A pyramid-based image denoising method

Abstract

The present invention provides a pyramid-based image denoising method, which relates to the technical field of image processing and includes the steps of: collecting a noisy image; performing pyramid decomposition on the noisy image, first constructing Gaussian pyramid images of different scales step by step, and using a fractional integral algorithm to remove the noise contained in each scale of Gaussian pyramid images; then, based on the Gaussian pyramid denoised images, constructing multi-scale Laplacian pyramid images step by step, using a median filtering algorithm to remove the salt-and-pepper noise and impulse noise contained in each scale of Laplacian images, and then using a fractional integral algorithm to remove other noise contained in each scale of Laplacian images; finally, constructing a reconstruction template to achieve pyramid reconstruction and complete the denoising process of the image. The present invention can well maintain the clarity of the image while denoising, and solves the problem that the existing denoising algorithms sacrifice the clarity of the image while denoising.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, and in particular to an image denoising method based on a pyramid. Background Art

[0002] Image denoising is the process of reducing noise in digital images. Real-world digital images are often affected by interference from the imaging device and the external environment during digitization and transmission, resulting in noisy images. Noise is a major cause of image interference. In real-world applications, an image may contain various types of noise, which can be generated during transmission or during processing such as quantization.

[0003] According to the relationship between noise and signal, it can be divided into three forms: f(x,y) represents the given original image, g(x,y) represents the image signal, and n(x,y) represents the noise.

[0004] (1) Image noise can be divided into external noise and internal noise according to its cause. External noise refers to noise caused by external interference, such as electromagnetic interference from external electrical equipment and pulse interference from celestial discharges. Internal noise refers to noise caused by the system's electrical equipment, such as mutual interference between internal circuits.

[0005] (2) According to statistical characteristics, image noise can be divided into stationary noise and non-stationary noise. Noise whose statistical characteristics do not change with time is called stationary noise, and noise whose statistical characteristics change with time is called non-stationary noise.

[0006] (3) According to the amplitude distribution, image noise can be divided into impulse noise, salt and pepper noise, Rayleigh noise, etc. Impulse noise refers to the irregular, sudden, discrete noise with short duration and large amplitude. Salt and pepper noise is also an impulse noise, consisting of randomly distributed white dots (salt noise) and black dots (pepper noise). Noise whose amplitude distribution follows a Gaussian distribution is called Gaussian noise, and noise whose amplitude distribution follows a Rayleigh distribution is called Rayleigh noise.

[0007] (4) Image noise can be classified into white noise and 1 / f noise according to the noise spectrum. Noise with a uniform power spectrum density in the frequency domain is called white noise. Noise with a power spectrum density inversely proportional to the frequency is called 1 / f noise.

[0008] (5) According to the relationship between noise and signal, image noise can be divided into additive noise and multiplicative noise. Assuming the signal is S(t) and the noise is n(t), if the mixed superposition waveform is in the form of S(t) + n(t), it is called additive noise; if the superposition waveform is in the form of S(t)[1 + n(t)], it is called multiplicative noise. Additive noise is not related to the signal intensity, while multiplicative noise is related to the signal intensity. For the convenience of analysis and processing, multiplicative noise is often approximately considered as additive noise, and it is always assumed that the signal and noise are independent of each other.

[0009] And the existing filtering methods are as follows:

[0010] 1. Mean filtering: The neighborhood averaging method is a linear low-pass filter. Its idea is to use the average value or weighted average value of the pixels in the neighborhood corresponding to the filter template as the output result of the central pixel to remove the mutated pixel points, thereby filtering out certain noise. To ensure that the output pixel value does not exceed the boundary, the sum of the convolution kernel coefficients of the neighborhood averaging is 1. The mean filter is not applicable to "salt and pepper" noise and is good at dealing with other noises such as Gaussian noise.

[0011] 2. Median filtering: It is a commonly used non-linear smoothing filter. Median filtering is a non-linear filtering that can well preserve the image edges while filtering out noise. The principle of median filtering is to sort the grayscales of all pixels in a small window centered on a certain pixel from small to large, and take the middle value of the sorting result as the grayscale value of that pixel. Median filtering is very effective for filtering out the salt and pepper noise in images, but it is not suitable to use the median filtering method for images with many details, especially images with many details such as points, lines, and sharp tops.

[0012] 3. Wiener filtering: It can adjust the output of the filter according to the local variance of the image. The larger the local variance, the stronger the smoothing effect of the filter. Its ultimate goal is to make the mean square error e 2 = E[(f(x, y) - f^(x, y) 2 minimum. The filtering effect of this method is better than that of the mean filter and is very useful for retaining the edges and other high-frequency parts of the image. However, the calculation amount is relatively large. The Wiener filter has the best filtering effect on images with white noise.

[0013] 4. Gaussian filtering: Design a Gaussian low-pass filter to achieve the filtering of high-frequency noise and achieve the purpose of denoising.

[0014] 5. Ideal low-pass filtering: Design an ideal low-pass filter to achieve the filtering of high-frequency noise and achieve the purpose of denoising.

