CN111696061A - Noise image reconstruction method with fusion of space domain and transform domain - Google Patents
Noise image reconstruction method with fusion of space domain and transform domain Download PDFInfo
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Abstract
The noise image reconstruction method fusing the space domain and the transform domain provided by the invention fuses the two improved methods on the basis of respectively improving and optimizing the bilateral filtering of the space domain and the wavelet transform shrinkage of the transform domain, thereby not only well removing the image noise, but also keeping the detail information and the edge characteristics of the image and simultaneously not generating the ringing phenomenon. Through multiple tests and demonstration, 3 iterations are the optimal iteration times of the algorithm, the result obtained by the algorithm obtains an image denoising effect better than that obtained by the BM3D algorithm, less low-frequency noise exists, the algorithm is simpler to realize, image detail information is enhanced while image edge characteristic information is kept, the identification degree of the image is greatly improved, a noise image is subjected to high-quality denoising reconstruction, and the reconstructed image has a better visual effect.
Description
Technical Field
The invention relates to a noise image reconstruction method, in particular to a noise image reconstruction method fusing a space domain and a transform domain, and belongs to the technical field of noise image denoising reconstruction.
Background
With the rapid development of computer and network information technologies, the society has entered a highly information-oriented big data stage, and the forms of information include various forms such as data, images, videos, and the like. Statistically, 65% of various information data obtained by human beings are derived from images. The digital image technology has been greatly developed and extended to various fields, playing a vital role. For example, doctors diagnose diseases of patients through B-ultrasonic images, geological exploration teams analyze mineral distribution through satellite remote sensing images, traffic polices monitor and manage urban traffic through monitoring videos, and the like. Currently, digital image processing has become a current research hotspot and popular application technology.
Digital images are susceptible to various factors during transmission and reception, so that the captured images contain noise for the most part. Noise is introduced in the image acquisition process because the sensor is influenced by the environment, noise is introduced in the image transmission process because the used transmission channel is interfered, and noise is introduced in the imaging system because of the imaging mechanism of the imaging system. The image noise can not only blur the digital image and seriously reduce the image quality, but also finally affect the acquisition of image information by people. Meanwhile, the digital image denoising is used as a preprocessing step of the image, and if the denoising effect is not good, some subsequent steps and further applications of the image processing, such as image segmentation, image recognition and image description, are also affected. Therefore, the denoising processing of the digital image is particularly important, and the method can help people to more accurately obtain the required image characteristic information, so that the method can be applied to various fields of geoscience, medicine, aerospace, physics, city management and the like. Therefore, the method effectively reduces the image noise, enhances the visual effect, improves the quality of the digital picture, and has important technical research and practical application values.
Image noise is random signal interference to digital images during acquisition and transmission, and prevents people from understanding information of source images. The digital image is affected by various factors such as equipment and surrounding environment in each acquisition link and is polluted by noise. The image noise is unpredictable, is a random error, can be considered as a multi-dimensional random process by analyzing the image noise, and can be described by using a probability distribution function and a probability density distribution function, but the method is only a theoretical idea and is very complex in practical application, so that the noise is described by using a relatively simple mean variance and a correlation function. Noise greatly affects people to extract information from images, so it is necessary to remove noise before processing the images. The current digital image system converts two-dimensional image signals into one-dimensional image signals through freezing and scanning input images, processes, stores, transmits and the like, and finally displays the signals on a terminal, wherein noise is subjected to complex changes as images.
The influence of various factors in the process of acquiring and transmitting images is the key source of digital image noise, and in the process of acquiring images by a sensor, ambient environmental conditions such as air humidity, illumination intensity and sensor quality can have great influence on the acquisition of the images, so that a great deal of noise is brought into the images. In the image transmission process, a transmission channel is the largest factor generating noise, and the transmission channel is interfered by illumination or atmospheric factors to greatly influence the transmitted image. Some electronic components also cause noise, and for example, resistors, vacuum devices, photocells, etc. generate various image noises such as thermal noise, shot noise, etc. Also optical noise in the image is caused by various optical phenomena. The source of image noise is very extensive and difficult to avoid.
Various image denoising algorithms are proposed according to different characteristics of images and noise. Such as a median filtering algorithm, a mean filtering algorithm, a denoising algorithm based on independent component analysis, a method based on partial differential equations, a denoising algorithm based on wavelet transformation, etc. in the prior art. Image denoising algorithms can be roughly classified into two categories according to different algorithm processing spaces: spatial domain based algorithms and transform domain based algorithms.
The spatial domain algorithm is processed on the pixel points of the image, such as a median filtering algorithm, a non-local mean filtering algorithm, and the like. The algorithm based on the transform domain is that firstly, an image is transformed from a space domain to the transform domain through Fourier transform, wavelet transform and the like in the prior art, then, different properties of the image signal and a noise signal in the transform domain are utilized to further process a transform coefficient to eliminate noise, and finally, the image is reconstructed by inverse transformation. In the transform domain, due to some characteristics of the wavelet transform, the wavelet transform has the unique advantage of denoising algorithm, the wavelet transform is a signal processing mode based on the Fourier transform in the prior art, the defects and the defects of the Fourier transform are overcome, and the time-frequency analysis can be carried out on signals in the wavelet domain. Meanwhile, the wavelet transform also has characteristics that the fourier transform does not have, such as diversity of wavelet base, decorrelation of the wavelet transform, multi-resolution analysis based on the wavelet transform and the like, and the characteristics enable the wavelet transform to have great advantages in image denoising.
