixing the estimated value of the auxiliary variable, the optimal estimation problem about the clear image is solved by using the conjugate gradient iteration method to obtain the estimated value of the clear image, and the clear image value and the penalty coefficient are updated;

[0015] Step 8), steps 6) and 7) are executed in a loop until the penalty coefficient reaches the maximum value, and the estimated value of the clear image, i.e. the restored image, is obtained.

[0016] Preferably, the expression for modeling the noise in step 1) by using the Gaussian probability model is The expression for modeling the image by using the gradient l0 norm is -ln[P(o)]∝∑ i sign[|(d x o) i |+|(d y o) i |]; The expression for modeling the image by using the gradient l1 norm is -ln[P(o)]∝∑ i [|(d x o) i |+|(d y o) i |];

[0017] Wherein, g represents the noise image, o represents the clear image, h represents the point spread function; P(g|o) is the random noise probability distribution, P(o) is the probability distribution of the clear image, d x And d y respectively represent the horizontal and vertical gradient operators, and i represents the pixel index in the clear image;

[0018]

[0019] Preferably, the regularization coefficients in step 2) are λ, μ and η, and the noise image restoration problem model is:

[0020]

[0021] Preferably, in step 3), the two auxiliary variables introduced are w and u, and the penalty coefficient introduced is β, and the noise image restoration problem model is converted to:

[0022] .

[0023] Preferably, in step 4), the two optimal estimation problems of the clear image and the auxiliary variable are respectively:

[0024]

[0025]

[0026] Preferably, in step 5), the estimate of the clear image by the noise image is initialized as o = g, and the initial value of the penalty coefficient is set as β = β initial , and the maximum value is β max , and the iteration coefficient is r.

[0027] Preferably, in step 6), the estimate of the clear image is fixed, and the optimal estimation problem of the auxiliary variable is solved to obtain the estimate of the auxiliary variable, and the step of updating the value of the auxiliary variable is:

[0028] 1) Fix η∑ i sign[|w i |+|u i |], and decompose the sub-problem into independent problem solutions The result is:

[0029] 2) Classify and compare |(d x o) i |, |(d y o) i | and to solve w i and u i ;

[0030] 3) Update w and u.

[0031] Preferably, in step 7), the estimate of the auxiliary variable is fixed, and the conjugate gradient iteration method is used to solve the optimal estimation problem of the clear image to obtain the estimate of the clear image, and the steps of updating the value of the clear image and the penalty coefficient are:

[0032] 1) Adopt conjugate gradient iterative method to solve formula:

[0033] 2) Update o;

[0034] 3) Update penalty coefficient β: β=β*r.

[0035] The beneficial effects of the present application are:

[0036] The present application provides a kind of noise image smoothing denoising method, under the framework of Bayes maximum posteriori estimation, by introducing the l0 norm and l1 norm of image gradient, clear image is modeled, regularization constraint condition is formed, and optimal estimation problem is comprehensively constructed, then iterative optimization algorithm is designed, can effectively suppress noise, and sharpen and enhance significant edge, to generate high quality restored image. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 It is the flow chart of the noise image smoothing denoising method of the present application;

[0038] Figure 2 It is the clear image in the embodiment of the present application;

[0039] Figure 3 It is the noise image in the embodiment of the present application;

[0040] Figure 4 It is the restored image obtained in the embodiment of the present application. DETAILED DESCRIPTION

[0041] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0042] Embodiment:

[0043] Please refer to Figure 1 The present application provides a technical solution: a noise image smoothing denoising method, comprising the following steps:

[0044] Step 1), under the framework of Bayes probability, model the noise with Gaussian probability model, and model the clear image with gradient l0 norm and l1 norm;

[0045] Step 2), introduce three regularization constraint coefficients, weight sum the three models in step 1), and construct noise image restoration problem model;

[0046] Step 3) The quadratic penalty function method is used to solve the problem. Two auxiliary variables are introduced, corresponding to the horizontal gradient and vertical gradient of the clear image, respectively. A penalty coefficient is also introduced to transform the model of the noisy image restoration problem.