[0015] 6. Fractional integral filtering denoising: Construct a fractional integral template to achieve image denoising. The fractional integral algorithm can non-linearly retain the very high-frequency information of the image while attenuating the high-frequency information of the image to achieve image denoising, thereby retaining the texture detail information of the image to a certain extent, enabling the image to better retain the texture detail information while denoising and improving the image clarity.

[0016] Among the above methods, the mean filtering denoising algorithm, median filtering denoising algorithm, Wiener filtering denoising algorithm, Gaussian filtering denoising algorithm, and ideal low-pass filtering denoising algorithm. These algorithms remove some high-frequency texture detail information of the image while removing noise. When filtering out noise, they all sacrifice the clarity of the image at the cost, making the image blurred, with poor denoising effect and unable to maintain the clarity of the image; the fractional integral algorithm enables the image to better retain the texture detail information while denoising and improves the image clarity. Therefore, in terms of denoising effect and improving image clarity, it is improved compared with the median filtering denoising algorithm, mean filtering denoising algorithm, Wiener filtering denoising algorithm, Gaussian filtering denoising algorithm, and ideal low-pass filtering denoising algorithm, but there is still a problem of sacrificing image clarity, and the denoising effect still needs to be further improved. Summary of the Invention

[0017] The present invention provides a pyramid-based image denoising method, aiming to solve the disadvantages existing in the prior art.

[0018] To achieve the above object, the present invention provides the following technical solution: A pyramid-based image denoising method, including the following steps:

[0019] Collect a noisy image;

[0020] Perform Gaussian filtering and downsampling on the noisy image, and gradually construct Gaussian pyramid images of different scales;

[0021] Remove the noise contained in the Gaussian pyramid images of each scale through the fractional integral algorithm;

[0022] Starting from the highest layer of the denoised Gaussian pyramid image, perform upsampling and Gaussian filtering step by step to construct Laplacian pyramid images of different scales;

[0023] Remove the salt-and-pepper noise and impulse noise contained in the Laplacian pyramid images of each scale through median filtering, and use the fractional integral algorithm to remove other noises from the median-filtered Laplacian pyramid images;

[0024] Construct a reconstruction template, start upsampling from the highest layer of the denoised Gaussian pyramid image, and obtain a new image through the reconstruction template after upsampling. Add the new image to the Laplacian pyramid image of the previous layer after denoising to obtain the reconstructed image of the current layer pyramid, and use the reconstructed pyramid image of the current layer to construct a new image again. Repeat the above reconstruction steps step by step to obtain the denoised image.

[0025] Preferably, perform Gaussian filtering and downsampling on the noisy image, and construct Gaussian pyramid images of different scales step by step, specifically including the following steps:

[0026] Perform convolution on the noisy image using a Gaussian template, and perform downsampling on the convolved image. The calculation process is as follows:

[0027]

[0028] where w is the Gaussian template, G k is the k-th layer Gaussian pyramid image, G k+1 represents the (k + 1)-th layer Gaussian pyramid image, represents that the convolution operation realizes Gaussian filtering, and Down represents downsampling;

[0029] The Gaussian template w is:

[0030]

[0031] Perform convolution operation and downsampling on the image using a Gaussian template. The specific formula is:

[0032]

[0033] where x and y represent the positions of the pixels in the image, w(m, n) is the Gaussian template, m and n represent the positions of the template coefficients, G k (2x - m, 2y - n) represents the reverse translation of the image G k (m, n) and downsampling at an interval of 2, G k+1 (x, y) represents the (k + 1)-th layer low-frequency Gaussian pyramid image obtained by performing convolution operation on the k-th layer Gaussian pyramid image using a Gaussian template and then downsampling;

[0034] Perform downsampling on the convolved image at an interval of 2 to obtain an image with 1 / 2 of the original size;

[0035] Perform Gaussian template convolution on the downsampled image again, and then perform downsampling on it to obtain an image with 1 / 2 n of the original size;

[0036] Repeat the above steps to obtain Gaussian pyramid images of different scales.

[0037] Preferably, removing the noise contained in the Gaussian pyramid images at each scale through the fractional integral algorithm includes the following steps:

[0038] Derive the difference expression through the Gumumwald—letnikow fractional differential definition, and sequentially obtain the fractional integral formula and the fractional integral template;

[0039] After traversing the entire Gaussian pyramid image with the given fractional integral template, obtain the denoised Gaussian pyramid image;

[0040]

[0041] Among them, w * (m,n) is the fractional integral filtering template, m and n represent the positions of the template coefficients, M represents the number of rows of the image, N represents the number of columns of the image, x and y represent the pixel positions of the image, and G k+1 (x - m, y - n) represents the noisy Gaussian pyramid image to be processed, is the Gaussian pyramid image after denoising using fractional integral;

[0042] Starting from the highest layer, repeat the above steps to obtain the Gaussian pyramid images after denoising at different scales.

[0043] Preferably, starting from the highest layer of the denoised Gaussian pyramid image, perform upsampling and Gaussian filtering step by step to construct Laplacian pyramid images at different scales, specifically including the following steps:

[0044] Enlarge the denoised Gaussian pyramid image by a factor of two in each direction, and fill the newly added rows and columns with 0 to achieve upsampling;

[0045] Convolve the upsampled Gaussian pyramid image with the same kernel as the Gaussian filter to obtain the approximation of the newly added pixels, that is, the predicted image;

[0046] Subtract the previous layer image from the current predicted image to obtain the Laplacian pyramid image;

[0047] Repeat the above steps to obtain the Laplacian pyramid image.