In the prior art, the Mallat algorithm introduces a multi-resolution analysis idea into wavelet transformation, performs multi-resolution decomposition and reconstruction on signals, proves that the wavelet transformation can detect the distribution and the intensity of singular points of the signals, can remove the modulus maximum point corresponding to noise according to different characteristics of wavelet coefficients on various scales after the wavelet transformation of the signals and the noise, retains the modulus maximum point generated by the signals, and then reconstructs the wavelet coefficients to restore the signals. According to the correlation of wavelet coefficients of signals and noise in different decomposition scales, the prior art also provides a spatial correlation filtering denoising method and a general critical value-based wavelet denoising method, which are theoretically optimal critical values, but the practical application effect is not consistent with the theory, the critical value is not well processed, and the denoising effect is not ideal.
In the prior art, a soft critical value denoising method and a hard critical value denoising method based on wavelet shrinkage are proposed by further processing the critical value, but the soft critical value function and the hard critical value function have respective obvious defects. The soft critical value function and the hard critical value function are combined to generate a semi-soft critical value function, so that the defects of discontinuity of the soft critical value function and the hard critical value function and excessive elimination of wavelet coefficients are overcome.
In the prior art, a Bayesian Shrink critical value denoising method appears later, and the Bayesian Shrink critical value is based on the premise that the wavelet coefficient of a noise-free image obeys Gaussian distribution, then an optimal critical value which is self-adaptively adjusted according to the image statistical characteristics is selected according to a minimized Bayesian risk function, and finally the critical value is softened to obtain a better image denoising effect. However, the bayesian shrink critical value is based on the wavelet coefficient independence as a premise, the correlation characteristic between coefficients is not considered, the denoising effect is still not as satisfactory as possible, and the time complexity of the algorithm is relatively high.
In summary, the present invention is intended to solve the following problems, in view of some of the drawbacks of the prior art:
firstly, in the prior art, the spatial domain bilateral filtering keeps the image edge with strong contrast, but noise is easily introduced when the image detail with weak contrast is kept; the transform domain wavelet transform shrinkage keeps the image details with weak contrast, but generates ringing phenomenon, and the two main methods have obvious defects, so that the problem that a method for respectively improving and optimizing fusion for bilateral filtering of a spatial domain and the transform domain wavelet transform shrinkage is lacked is solved, the image noise cannot be well removed, the detail information and the edge characteristics of the image cannot be kept, and the ringing phenomenon cannot be generated. The prior art can not solve the problems simultaneously, and has the disadvantages of large limitation and low application value.
Secondly, the selection of the iteration times of the denoising method in the prior art is not scientific, the selection of the iteration times is excessive, the improvement of the image denoising effect is small, the calculation complexity of the algorithm is increased, the selection of the iteration times is too small, the image denoising effect is too poor, the problem of better denoising precision in all aspects is solved, the algorithm time is generally prolonged, and the two problems are mutually contradictory.
Thirdly, the problem that the wavelet shrinkage critical value cannot be well processed due to poor smoothing effect of the binocular stereo vision matching method in the prior art is solved, the wavelet shrinkage critical value is selected to be too small, the wavelet coefficient with low amplitude is not completely removed, the denoising effect of the image processed by the critical value is not obvious, and excessive noise remains; if the wavelet shrinkage critical value is estimated to be too large, the detail information of the image is lost while noise is removed, so that the image obtained after coefficient reconstruction becomes fuzzy, the edge detail characteristics of the image are lost, and larger deviation is caused, and the visual effect of the image is not ideal. The incorrect selection of the wavelet shrinkage critical value in the prior art has great influence on the subsequent work of image denoising.
Fourthly, the hard critical value and soft critical value method in the prior art has obvious defects in image denoising, the soft critical value function is fuzzy in the whole image, the image processed by the hard critical value function can well keep the detailed part of the image, but the edge is not ideal, and the continuity ratio of the image is poor due to the characteristics of the hard critical value function; the critical value function in the prior art can not be satisfactorily reserved in details or edge parts, the recovery effect after image denoising is poor, the algorithm complexity is high, the realization is not easy, the effect is poor, and the robustness of the algorithm is poor.
Disclosure of Invention
Aiming at the defects of the prior art, the noise image reconstruction method fusing the space domain and the transform domain provided by the invention fuses the improved two methods on the basis of respectively improving and optimizing the bilateral filtering of the space domain and the wavelet transform shrinkage of the transform domain, thereby not only well removing the image noise, but also keeping the detail information and edge characteristics of the image and simultaneously not generating the ringing phenomenon. Through multiple tests and demonstration, 3 iterations are the optimal iteration times of the algorithm, the result obtained by the algorithm obtains an image denoising effect better than that obtained by the BM3D algorithm, less low-frequency noise exists, the algorithm is simpler to realize, image detail information is enhanced while image edge characteristic information is kept, the identification degree of the image is greatly improved, a noise image is subjected to high-quality denoising reconstruction, and the reconstructed image has a better visual effect.