[0047] Step 4) Decompose the model in Step 3) into two optimal estimation problems concerning the sharp image and auxiliary variables;

[0048] Step 5): Initialize the estimated value of the clear image with the noisy image, and set the initial value and maximum value of the penalty coefficient;

[0049] Step 6): Fix the estimated value of the clear image, solve the optimal estimation problem of the auxiliary variable, obtain the estimated value of the auxiliary variable, and update the value of the auxiliary variable;

[0050] Step 7): Fix the estimated values ​​of the auxiliary variables, use the conjugate gradient iteration method to solve the optimal estimation problem of the sharp image, obtain the estimated value of the sharp image, and update the sharp image value and penalty coefficient.

[0051] Step 8) Repeat steps 6) and 7) until the penalty coefficient reaches its maximum value, and obtain the estimated value of the clear image, i.e. the restored image.

[0052] In specific implementation, such as Figure 2 The image shown is a clear image. Adding Gaussian noise to the clear image yields... Figure 3 The noisy image in the image.

[0053] Step 1), the expression for modeling noise using a Gaussian probability model is: The expression for modeling an image using the gradient l0 norm is -ln[P(o)]∝∑ i sign[|(d x o) i |+|(d y o) i The expression for modeling an image using the gradient l1 norm is -ln[P(o)]∝∑ i [|(d x o) i |+|(d y o) i |].

[0054] Where g represents the noisy image, o represents the sharp image, and h represents the point spread function; P(g|o) is the probability distribution of random noise, P(o) is the probability distribution of the sharp image, and d x and d y Let represent the gradient operators in the horizontal and vertical directions, respectively, and let i represent the pixel index in the sharp image.

[0055]

[0056] Step 2), three regularization coefficients are introduced as λ, μ and η, and the model in step 1) is weighted and summed, so that the noise image restoration problem model is obtained as follows:

[0057]

[0058] Step 3), the quadratic penalty function method is used for solving, two auxiliary variables w and u are introduced, a penalty coefficient β is introduced, and the noise image restoration problem model is converted as follows:

[0059]

[0060] Step 4), the model is decomposed into two optimal estimation problems about the clear image and the auxiliary variable, respectively as follows:

[0061]

[0062]

[0063] Step 5), the estimation value of the noise image to the clear image is initialized as o = g in the present application, the initial value of the penalty coefficient is set as β = β initial , the maximum value is β max , and the iteration coefficient is r. Wherein, the initial value of β is 1, β max = 2 20 , and r = 1.

[0064] Step 6), the estimation value of the clear image is fixed, the optimal estimation problem about the auxiliary variable is solved, the estimation value of the auxiliary variable is obtained, and the step of updating the auxiliary variable value is as follows:

[0065] The η∑ i sign[|w i |+|u i |] is fixed, the sub-problem is decomposed into independent problems for solving The result is obtained as follows:

[0066]

[0067] The |(d x o) i |, |(d y o) i | and are classified and compared, and w i and u i are solved;

[0068] w and u are updated.

[0069] In step 7), the estimation value of the auxiliary variable is fixed, the conjugate gradient iteration method is used to solve the optimal estimation problem about the clear image, the estimation value of the clear image is obtained, and the steps of updating the clear image value and the penalty coefficient are:

[0070] The conjugate gradient iteration method is used to solve the formula:

[0071] The o is updated.

[0072] The penalty coefficient β is updated: β = β * r.

[0073] In step 8), steps 6) and 7) are executed in a loop until the penalty coefficient reaches the maximum value, and the estimation value of the clear image, that is, the restored image, is obtained as shown in formula (5). Figure 4

[0074] The present application provides a noise image smoothing denoising method with l0 norm and l1 norm regularization constraint, which can suppress the noise in the noise image, decompose the problem model into two optimal estimation sub-problems about the clear image and the auxiliary variable, iteratively solve the two sub-problems, and update the estimation value of the clear image and the estimation value of the auxiliary variable according to the iteration result, realize the smoothing denoising of the noise image, and restore the noise image with high quality, significantly improve the image quality, and improve the resolution capability of the image details. Figure 4 Figure 3 Compared with the prior art, the noise of the image is effectively removed, and the image details are effectively restored. Compared with the traditional image restoration method, the present application can retain large-scale changes in intensity while suppressing noise with low gradient amplitude and sharpening and enhancing significant edges, thereby producing a high-quality restored image.