[0048] Preferably, the upsampling and Gaussian filtering process is as follows:

[0049]

[0050] Among them, w is the Gaussian template, is the denoised image of the Gaussian pyramid at the k + 1 layer, Convolution operation represents Gaussian filtering, up represents upsampling the denoised Gaussian pyramid image of the (k + 1)-th layer, and G * k+1 represents the predicted image obtained by performing convolution operation on the upsampled image using a Gaussian template.

[0051] Preferably, the same Gaussian filtering kernel used for constructing the Gaussian pyramid image is convolved with the upsampled Gaussian pyramid image, and its calculation formula is as follows:

[0052]

[0053] where w(m, n) is the Gaussian template, and m and n are the positions of the template coefficients. is the upsampling and reverse translation of the denoised image of the Gaussian pyramid of the (k + 1)-th layer at an interval of 2, and G * k+1 (x, y) represents performing convolution operation on the upsampled image using a Gaussian template to obtain the predicted image G * k+1 (x, y) of the (k + 1)-th layer, where x and y are the pixel positions of the image.

[0054] Preferably, subtracting the previous layer image from the current predicted image to obtain the Laplacian pyramid image, and its calculation formula is as follows:

[0055]

[0056] Subtracting the Gaussian pyramid image of the k-th layer from the predicted image G * k+1 (x, y) of the (k + 1)-th layer to obtain the Laplacian pyramid image L k (x, y) of the k-th layer.

[0057] Preferably, removing the salt-and-pepper noise and impulse noise contained in each scale Laplacian pyramid image through median filtering, which specifically includes the following steps:

[0058] Constructing a Laplacian pyramid structure;

[0059] Adding median filtering to the Laplacian pyramid structure to remove salt-and-pepper noise and impulse signals, which includes the following steps:

[0060] Obtaining each pixel point of the Laplacian pyramid image;

[0061] Sorting the grayscales of all pixels within a small window centered on a certain pixel point from smallest to largest;

[0062] Taking the middle value of the sorting result as the gray value of this pixel;

[0063] Output the Laplacian pyramid image after sorting the grayscale values.

[0064] Preferably, the following steps are included for filtering other noises from the Laplacian pyramid images of each scale after filtering salt-and-pepper noise and impulse noise using the fractional integral algorithm:

[0065] Derive the difference expression through the Gumumwald—letnikow fractional differential definition, and sequentially obtain the fractional integral formula to obtain the fractional integral template;

[0066] After traversing the entire image with the given fractional integral template, the denoised image can be obtained;

[0067]

[0068] Among them, w * (m,n) is the fractional integral filtering template, m and n represent the positions of the template coefficients, M represents the number of rows of the image, N represents the number of columns of the image, x and y represent the pixel positions of the image, and L k (x - m, y - n) represents the noisy Laplacian pyramid image to be processed, The Laplacian pyramid denoised image after denoising using the fractional integral;

[0069] Repeat the above steps to obtain the Laplacian pyramid denoised images of different scales.

[0070] Preferably, construct a reconstruction template, start upsampling from the highest layer of the denoised Gaussian pyramid image, and obtain the new added image through the reconstruction template after upsampling. Add the new added image to the denoised Laplacian pyramid image of the previous layer to obtain the reconstructed image of the current layer pyramid, specifically including:

[0071] Construct the reconstruction template:

[0072]

[0073] The calculation process for obtaining the new added image is as follows:

[0074]

[0075] Among them, w c (m,n) is the reconstruction template, m and n represent the positions of the template coefficients, M represents the number of rows of the image, N represents the number of columns of the image, x and y represent the pixel positions of the new added image, is the upsampling of the denoised image of the (k + 1)-th layer Gaussian pyramid at an interval of 2 and reversed translation, and G c k+1 (x,y) represents the new added image of the (k + 1)-th layer;

[0076] Among them, the calculation expression of the reconstructed image of the k-th layer is:

[0077]

[0078] Among them, G c k+1 (x, y) represents the newly added image of the (k + 1)-th layer, the denoised image of the Laplacian pyramid of the k-th layer, G c k is the reconstructed image of the k-th layer.

[0079] Compared with the prior art, the present invention has the following beneficial effects: The present invention performs pyramid decomposition on an image, which can layer the image to obtain low-frequency and high-frequency images with different resolutions, separate the low-frequency and high-frequency information of the image. Since most of the noise spectrum is distributed in the high-frequency part, after pyramid decomposition, fractional integral denoising is used for the Gaussian pyramid decomposed image, and median filtering is first used for the Laplacian pyramid image and then fractional integral algorithm for denoising, which can achieve a good denoising effect. At the same time, the present invention can well maintain the clarity of the image while denoising, solving the problem that the existing denoising algorithms sacrifice the clarity of the image while denoising. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is the overall flowchart of the present invention provided by the present invention;

[0081] Figure 2 is the comparison diagram of adding noise to the original image provided by the present invention;

[0082] Figure 3 is the result diagram of the 1st - 4th layer downsampling of the Gaussian pyramid provided by the present invention;