In order to achieve the technical effects, the technical scheme adopted by the invention is as follows:
a noise image reconstruction method with fusion of a space domain and a transform domain adopts bilateral filtering in the space domain, wavelet transform and contraction are adopted in the transform domain, the bilateral filtering in the space domain keeps the image edge with strong contrast, and the wavelet transform contraction in the transform domain keeps the image detail with weak contrast;
on the basis of respectively improving and optimizing the bilateral filtering of a space domain and the wavelet transform shrinkage of a transform domain, the invention fuses two improved methods, and the flow steps are as follows:
firstly, carrying out spatial domain bilateral filtering processing on a noise image, wherein an image obtained after bilateral filtering processing is a strong-contrast image;
secondly, subtracting the original noise image from the strong contrast image to obtain a weak contrast image,
thirdly, performing wavelet transformation processing on the image with the weak contrast to obtain a wavelet transformation image;
fourthly, performing wavelet shrinkage processing on the wavelet transformed image to obtain a wavelet shrinkage image;
fifthly, reconstructing the wavelet coefficient to obtain a wavelet reconstructed image;
sixthly, adding the wavelet reconstruction image and the strong contrast image to obtain a final de-noised image and finish the reconstruction of the noise image;
and carrying out three iterations on the whole algorithm process, taking the denoising image obtained in the previous time as a guide image, and calculating a filter kernel of bilateral filtering by using the denoising image obtained in the previous time for bilateral filtering in the next iteration.
Further, in the whole algorithm process, the standard deviation a of Gaussian white noise is 26, the radius b of a bilateral filtering window is 16, and the standard deviation a of geometric measure is 16s6.8, standard deviation of gray scale measure abThe wavelet transform adopts db8 wavelet as wavelet function, the decomposition layer number is 3, the wavelet shrinkage critical value adopts the wavelet shrinkage critical value related to the decomposition layer number of the wavelet, the wavelet shrinkage critical value function adopts the constant non-oscillation critical value function provided by the invention, the best image denoising effect can be obtained after the algorithm flow is iterated for three times, each iteration can further denoise, only micro deviation is introduced, the iteration times are continuously increased after the iteration is iterated for three times, the image denoising effect is improved very little, and the algorithm calculation complexity is increased on the contrary.
The method for reconstructing the noise image with the fusion of the space domain and the transform domain further comprises the steps of carrying out wavelet transformation and wavelet shrinkage on a low-contrast image after carrying out bilateral filtering on the noise image to obtain an image with strong contrast according to typical white Gaussian noise denoising, and providing a wavelet shrinkage critical value associated with the number of wavelet decomposition layers to weaken the influence of the total number of wavelet coefficients and associate the wavelet shrinkage critical value with the number of wavelet decomposition layers when selecting the critical value of the wavelet shrinkage; when selecting the wavelet shrinkage critical value function, a constant non-oscillation critical value function is provided on the basis of the soft critical value function and the hard critical value function; and finally, performing iterative substitution on the whole algorithm process, and eliminating the ringing phenomenon caused by wavelet shrinkage by utilizing bilateral filtering.
The method for reconstructing the noise image with the fusion of the space domain and the transformation domain comprises the following steps that in the process of carrying out space domain bilateral filtering processing on the noise image, a bilateral filter is realized in a weighting mode, the distance between image pixels and the intensity between the pixels are considered, the weighting coefficient of the bilateral filter is the product of two filtering kernels, and a first filtering kernel function is determined by the geometric distance between the adjacent pixels of the central sampling pixel and is called as the space geometric measure; the second filtering kernel function is determined by the difference between the gray value of the central pixel and the gray value of the neighboring pixels, and is called gray measurement;
the bilateral filter fully protects the image edge while smoothing the image, the gray value of the pixel processed at present is the weighted average of the neighborhood pixels after filtering, the weighting coefficient is equal to the product of the space geometric measure and the gray measure, and the filtering output of the central pixel point is influenced only by the neighborhood pixels with close space distance and small gray value difference.
A noise image reconstruction method fusing a space domain and a transform domain further sets the gray value of an image A at a pixel point c (x, y) as AcAnd the gray value of the image B obtained after filtering at the pixel point c (x, y) is BcThe formula of bilateral filtering is:
Dc＝BEBF
in the above formula, D is the neighborhood pixel of the center pixel c, I is the set of neighborhood pixels, DcFor bilateral filtering kernels, BEIs a geometric measure, BFIs gray scaleMeasure, the expression is:
in the expression, E is a geometric measure standard deviation obtained through a Gaussian function, F is a gray measure standard deviation obtained through the Gaussian function, and the two determine the shapes of two filtering kernel functions;
each pixel point of the image replaces the original gray value of the pixel point by the average value of pixels with similar geometric distances in the neighborhood and small gray value difference, the gray value of the pixel point changes slowly in the area containing a large amount of details, the bilateral filter is degraded into a low-pass filter, and the difference of the pixel values with weak correlation caused by noise can be weakened and eliminated by solving the average value of the pixel points in the neighborhood; in the area with severe image change, the gray value similarity factor of the pixel point on the same side of the edge approaches 1, the gray value similarity factor of the pixel point on the different side of the edge approaches 0, and at the moment, after bilateral filtering, the gray value of the pixel point to be processed on the edge of the image is replaced by the gray average value of the pixel points with similar gray in the neighborhood;
two parameters E and F of the bilateral filter directly determine the integral smoothness degree of the image, respectively express the size and contrast of the kept image characteristics, and are key factors for determining the performance of the bilateral filter; namely, when the E value is larger, the neighborhood pixel points far away from each other can also influence the central pixel point, and when the F value is larger, the gray value of the pixel points in the neighborhood can also act on the output of the central pixel point even if the difference between the gray value of the pixel points in the neighborhood and the central pixel is larger;
the larger the values of the parameters E and F are, the stronger the smoothing effect of the bilateral filter is; when the values of the two parameters E and F are close to 0, the value of the bilateral filter kernel approaches to 0, and the bilateral filter cannot generate a smoothing effect on an input image; the parameter F controls the degree of the bilateral filter for keeping the image edge, the change of the parameter F can influence the edge characteristic of the image more than that of the parameter E, and the parameter E determines the smoothness of the bilateral filter to the image detail;
the denoising performance of the bilateral filter is reduced along with the increase of the filtering radius, and when the filtering radius is 3, the bilateral filtering denoising image obtains the best visual effect.