[0075] The basic principles, main features and advantages of the present application are shown and described above. Those skilled in the art should understand that the present application is not limited by the above examples, and the above examples and descriptions in the specification are only the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection claimed by the present application is defined by the appended claims and their equivalents.​​

Claims

1. A method for smoothing and denoising noisy images, characterized in that: Includes the following steps: Step 1): Within the Bayesian probabilistic framework, use a Gaussian probability model to model the noise, and use the gradient l0 norm and l1 norm to model the clear image. Step 2) Introduce three regularization constraint coefficients and sum the three models in Step 1) with weights to construct a model for the noisy image restoration problem; Step 3) The quadratic penalty function method is used to solve the problem. Two auxiliary variables are introduced, corresponding to the horizontal gradient and vertical gradient of the clear image, respectively. A penalty coefficient is also introduced to transform the model of the noisy image restoration problem. Step 4) Decompose the model in Step 3) into two optimal estimation problems concerning the sharp image and auxiliary variables; The two optimal estimation problems concerning the sharp image and auxiliary variables are as follows: Where o represents the sharp image, g represents the noisy image, h represents the point spread function, w and u are two auxiliary variables, β is the penalty coefficient, and d x and d y Let represent the gradient operators in the horizontal and vertical directions, respectively; λ, μ, and η are regularization coefficients; and i represents the pixel index in the sharp image. Step 5): Initialize the estimated value of the clear image with the noisy image, and set the initial value and maximum value of the penalty coefficient; Step 6): Fix the estimated value of the clear image, solve the optimal estimation problem of the auxiliary variable, obtain the estimated value of the auxiliary variable, and update the value of the auxiliary variable; Step 7): Fix the estimated values ​​of the auxiliary variables, use the conjugate gradient iteration method to solve the optimal estimation problem of the sharp image, obtain the estimated value of the sharp image, and update the sharp image value and penalty coefficient. Step 8) Repeat steps 6) and 7) until the penalty coefficient reaches its maximum value, and obtain the estimated value of the clear image, i.e. the restored image.

2. The method for smoothing and denoising noisy images according to claim 1, characterized in that: The expression for modeling the noise using a Gaussian probability model in step 1) is: The expression for modeling an image using the gradient l0 norm is -ln[P(o)]∝∑isign[|(d x o)i|+|(d y The expression for modeling an image using the gradient l1 norm is -ln[P(o)]∝∑ i [|(d x o) i |+|(d y o) i |]; Where g represents the noisy image, o represents the sharp image, and h represents the point spread function; P(g|o) is the probability distribution of random noise, P(o) is the probability distribution of the sharp image, and d x and d y represents the gradient operators in the horizontal and vertical directions, respectively, and i represents the pixel index in the sharp image; 3. The method for smoothing and denoising noisy images according to claim 1, characterized in that: The regularization coefficients in step 2) are λ, μ, and η, and the model for the noisy image restoration problem is:

4. The method for smoothing and denoising noisy images according to claim 1, characterized in that: In step 3), the quadratic penalty function method is used to solve the problem. Two auxiliary variables, w and u, are introduced, and the penalty coefficient is β. The noisy image restoration problem model is then transformed into:

5. The method for smoothing and denoising noisy images according to claim 1, characterized in that: In step 5), the estimated value of the clear image using the noisy image is initialized to o = g, and the initial value of the penalty coefficient is set to β = β. initial The maximum value is β max , iteration coefficient r.

6. The method for smoothing and denoising noisy images according to claim 1, characterized in that: In step 6), the steps of fixing the estimated value of the clear image, solving the optimal estimation problem of the auxiliary variable, obtaining the estimated value of the auxiliary variable, and updating the value of the auxiliary variable are as follows: 1) Fix η∑ i sign[|w i |+|u i |], decompose the subproblem into independent problem solutions. The result is: 2) Set |(d) x o) i |,|(d y o) i |and Perform classification and comparison, and calculate w. i and u i ; 3) Update w and u.

7. The method for smoothing and denoising noisy images according to claim 1, characterized in that: In step 7), the estimated values ​​of the auxiliary variables are fixed, and the optimal estimation problem for the sharp image is solved using the conjugate gradient iteration method to obtain the estimated value of the sharp image. The steps for updating the sharp image value and the penalty coefficient are as follows: 1) Solve the formula using the conjugate gradient iteration method: 2) Update o; 3) Update the penalty coefficient β: β = β * r.

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