[0083] Figure 4 is the result diagram of the 1st - 3rd layer upsampling of the Laplacian pyramid provided by the present invention;

[0084] Figure 5 is the result diagram of median filtering denoising of the 1st - 3rd layer of the Laplacian pyramid provided by the present invention;

[0085] Figure 6 is the diagram of median filtering and fractional integral denoising of the Laplacian pyramid image provided by the present invention;

[0086] Figure 7 is the result diagram of the 1st - 4th level reconstruction of the pyramid reconstruction structure provided by the present invention;

[0087] Figure 8 is the comparison diagram of the denoising effect provided by the present invention;

[0088] Figure 9 The comparison chart between the present invention and existing algorithms provided by the present invention. Detailed implementation manners

[0089] The following further describes the detailed implementation manners of the present invention with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and cannot be used to limit the protection scope of the present invention.

[0090] A pyramid-based image denoising method provided by the present invention performs pyramid decomposition on an image to obtain multi-scale Gaussian pyramid images. First, the multi-scale Gaussian pyramid images are denoised using a fractional integral algorithm. Then, on this basis, multi-scale Laplacian pyramid images are constructed. Next, median filtering is used to remove impulse noise from the multi-scale Laplacian pyramid images, and the fractional integral algorithm is used to remove non-impulse noise. During pyramid reconstruction, a reconstruction template is constructed, and the reconstruction template is used to reconstruct the filtered and denoised image to construct a reconstructed image. The denoising effect of the present invention is better than that of existing algorithms, and it can well maintain the clarity of the image while denoising, improving the problem that existing denoising algorithms sacrifice the image clarity while denoising.

[0091] Specifically, the algorithms mentioned in the present invention are described as follows:

[0092] ① Advantages of using the fractional integral algorithm for denoising:

[0093] The fractional integral algorithm can better maintain the very high-frequency information in the image while denoising, so it can better maintain the clarity of the image.

[0094] ② Advantages of using median filtering:

[0095] Median filtering can remove salt-and-pepper noise and impulse noise.

[0096] ③ Reasons for using pyramid decomposition of the image:

[0097] Performing pyramid decomposition on the image can layer the image to obtain low-frequency and high-frequency images of different scales, separate the low-frequency and high-frequency information of the image. Since most of the noise spectrum is distributed in the high-frequency part, after pyramid decomposition, the fractional integral denoising is used for the Gaussian pyramid decomposition image, and median filtering is first used for the Laplacian pyramid image and then the fractional integral algorithm is used for denoising, which can achieve a good denoising effect and can well maintain the clarity of the image at the same time.

[0098] ④ Constructing a reconstruction template for pyramid reconstruction:

[0099] During pyramid reconstruction, a reconstruction template is constructed, and the reconstruction template is used to reconstruct the filtered and denoised image again to construct a reconstructed image, which can achieve a better denoising effect.

[0100] ⑤ Compared with existing denoising algorithms such as mean filtering, Gaussian filtering, and Wiener filtering:

[0101] Existing denoising algorithms will sacrifice the clarity of the image while denoising, making the image blurred. The denoising effect of this algorithm is better than that of existing algorithms and can maintain the clarity of the image.

[0102] For the sake of understanding and illustration, a pyramid-based image denoising method provided by an embodiment of the present invention is described in detail below, which includes the following steps:

[0103] Step 1: Collect the noisy image.

[0104] Step 2: Perform Gaussian filtering and downsampling on the noisy image, and gradually construct Gaussian pyramid images of different scales.

[0105] Step 3: Remove the noise contained in each scale of Gaussian pyramid images through the fractional integral algorithm.

[0106] Step 4: Starting from the highest layer of the denoised Gaussian pyramid image, perform upsampling and Gaussian filtering step by step to construct Laplacian pyramid images of different scales.

[0107] Step 5: Remove the salt-and-pepper noise and impulse noise contained in each scale of Laplacian pyramid images through median filtering, and use the fractional integral algorithm to remove other noises from the median-filtered Laplacian pyramid images.

[0108] Step 6: Construct a reconstruction template, perform upsampling starting from the highest layer of the denoised Gaussian pyramid image, and obtain a new image through the reconstruction template after upsampling. Add the new image to the denoised Laplacian pyramid image of the previous layer to obtain the reconstructed image of the current layer pyramid, and use the reconstructed pyramid image of the current layer to construct a new image again. Repeat the above reconstruction steps step by step to obtain the denoised image.

[0109] As Figures 1-9 shown, the detailed process of the present invention is as follows:

[0110] 1. The construction of Gaussian pyramid images and the denoising of Gaussian pyramid images included in Step 2 and Step 3 specifically include:

[0111] 1.1. Construct Gaussian pyramid images.

[0112] ① Convolve the sampled image with a Gaussian template.

[0113] ② Downsample the image at an interval of 2, and the size of the image will become 1 / 2 of the original.

[0114] ③ Convolve with a Gaussian template again.

[0115] ④ When downsampling the current image, the size of the image will become 1 / 4 of the original size.

[0116] ⑤ Repeat the above steps.