The method for reconstructing the noise image with the fusion of the space domain and the transform domain further comprises the following steps that the most key of wavelet shrinkage denoising is the estimation of a wavelet shrinkage critical value, the number of wavelet coefficients influences the performance of the wavelet shrinkage critical value and the effect of the wavelet shrinkage critical value needs to be weakened; the low frequency sub-band in the image contains key information of the image, while the image noise exists more in the high frequency sub-band, a critical value larger than the low frequency sub-band is selected in the high frequency sub-band, and H is increased along with the increase of the decomposition layer number kkIs correspondingly reduced, HkIs the adjustment coefficient of the k layer in the wavelet domain.
The invention provides a noise image reconstruction method with fusion of a space domain and a transform domain, and further provides a wavelet shrinkage critical value associated with wavelet decomposition layer number aiming at the estimation of the wavelet shrinkage critical value, wherein the critical value formula is as follows:
wherein J is the wavelet shrinkage threshold, anIs the standard deviation of noise, N is the number of wavelet coefficients, HkIs the adjustment coefficient of the k-th layer in the wavelet domain, ak,fIs the standard deviation, e, of the noise-free image f at the k-th layer after wavelet transform1,e2As adjustable parameters, the sum of the two adjustable parameter parameters is 1, and for the wavelet shrinkage critical value function of the related wavelet decomposition layer number, the standard deviation of noise and the standard deviation of a noise-free image f at the k-th layer after wavelet transformation, and the standard deviation a of noise are required to be obtainednThe following formula is given:
wherein the content of the first and second substances,
is the wavelet coefficient of a noisy image,
taking wavelet coefficient of noise image in highest sub-band
To find the standard deviation a of the noisen；
Wavelet coefficients of noisy images
The sum of the wavelet coefficients represented as a noise-free image and the noise wavelet coefficients, i.e.:
according to the linear characteristic of wavelet transformation, the relation among the standard deviations of the wavelet coefficient of the noise image, the wavelet coefficient of the noiseless image and the noise wavelet coefficient on the kth layer is obtained, namely:
ai，k 2＝af，k 2+an 2
standard deviation a of noise image wavelet coefficient at k-th layeri，kWavelet coefficient at k-th layer capable of passing image i
To obtain:
wherein M and n are the number of rows and columns of wavelet coefficients, and M is the total number of wavelet coefficients, and the standard deviation of the wavelet coefficients of the k-th layer of the noiseless image is obtained as follows:
thus, a wavelet shrinkage threshold value J associated with the number of wavelet decomposition layers is calculated.
The method for reconstructing the noise image with the fusion of the space domain and the transform domain further comprises the steps of firstly estimating a proper critical value in a wavelet denoising algorithm, and then obtaining a wavelet coefficient through a critical value function, wherein the wavelet shrinkage algorithm comprises a hard critical value method and a soft critical value method, and the hard critical value method has the following formula:
in the formula, hk，eExpressing the wavelet transform coefficients of the noisy image, the critical value is denoted by J, Ghard(hk，e) Expressing the function value of a hard critical value, eliminating the coefficient smaller than the critical value in all the coefficient amplitudes after wavelet transformation, and keeping the wavelet domain coefficient of which the coefficient amplitude is larger than the critical value unchanged;
the mathematical expression for the soft threshold function is as follows:
in the formula, sgn (h)k，e) Expressing the wavelet coefficients hk，eSign function of Gsoft(hk，e) In order to correspond to wavelet coefficients after soft thresholding, the soft threshold function is to eliminate coefficients whose wavelet coefficient magnitudes are less than the threshold, but not to retain wavelet coefficients whose magnitudes are greater than the threshold magnitude, but to retain their difference from the threshold absolute value.
The method for reconstructing the noise image with the fusion of the spatial domain and the transform domain further improves the following steps aiming at the defects of the hard critical value method and the soft critical value method:
threshold function method one, the threshold function is shown as follows:
the threshold function is set continuously at-J and J, no oscillation is generated at the abrupt change position when the image is reconstructed, and the difference between the wavelet coefficient subjected to threshold processing and the real wavelet coefficient is along with the wavelet coefficient hk，eGradually decreases and finally approaches to the real wavelet coefficient, but the first critical value function method has no adjusting factor;
in the second threshold function method, a threshold function between the hard threshold and the soft threshold can be obtained by appropriately changing the parameter p, but the second threshold function method does not solve the constant deviation problem of the wavelet coefficients well.
The invention provides a noise image reconstruction method with fusion of a space domain and a transform domain, and further provides a constant vibration-free critical value function by combining a critical value function method I and a critical value function method II:
adjustable parameters p and q are added into a constant vibration-free critical value function, the constant vibration-free critical value function is continuous at-J and J, no vibration is generated during image reconstruction, and the constant vibration-free critical value function is used
Is an asymptotic line, and follows with hk，eThe wavelet coefficient after the critical value processing gradually approaches to the real wavelet coefficient, so that the problem of constant deviation of the wavelet coefficient is solved; by adjusting the parameters p and q, the constant no-vibration critical value function can be adjusted between the soft critical value and the hard critical value, and the flexibility is better.