[0117] Specifically, the sampling process:

[0118]

[0119] Gaussian template:

[0120]

[0121] where w is the Gaussian template, G k is the k-th layer Gaussian pyramid image, G k+1 represents the (k + 1)-th layer Gaussian pyramid image, represents the implementation of Gaussian filtering by convolution operation, and Down represents downsampling.

[0122] The specific formula for performing convolution operation and downsampling on the image using the Gaussian template is:

[0123]

[0124] where x, y represent the positions of the pixels in the image, w(m, n) is the Gaussian template, m, n represent the positions of the template coefficients, G k (2x - m, 2y - n) represents the inverse translation and downsampling at an interval of 2 of the image G k (m, n), and G k+1 (x, y) represents the (k + 1)-th layer low-frequency Gaussian pyramid image obtained by performing convolution operation on the k-th layer Gaussian pyramid image using the Gaussian template and then downsampling.

[0125] 1.2. Denoise the decomposed images of each layer of the Gaussian pyramid using fractional integration.

[0126] Derive the difference expression through the Gumumwald - letnikow fractional differential definition, and sequentially obtain the fractional integration formula and the fractional integration template.

[0127] Among them:

[0128] 1) Derive the difference expression from the Gumumwald - letnikow fractional differential definition.

[0129] Gumumwald - letnikow fractional integration definition:

[0130]

[0131] Among them, the Gamma function:

[0132] If the one-dimensional function f(t) is defined on the interval [a, t] and is equally divided into units of h = 1, it can be deduced that Then the difference expression of the one-dimensional signal is:

[0133]

[0134] When 1 > v > 0, the formula is differentiated, and when -1 < v < 0, the formula is integrated.

[0135] 2) Fractional integral formula.

[0136]

[0137]

[0138]

[0139] 3) Integration template derived from the expression.

[0140] Derive the coefficients of the differential template according to equation (2), and let the coordinate of the center position of the template be w * (0, 0), then the coordinate in the positive x-axis direction is w * (1, 0), w * (2, 0), w * (3, 0)…; then the coordinate in the negative x-axis direction is w * (-1, 0), w * (-2, 0), w * (-3, 0)…; then the coordinate in the positive y-axis direction is w * (0, 1), w * (0, 2), w * (0, 3)…; then the coordinate in the negative y-axis direction is w * (0, -1), w * (0, -2), w * (0, -3)…; The coordinate values in the diagonal direction of the template can be deduced by analogy. The template coefficient values in the horizontal, diagonal, and vertical eight directions obtained according to formula (2) are as follows:

[0141] Table 1: Table of fractional integral template coefficient values in the horizontal, diagonal, and vertical eight directions obtained from formula (2)

[0142]

[0143]

[0144] 4) Image denoising operation of fractional integral.

[0145] According to the image processing principle of the spatial filter, the image pixel point f(x, y) to be processed is located at the exact center of the template. After traversing the entire image with the given 8-direction template, the denoised image f q (x, y) can be obtained:

[0146]

[0147] Where M represents the number of rows of the image, N represents the number of columns of the image, and w * (m, n) is the fractional integral template, and f(x, y) is the image pixel value.

[0148] While the fractional integral algorithm realizes image denoising by attenuating the high-frequency information of the image, it can non-linearly retain the very high-frequency information of the image, thereby retaining the texture detail information of the image to a certain extent, enabling the image to better retain the texture detail information while denoising and improving the image blurring phenomenon.

[0149] After traversing the entire Gaussian pyramid image with the given fractional integral template, the denoised Gaussian pyramid image is obtained.

[0150]

[0151] Among them, w * (m, n) is the fractional integral filtering template, m and n represent the positions of the template coefficients, M represents the number of rows of the image, N represents the number of columns of the image, x and y represent the pixel positions of the image, and G k+1 (x - m, y - n) represents the noisy Gaussian pyramid image to be processed, is the Gaussian pyramid image after denoising using fractional integral; the Gaussian pyramid image after denoising.

[0152] Starting from the highest layer, repeat the above steps to obtain the Gaussian pyramid images with different scales after denoising.

[0153] 2. Construction of the Laplacian pyramid image and denoising of the Laplacian pyramid image in steps 4 and 5 specifically include:

[0154] 2.1 Construction of the Laplacian pyramid image.

[0155] (1) Double the size of the Gaussian pyramid image in each direction, and fill the newly added rows and columns with 0 to achieve upsampling, and the image size is doubled.

[0156] (2) Convolve the enlarged image with the same kernel as the Gaussian filter to obtain an approximation of the "predicted pixels".

[0157] (3) Subtract the upper - layer image from the current "newly added pixels" to obtain the Laplacian pyramid image.

[0158] Repeat the above steps to obtain the Laplacian pyramid image.

[0159]

[0160] The obtained image is the enlarged image, but it will be found to be relatively blurred compared with the original image because some information has been lost during the scaling process. If we want to reduce the loss of information during the whole process of shrinking and enlarging, these data form the Laplacian pyramid.

[0161] Among them, Figure 4 The results of the first - to - third - layer upsampling of the Laplacian pyramid, Figure 4 (a) is the image of the first layer of the Laplacian pyramid, Figure 4 (b) is the image of the second layer of the Laplacian pyramid, Figure 4 (c) is the image of the third layer of the Laplacian pyramid.

[0162] Among them, the Laplacian upsampling and Gaussian template convolution processes are as follows:

[0163]

[0164] Subtract the upper - layer image from the current image to obtain the Laplacian pyramid image:

[0165]

[0166] Among them, G * k+1 (x, y) is the current image, is the upper - layer image.

[0167] 2.2. Denoise the Laplacian pyramid image.

[0168] (1) Use median filtering to remove impulse noise from the Laplacian pyramid image. [[ID=4I]]

[0169] After the Laplacian pyramid is constructed, median filtering should be added first to remove impulse signals. Therefore, median filtering is selected here. Median filtering can effectively remove single - pulse noise, and adding median filtering is also an important step in this algorithm. The flow block diagram of median filtering is as [[ID=SO]] Figure 5 shown.

[0170] (2) Use the fractional - order integral algorithm to denoise the Laplacian pyramid image.

[0171] Define the difference expression through the Gumumwald-Letnikow fractional-order derivative, and sequentially obtain the fractional-order integral formula and the fractional-order integral template;

[0172] After traversing the entire image with the given fractional-order integral template, the denoised image can be obtained.

[0173]

[0174] Among them, w * (m, n) is the fractional-order integral filtering template, where m and n represent the positions of the template coefficients, M represents the number of rows of the image, N represents the number of columns of the image, x and y represent the pixel positions of the image, and L k (x - m, y - n) represents the noisy Laplacian pyramid image to be processed, The Laplacian pyramid denoised image after fractional-order integral denoising.

[0175] As Figure 6 shown, the fractional-order integral algorithm is used to denoise the Laplacian pyramid images of each layer decomposed above. Among them, Figure 6 (a) is the denoising result of the first layer of the Laplacian pyramid by the fractional-order integral algorithm, Figure 6 (b) is the denoising result diagram of the second layer of the Laplacian pyramid, Figure 6 (c) is the denoising result diagram of the third layer of the Laplacian pyramid.

[0176] 3. The process of reconstructing the pyramid image in step 6 includes:

[0177] Construct the reconstruction template:

[0178]

[0179] Upsample the denoised Gaussian pyramid image. After traversing the entire upsampled image with the given reconstruction template, a new image is obtained;

[0180]

[0181] Among them, w c (m, n) is the reconstruction template, where m and n represent the positions of the template coefficients, M represents the number of rows of the image, N represents the number of columns of the image, x and y represent the pixel positions of the new image, is the upsampling by a factor of 2 with inversion and translation of the denoised image of the (k + 1)-th layer Gaussian pyramid, and G c k+1 (x, y) represents the (k + 1)-th layer new image;

[0182] Add the newly added image to the denoised Laplacian pyramid image of the previous layer to obtain the reconstructed image of the current layer of the pyramid;

[0183] Among them, the calculation expression of the k-th layer reconstructed image is:

[0184]

[0185] in, represents the newly added image in the k+1th layer, The k-th layer of Laplacian pyramid denoising image, Reconstruct the image for the kth layer.

[0186] The reconstructed image is reconstructed using the current layer reconstructed pyramid image, and the above reconstruction steps are repeated level by level to obtain the denoised image.

[0187] like Figure 7 As shown, the processed Gaussian pyramid images and Laplacian pyramid images of each layer are reconstructed.

[0188] The reconstruction template is constructed and convolved with the Gaussian pyramid image to realize reconstruction filtering and obtain a new image, the purpose of which is to further remove the noise of the Gaussian pyramid image.

[0189] in, Figure 7 (a) is the 4th level Gaussian pyramid diagram, Figure 7 (b) is the third-level reconstruction result. Figure 7 (c) is the second-level reconstruction result image. Figure 7 (d) is the first-level reconstruction result image.

[0190] 4. Simulate and analyze the present invention.

[0191] 4.1. Preprocess the original image.

[0192] By processing the original image, the image size is 512*512, and the noise is Gaussian noise or salt and pepper noise.

[0193] in, Figure 2 (a) is the original image, Figure 2 (b) is an image with Gaussian noise added. Figure 2 (c) is the image with salt and pepper noise added.

[0194] 4.2. Construct a Gaussian pyramid.

[0195] Starting from the original image, Gaussian filtering and downsampling are performed to obtain Gaussian pyramid images of different sizes and resolutions step by step.

[0196] like Figure 3 (a) Figure 3 (b) Figure 3(c) and Figure 3 As shown in (d), multi-scale sampling is performed on the image to form images with four resolutions. According to the simulation results, in the downsampling of the Gaussian pyramid, the higher the level, the smaller the image. Each time the image becomes smaller to 1 / 4 of the previous size, the image becomes blurrier.

[0197] 4.3. Construct the Laplacian pyramid.

[0198] The Laplacian pyramid is constructed based on the Gaussian pyramid. Starting from the highest-level image of the Gaussian pyramid, perform upsampling on it, then filter it using a Gaussian template, and then subtract the current image from the upper-level Gaussian pyramid image. The Laplacian pyramid image can be obtained by constructing it level by level.

[0199] The Laplacian pyramid image is as shown in Figure 4 (a), Figure 4 (b), Figure 4 (c).

[0200] 4.4. Median filtering of the Laplacian pyramid image.