The noise image reconstruction method with the fusion of the space domain and the transformation domain has the advantages that the noise image reconstruction method is more accurate,
compared with the prior art, the invention has the advantages and innovation points that:
the method for reconstructing the noise image with the fused space domain and transform domain adopts bilateral filtering in the space domain, adopts wavelet transform and contraction in the transform domain, and keeps the image edge with strong contrast, but easily introduces noise when keeping the details with weak contrast of the image; the invention provides a noise image reconstruction method integrating a space domain and a transform domain, which integrates the improved two methods on the basis of respectively improving and optimizing the bilateral filtering of the space domain and the wavelet transform shrinkage of the transform domain and can well remove image noise, retain the detail information and the edge characteristics of the image and simultaneously avoid the ringing phenomenon.
And secondly, according to the noise image reconstruction method with the fusion of the spatial domain and the transform domain, through multiple experimental demonstration, 3 times of iteration is the optimal iteration times of the algorithm, the iteration times are continuously increased, the image denoising effect is improved slightly, and the calculation complexity of the algorithm is increased. The result obtained by the algorithm of the invention has better image denoising effect than that of the BM3D algorithm, less low-frequency noise exists, the algorithm is simpler to realize, the image detail information is enhanced while the image edge characteristic information is kept, the image identification degree is greatly improved, the noise image is high-quality denoised and reconstructed, and the reconstructed image has better visual effect.
Thirdly, the invention provides a wavelet shrinkage critical value associated with the wavelet decomposition layer number, which solves the problems that the wavelet shrinkage critical value is selected too small, the wavelet coefficient of low amplitude is not completely removed, the image denoising effect after critical value processing is not obvious, and excessive noise remains; if the wavelet shrinkage critical value is estimated to be too large, the detail information of the image is lost while noise is removed, so that the image obtained after coefficient reconstruction becomes fuzzy, the edge detail characteristics of the image are lost, and large deviation is caused, and the visual effect of the image is not ideal. The accurate selection of the wavelet shrinkage critical value has an important effect on the subsequent work of image denoising.
Fourthly, the noise image reconstruction method fusing the space domain and the transform domain improves the method aiming at the obvious defect of the hard critical value and the soft critical value in image denoising, provides a constant vibration-free critical value function, and through comparison, the worst noise image reconstruction effect is the soft critical value function, and the whole image is fuzzy; the image processed by the hard critical value function can better keep the detail part of the image, but is not ideal at the edge, and the continuity ratio of the image is poor due to the characteristic of the hard critical value function; the constant non-oscillation critical value function provided by the invention is better preserved in detail or edge part, better recovered after image denoising, and more excellent in image reconstruction effect and visual effect.
Drawings
FIG. 1 is a flow chart of the method for reconstructing a noise image by fusing a spatial domain and a transform domain according to the present invention.
Fig. 2 is a comparison diagram of the effects of three iterations of the present invention.
Detailed Description
The technical solution of the method for reconstructing a noise image by fusing a spatial domain and a transform domain provided by the present invention is further described below with reference to the accompanying drawings, so that those skilled in the art can better understand the present invention and can implement the present invention.
According to the noise image reconstruction method with the fusion of the space domain and the transform domain, bilateral filtering is adopted in the space domain, wavelet transformation and contraction are adopted in the transform domain, the bilateral filtering in the space domain keeps the image edge with strong contrast, and noise is easy to introduce when the weak contrast details of the image are kept; the invention provides a noise image reconstruction method with the fusion of a space domain and a transform domain on the basis of respectively improving and optimizing the bilateral filtering of the space domain and the wavelet transform shrinkage of the transform domain, and obtains better image denoising effect. As shown in fig. 1, the method of the present invention comprises the following steps:
firstly, carrying out spatial domain bilateral filtering processing on a noise image, wherein an image obtained after bilateral filtering processing is a strong-contrast image;
secondly, subtracting the original noise image from the strong contrast image to obtain a weak contrast image,
thirdly, performing wavelet transformation processing on the image with the weak contrast to obtain a wavelet transformation image;
fourthly, performing wavelet shrinkage processing on the wavelet transformed image to obtain a wavelet shrinkage image;
fifthly, reconstructing the wavelet coefficient to obtain a wavelet reconstructed image;
and sixthly, adding the wavelet reconstruction image and the strong contrast image to obtain a final de-noised image, and completing reconstruction of the noise image.
The invention carries out three times of iteration on the whole algorithm process, takes the denoising image obtained in the previous time as a guide image, and calculates the filter kernel of bilateral filtering by using the denoising image obtained in the previous time for bilateral filtering in the next iteration.
In the whole algorithm process, the standard deviation a of Gaussian white noise is 26, the radius b of a bilateral filtering window is 16, and the standard deviation a of geometric measure is 16s6.8, standard deviation of gray scale measure abThe wavelet transform uses db8 wavelet as the wavelet function, the number of decomposition layers is 3 layers, and the wavelet shrinkage threshold and the threshold function use the threshold function of the present invention. Inputting a sine wave modulated rectangular function, adding white Gaussian noise, and performing bilateral filtering and wavelet shrinkage on a result graph, wherein the standard difference value of the gray measurement of the first bilateral filtering is large, the approximate frame of the rectangular function is kept, and other details of a signal are smoothly removed; the following wavelet shrinkage repairs the previously lost details without affecting the rectangular frame, but introduces ringing; the value of the standard difference of the second iteration gray level measurement is small, although the ringing phenomenon is introduced by the previous wavelet transformation, the bilateral filtering is regarded as noise and is filtered and removed; no new ringing is introduced after wavelet shrinkage. Therefore, the bilateral filtering can eliminate the ringing phenomenon introduced by the wavelet shrinkage.
Through multiple experimental demonstration, the best image denoising effect can be obtained after the algorithm flow is iterated for three times, and each iteration can further denoise and only introduce micro deviation. Fig. 2 is an image denoising effect graph and PSNR comparison of three iterations:
as can be seen from fig. 2, after the first iteration denoising, although the image denoising effect is good, excessive noise still remains, after the second iteration processing, the image denoising effect is obviously improved, the PSNR value and the visual effect are very excellent, and after the third iteration, the image denoising effect is not very obvious, but the image quality can still be seen from the PSNR value to be improved to a certain extent, and through multiple experimental demonstrations, 3 iterations are the optimal iteration number of the algorithm, the iteration number is continuously increased, the image denoising effect is improved very little, and the algorithm computation complexity is increased conversely.
The algorithm is subjected to experimental simulation, the obtained experimental result is compared with the image processed by the BM3D algorithm, the algorithm has better image denoising effect than that of the BM3D algorithm, less low-frequency noise exists, the algorithm is simpler to realize, image detail information is enhanced while image edge characteristic information is kept, the identification degree of the image is greatly improved, the noise image is subjected to high-quality denoising reconstruction, and the reconstructed image has better visual effect.
Aiming at typical white Gaussian noise removal, the noise image reconstruction method with the fusion of the space domain and the transform domain provided by the invention fuses the two improved methods on the basis of respectively improving and optimizing the bilateral filtering of the space domain and the wavelet transform shrinkage of the transform domain. After the noise image is subjected to bilateral filtering to obtain an image strong contrast image, wavelet transformation and wavelet shrinkage are carried out on the low contrast image. The threshold value of wavelet shrinkage is selected, and according to the advantages and disadvantages of the general threshold value, the threshold value of wavelet shrinkage which is related to the wavelet decomposition layer number is provided, the influence of the total number of wavelet coefficients is weakened, and the threshold value is related to the wavelet decomposition layer number. When the wavelet shrinkage critical value function is selected, a constant shock-free critical value function is provided on the basis of the soft critical value function and the hard critical value function, and the defects caused by the soft critical value function and the hard critical value function are avoided while the advantages of the soft critical value function and the hard critical value function are inherited. And finally, iterating the whole algorithm process, and eliminating ringing phenomena caused by wavelet shrinkage by utilizing bilateral filtering.
One, two-sided filtering process in space domain
The first step, in the process of carrying out spatial domain bilateral filtering processing on a noise image, a bilateral filter is realized in a weighting mode and is regarded as the combination of neighborhood filtering and Gaussian filtering, the distance between image pixels and the intensity between the pixels are considered, the weighting coefficient of the bilateral filter is the product of two filtering kernels, and a first filtering kernel function is determined by the geometric distance between the neighborhood pixels of a central sampling pixel and is called as spatial geometric measure; the second filter kernel is determined by the difference between the gray value of the central pixel and the gray value of the neighboring pixels, called the gray measure.
The bilateral filter fully protects the image edge while smoothing the image, the gray value of the currently processed pixel after filtering is the weighted average of the neighborhood pixels, the weighting coefficient is equal to the product of the space geometric measure and the gray measure, the pixel point at the image edge mutation position is protected, and the filtering output of the central pixel point is influenced only by the neighborhood pixels with close space distance and small gray value difference.
Let the gray value of the image A at the pixel point c (x, y) be AcAnd the gray value of the image B obtained after filtering at the pixel point c (x, y) is BcThe formula of bilateral filtering is:
Dc＝BEBF
in the above formula, D is the neighborhood pixel of the center pixel c, I is the set of neighborhood pixels, DcFor bilateral filtering kernels, BEIs a geometric measure, BFIs a measure of the gray level, the expression is:
in the expression, E is a geometric measure standard deviation obtained through a Gaussian function, F is a gray measure standard deviation obtained through the Gaussian function, the two determine the shapes of two filtering kernel functions, when the value is too large, bilateral filtering is degraded into mean filtering, and when the value is too small, the smoothing effect of the filter is weakened.
Each pixel point of the image replaces the original gray value of the pixel point by the average value of pixels with similar geometric distances in the neighborhood and small gray value difference, the smoothness of a spatial domain is enhanced by bilateral filtering, the gray value of the pixel point changes slowly in an area containing a large amount of details, the bilateral filter is degraded into a low-pass filter, and the difference of the pixel values with weak correlation caused by noise can be weakened and eliminated by solving the average value of the pixel points in the neighborhood; in the area with severe image change, the gray value similarity factor of the pixel point on the same side of the edge approaches 1, the gray value similarity factor of the pixel point on the different side of the edge approaches 0, at the moment, after bilateral filtering, the gray value of the pixel point to be processed on the edge of the image is replaced by the gray average value of the pixel point with similar gray in the neighborhood, which is the characteristic of the gray value similarity factor, so that the bilateral filter can maintain the edge of the image while denoising.
Two parameters E and F of the bilateral filter in the formula directly determine the integral smoothness degree of the image, respectively express the size and contrast of the kept image characteristics, and are key factors for determining the performance of the bilateral filter. By adjusting both the parameters E and F, a trade-off can be made between excessive blurring of image features and leaving excessive amounts of discontinuities in the smoothed image. Namely, when the E value is larger, the neighborhood pixels far away from each other can also influence the center pixel, and when the F value is larger, the gray value of the pixels in the neighborhood can also act on the output of the center pixel even if the difference between the gray value of the pixels in the neighborhood and the center pixel is larger.