[0201] Perform median filtering on the Laplacian pyramid image. Among them, the median filtering results of the first to third layers are as shown in Figure 5 (a), Figure 5 (b), and Figure 5 (c). The salt-and-pepper noise is effectively removed.

[0202] 4.5. Fractional integral denoising of the Laplacian pyramid image.

[0203] Perform further fractional integral denoising on the Laplacian pyramid image. The denoising effect is as shown in Figure 6 (a), Figure 6 (b), Figure 6 (c). The Gaussian noise in the image is effectively removed.

[0204] 4.6. Pyramid reconstruction of the image.

[0205] Construct a reconstruction template, reconstruct the pyramid-decomposed image, and restore the image size. As shown in Figure 7 (a), Figure 7 (b), Figure 7 (c), Figure 7 (d). The image is reconstructed level by level from small to large to obtain the final denoised image, as shown in Figure 7 (d).

[0206] 4.7. Denoising effect of the pyramid-based image denoising algorithm.

[0207] As shown in Figure 8As shown, this algorithm can not only effectively remove noise, but also well maintain the clarity of the image and enhance the image brightness. Among them, Figure 8 (a), Figure 8 (b) and Figure 8 (c) are the comparison diagrams of the first group of images, which are the original image, the image with added noise, and the denoising result image respectively; Figure 8 (d), Figure 8 (e) and Figure 8 (f) are the comparison diagrams of the second group of images, which are the original image, the image with added noise, and the denoising result image respectively; Figure 8 (g), Figure 8 (h) and Figure 8 (i) are the comparison diagrams of the third group of images, which are the original image, the image with added noise, and the denoising result image respectively; It can be seen from the above three groups of images that the pyramid-based image denoising algorithm proposed by the present invention has generality.

[0208] 4.8. Comparison with existing algorithms.

[0209] First: Through experimental comparison, it is found that the denoising effect of the pyramid-based image denoising algorithm is better than that of existing denoising algorithms such as Wiener filtering, Gaussian filtering, and mean filtering.

[0210] Second: The pyramid-based image denoising algorithm can well maintain the clarity of the image while denoising, and the image brightness is also improved; Gaussian filtering denoising, Wiener filtering denoising, and mean filtering denoising algorithms will make the image blurred while denoising.

[0211] As Figure 9 shown, image comparisons of various algorithms were carried out. Figure 9 (a) is the original image, Figure 9 (b) is the noisy image, Figure 9 (c) is the Gaussian filtering denoised image, Figure 9 (d) is the Wiener filtering denoised image, Figure 9 (e) is the 3×3 template suppressing Gaussian noise denoised image, Figure 9 (f) is the image denoised by the pyramid-based image denoising algorithm.

[0212] The above-described embodiments are only the preferred specific embodiments of the present invention, and the protection scope of the present invention is not limited thereto. Any simple changes or equivalent replacements of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope disclosed by the present invention all belong to the protection scope of the present invention.

Claims

1. A pyramid-based image denoising method, characterized in that, It includes the following steps: Collect the noisy image; Perform Gaussian filtering and downsampling on the noisy image, and gradually construct Gaussian pyramid images of different scales; Remove the noise contained in the Gaussian pyramid images of each scale through the fractional integral algorithm; Starting from the top layer of the denoised Gaussian pyramid images, perform upsampling and Gaussian filtering step by step to construct Laplacian pyramid images of different scales; Remove the salt-and-pepper noise and impulse noise contained in the Laplacian pyramid images of each scale through median filtering, and use the fractional integral algorithm to remove other noises from the median-filtered Laplacian pyramid images; Construct a reconstruction template, start upsampling from the top layer of the denoised Gaussian pyramid images, and obtain a new image through the reconstruction template after upsampling. Add the new image to the denoised Laplacian pyramid image of the previous layer to obtain the reconstructed image of the current layer pyramid, and use the reconstructed pyramid image of the current layer to construct a new image again. Repeat the above reconstruction steps step by step to obtain the denoised image.

2. The image denoising method based on a pyramid according to claim 1, wherein Perform Gaussian filtering and downsampling on the noisy image, and gradually construct Gaussian pyramid images of different scales, which specifically includes the following steps: Convolve the noisy image using a Gaussian template, and perform downsampling on the convolved image. The calculation process is as follows: Among them, is a Gaussian template, is the layer Gaussian pyramid image, represents the layer Gaussian pyramid image, represents that the convolution operation realizes Gaussian filtering, represents downsampling; The Gaussian template is as follows: Perform convolution operation and downsampling on the image using a Gaussian template. The specific formula is: Among them, x, y represents the position of the pixel where the image is located, is the Gaussian template, m, n represents the position of the template coefficient, represents the image after reverse translation and downsampling at an interval of 2, represents the convolution operation of the Gaussian template on the layer of the Gaussian pyramid image and the resulting layer of the low-frequency Gaussian pyramid image after downsampling; Perform downsampling on the convolved image at an interval of 2 to obtain an image with 1 / 2 of the original size; Perform Gaussian template convolution on the downsampled image again, and then perform downsampling on it to obtain an image with a size of 1 / 2 of the original size n of the image; Repeat the above steps to obtain Gaussian pyramid images of different scales.