The larger the values of the parameters E and F are, the stronger the smoothing effect of the bilateral filter is; when the values of the two parameters E and F are close to 0, the value of the bilateral filter kernel approaches to 0, and the bilateral filter cannot generate a smoothing effect on the input image. The parameter F controls the degree of the bilateral filter for keeping the image edge, the change of the parameter F can influence the edge characteristic of the image more than that of the parameter E, the gray scale kernel function curve approaches to a straight line along with the continuous increase of the parameter F, and the bilateral filter is equivalent to be degraded into a Gaussian filter. And the parameter E determines the smoothness of the bilateral filter to the image details, and the proper value of the parameter F enables the bilateral filter to effectively and smoothly remove the image noise and simultaneously protect the edge details of the image.
The weighting coefficient of the bilateral filter is continuously and dynamically adjusted along with the change of the difference between the geometric distance between the pixels and the gray value. When the geometric distance or the gray difference between the central filtering point and the neighborhood pixel point is increased, the bilateral filtering effect is weakened, the edge mutation of the image means the sharp change of the pixel gray value, and the bilateral filtering achieves the effect of keeping the edge.
The denoising performance of the bilateral filter is reduced along with the increase of the filtering radius, and when the filtering radius is 3, the bilateral filtering denoising image obtains the best visual effect image.
Improvement of wavelet shrinkage critical value
The most key of the wavelet shrinkage denoising is the estimation of a wavelet shrinkage critical value, and the selection of the wavelet shrinkage critical value has great influence on the subsequent work of image denoising. The wavelet shrinkage critical value is selected to be too small, the wavelet coefficient with low amplitude is not completely removed, the image denoising effect after the critical value processing is not obvious, and excessive noise is remained; if the wavelet shrinkage critical value is estimated to be too large, the detail information of the image is lost while noise is removed, so that the image obtained after coefficient reconstruction becomes fuzzy, the edge detail characteristics of the image are lost, and large deviation is caused, and the visual effect of the image is not ideal.
The number of wavelet coefficients directly influences the performance of the wavelet shrinkage critical value and needs to weaken the function of the wavelet shrinkage critical value correspondingly; in the bayesian shrin threshold formula, the low frequency subbands in the image contain key information of the image,and the image noise exists more in the high-frequency sub-band, so a critical value larger than that of the low-frequency sub-band is selected in the high-frequency sub-band, and H is increased along with the increase of the decomposition layer number kkIs correspondingly reduced, HkIs an adjustable parameter, namely an adjusting coefficient of a k-th layer in a wavelet domain.
In summary, the present invention provides a wavelet shrinkage threshold value associated with the number of wavelet decomposition layers, wherein the threshold value formula is:
wherein J is the wavelet shrinkage threshold, anIs the standard deviation of the noise, N is the number of wavelet coefficients, ak,fIs the standard deviation, e, of the noise-free image f at the k-th layer after wavelet transform1,e2As adjustable parameters, the sum of two adjustable parameter parameters is made to be 1, and the parameter e is changed1,e2And HKThe value can freely control the critical value to be converted into a universal critical value and a Bayesian shrin critical value, the influence of the number N of wavelet coefficients on the critical value can be weakened by adjusting the parameters, the optimality of functions of the Bayesian shrin critical value can be combined, the obtained wavelet shrinkage critical value is more reasonable, and the denoising effect is better. For the wavelet shrinkage critical value function related to the wavelet decomposition layer number, the standard deviation of noise and the standard deviation a of the noise of the k-th layer of the noiseless image f after wavelet transformation and the standard deviation a of the noise need to be obtainednThe following formula is given:
wherein the content of the first and second substances,
is the wavelet coefficient of a noisy image,
taking wavelet coefficient of noise image in highest sub-band
To find the standard deviation a of the noisen。
Wavelet coefficients of noisy images
The sum of the wavelet coefficients expressed as a noise-free image and the noise wavelet coefficients, i.e.:
according to the linear characteristic of wavelet transformation, the relation among the standard deviations of the wavelet coefficient of the noise image, the wavelet coefficient of the noiseless image and the noise wavelet coefficient on the kth layer is obtained, namely:
ai，k 2＝af，k 2+an 2
the standard deviation a of the wavelet coefficient of the noise image on the k-th layer is calculated in the same way as the standard deviation of the noisei，kWavelet coefficient at k-th layer capable of passing image i
To obtain:
wherein M and n are the number of rows and columns of wavelet coefficients, and M is the total number of wavelet coefficients, and the standard deviation of the wavelet coefficients of the k-th layer of the noiseless image is obtained as follows:
thus, a wavelet shrinkage threshold value J associated with the number of wavelet decomposition layers is calculated.
Third, wavelet shrinkage critical value function
In the wavelet denoising algorithm, a suitable critical value is estimated first, and then wavelet coefficients are obtained through a critical value function. The wavelet shrinkage algorithm comprises a hard critical value method and a soft critical value method, wherein the hard critical value method has the following formula:
in the formula, hk，eExpressing the wavelet transform coefficients of the noisy image, the critical value is denoted by J, Ghard(hk，e) And expressing the function value of the hard critical value, eliminating the coefficient smaller than the critical value in all the coefficient amplitudes after the wavelet transformation, and keeping the wavelet domain coefficient of which the coefficient amplitude is larger than the critical value unchanged, which is a hard critical value function method.
The mathematical expression for the soft threshold function is as follows:
in the formula, sgn (h)k，e) Expressing the wavelet coefficients hk，eSign function of Gsoft(hk，e) The soft threshold function also eliminates coefficients whose wavelet coefficient amplitudes are less than the threshold value in order to correspond to wavelet coefficients after soft thresholding, but does not directly preserve wavelet coefficients whose wavelet coefficients are greater than the threshold value in amplitude, but preserves their difference from the threshold absolute value.