3. The image denoising method based on a pyramid according to claim 1, characterized in that The removal of the noise contained in the Gaussian pyramid images of each scale through the fractional integral algorithm includes the following steps: Derive the difference expression through the Gumumwald—letnikow fractional differential definition, and sequentially obtain the fractional integral formula and the fractional integral template; After traversing the entire Gaussian pyramid image with the given fractional integral template, obtain the denoised Gaussian pyramid image; Among them, , is a fractional-order integral filtering template, where m and n represent the positions of the template coefficients, M represents the number of rows of the image, N represents the number of columns of the image, x, y represents the pixel position of the image, represents the noisy Gaussian pyramid image to be processed, is the Gaussian pyramid image after denoising using fractional-order integration; Starting from the top layer, repeat the above steps to obtain denoised Gaussian pyramid images of different scales.

4. The image denoising method based on a pyramid as claimed in claim 1, wherein, Starting from the top layer of the denoised Gaussian pyramid images, perform upsampling and Gaussian filtering step by step to construct Laplacian pyramid images of different scales, which specifically includes the following steps: Enlarge the denoised Gaussian pyramid image by a factor of two in each direction, and fill the newly added rows and columns with 0 to achieve upsampling; Perform convolution on the upsampled Gaussian pyramid image using the same kernel as Gaussian filtering to obtain an approximation of the newly added pixels, that is, the predicted image; Subtract the previous layer image from the current predicted image to obtain the Laplacian pyramid image; Repeat the above steps to obtain the Laplacian pyramid image.

5. The image denoising method based on a pyramid as claimed in claim 4, wherein, The above upsampling and Gaussian filtering process is: Among them, is a Gaussian template, is the -layer denoised image of the Gaussian pyramid, represents the implementation of Gaussian filtering through convolution operation, represents the upsampling of the -layer denoised Gaussian pyramid image, represents the predicted image obtained by performing convolution operation on the upsampled image using the Gaussian template.

6. The image denoising method based on a pyramid as claimed in claim 5, wherein Perform convolution on the upsampled Gaussian pyramid image using the same Gaussian filtering kernel as when constructing the Gaussian pyramid image. The calculation formula is as follows: Among them, is a Gaussian template, where m and n are the positions of the template coefficients, is the upsampling and reverse translation at an interval of 2 of the image after denoising by the -th layer Gaussian pyramid, represents the convolution operation of the upsampled image using the Gaussian template, and the obtained -th layer predicted image , where x and y are the pixel positions of the image.

7. The image denoising method based on a pyramid according to claim 6, wherein The subtraction of the previous layer image from the current predicted image to obtain the Laplacian pyramid image has the following calculation formula: Subtract the Gaussian pyramid image of the th layer from the predicted image of the th layer to obtain the Laplacian pyramid image of the th layer .

8. A pyramid-based image denoising method according to claim 1, characterized in that, Removing the salt-and-pepper noise and impulse noise contained in the Laplacian pyramid images of each scale through median filtering specifically includes the following steps: Constructing a Laplacian pyramid structure; Adding median filtering to the Laplacian pyramid structure to remove salt-and-pepper noise and impulse signals, which includes the following steps: Obtaining each pixel point of the Laplacian pyramid image; Sorting the grayscales of all pixels within a small window centered on a certain pixel point from smallest to largest; Taking the middle value of the sorting result as the grayscale value of this pixel; Outputting the Laplacian pyramid image after grayscale value sorting.

9. A pyramid-based image denoising method according to claim 1, characterized in that, Using the fractional integral algorithm to filter other noises for the Laplacian pyramid images of each scale after filtering salt-and-pepper noise and impulse noise, including the following steps: Deriving a difference expression through the Gumumwald—letnikow fractional derivative definition, and sequentially obtaining a fractional integral formula to obtain a fractional integral template; After traversing the entire image with the given fractional integral template, a denoised image can be obtained; Among them, , is a fractional-order integral filtering template, where m and n represent the positions of the template coefficients, M represents the number of rows of the image, N represents the number of columns of the image, x, y represents the pixel position of the image, represents the noisy Laplacian pyramid image to be processed, is the denoised Laplacian pyramid image after using fractional-order integral denoising; Repeating the above steps to obtain Laplacian pyramid denoised images of different scales.

10. A pyramid-based image denoising method according to claim 9, characterized in that, Constructing a reconstruction template, starting from the highest layer of the denoised Gaussian pyramid image for upsampling, and obtaining a new image through the reconstruction template after upsampling, adding the new image to the denoised Laplacian pyramid image of the previous layer to obtain the reconstructed image of the current layer pyramid, specifically including: Constructing a reconstruction template: The calculation process for obtaining the new image is as follows: Among them, , is a reconstruction template, where m and n represent the template coefficient positions, M represents the number of rows of the image, and N represents the number of columns of the image. x, y represents the pixel position of the new image. is the upsampling with an interval of 2 and reverse translation of the image after denoising by the -layer Gaussian pyramid. represents the -layer new image. Among them, the layer reconstruction image calculation expression is: Among them, represents the newly added image of the th layer, represents the Laplacian pyramid denoised image of the th layer, and is the reconstructed image of the

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