As can be seen from the equation, the hard threshold function is discontinuous in the wavelet domain, Ghard(hk，e) The discontinuity between J and-J makes the subsequent processing extremely complicated and generates large oscillation at the abrupt change of the signal, so that the critical value G is passedhard(hk，e) After the processed wavelet coefficient is reconstructed, image distortion phenomena such as pseudo Gibbs and ringing phenomena appear after the image is suddenly changed. Moreover, the wavelet coefficient distribution of signals and noise in the wavelet domain is not absolute, and the wavelet coefficient processed by the hard critical value function also contains certain noise energy, so that certain noise still remains in the reconstructed signals.
And the soft critical value function image does not have a breakpoint, and the processed image does not generate image distortion phenomena such as larger oscillation and ringing at the abrupt change position of the image. However, the soft threshold method shrinks the wavelet coefficients above the threshold, and some wavelet coefficients of the high-frequency information of the image are lost to a certain extent, so that the edges of the de-noised image are blurred.
Improvement of four, wavelet shrinkage critical value function
The hard critical value and soft critical value methods have good effect on image denoising, but have obvious defects. The following improvements were made in view of their disadvantages.
Threshold function method one, the threshold function is shown as follows:
the critical value function is set continuously at-J and J, the image reconstruction does not generate oscillation at the abrupt change position, the pseudo Gibbs and ringing phenomena occur, and the difference between the wavelet coefficient processed by the critical value and the real wavelet coefficient follows the wavelet coefficient hk，eGradually decreases and finally approaches to the real wavelet coefficient, thereby solving the problem of constant deviation of the soft critical value function. However, the threshold function method is not flexible enough as it has no adjustment factor.
In the second threshold function method, a threshold function between the hard threshold and the soft threshold can be obtained by only appropriately changing the parameter p, so that the defects caused by processing the hard and soft thresholds are avoided, a better image denoising effect is obtained, and the second threshold function method has good flexibility, but the second threshold function method does not well solve the problem of constant deviation of the wavelet coefficient.
In combination with the above two methods, the present invention provides a constant no-shock threshold function:
adjustable parameters p and q are added into a constant vibration-free critical value function, the constant vibration-free critical value function is continuous at-J and J, no vibration is generated during image reconstruction, and the constant vibration-free critical value function is used
Is an asymptotic line, and follows with hk，eThe wavelet coefficient after the critical value processing gradually approaches to the real wavelet coefficient, and the problem of constant deviation of the wavelet coefficient is solved. By adjusting the parameters p and q, the constant no-vibration critical value function can be adjusted between the soft critical value and the hard critical value, and the method has better flexibility and practical application value.
To validate the improved wavelet shrinkage algorithm of the present invention, it is compared to soft and hard threshold algorithms. The invention solves the denoising problem of typical white Gaussian noise, artificially adds the white Gaussian noise with different standard deviations in a simulation experiment, and tests the denoising effect of the denoising method on a specific noise model. In the quality evaluation of the denoised image, the evaluation criterion is based on the following points: firstly, the added noise is as close to natural random distribution as possible; secondly, the image is free of noise as much as possible after denoising and reconstruction; thirdly, the edge detail features of the image cannot be removed smoothly due to image denoising, so that the image becomes fuzzy; fourthly, higher peak signal-to-noise ratio is obtained after denoising.
On an MATLAB software platform, selecting a pair of images with pixels of 512 multiplied by 512, adding noise to the images, then performing two-dimensional wavelet decomposition on the images after noise addition in a multi-scale space, reserving low-frequency coefficients, extracting high-frequency coefficients on all scales, performing corresponding critical value processing on the extracted high-frequency coefficients, and finally reconstructing the wavelet coefficients to obtain the images after noise removal. In order to verify the image denoising effect of the new method on different noises, Gaussian white noises with standard deviations of 20 to 40 are respectively added.
The higher the wavelet decomposition level is, the better the image denoising effect is, but the more difficult the corresponding reconstructed image is, so the wavelet base selected by the invention is db8 wavelet, and the maximum decomposition level is 3. The variables of the three experimental displacements are only wavelet shrinkage method, and the rest are all the same. Experiments show that the image denoising effects of different noises are achieved by using several contraction and expansion methods, and the improved wavelet contraction has a better image denoising effect.
From the perspective of human eyes, the worst noise image reconstruction effect is a soft critical value function, and the whole image is blurred; the image processed by the hard critical value function can better keep the detail part of the image, but is not ideal at the edge, and the continuity ratio of the image is poor due to the characteristic of the hard critical value function; the constant non-oscillation critical value function provided by the invention is better preserved in detail or edge part, better recovered after image denoising, and more excellent in image reconstruction effect and visual effect.
Claims (10)
1. The method for reconstructing the noise image with the fusion of the space domain and the transform domain is characterized in that bilateral filtering is adopted in the space domain, wavelet transformation and contraction are adopted in the transform domain, the bilateral filtering in the space domain keeps the image edge with strong contrast, and the wavelet transformation and contraction in the transform domain keeps the image detail with weak contrast;
on the basis of respectively improving and optimizing the bilateral filtering of a space domain and the wavelet transform shrinkage of a transform domain, the invention fuses two improved methods, and the flow steps are as follows:
firstly, carrying out spatial domain bilateral filtering processing on a noise image, wherein an image obtained after bilateral filtering processing is a strong-contrast image;
secondly, subtracting the original noise image from the strong contrast image to obtain a weak contrast image,
thirdly, performing wavelet transformation processing on the image with the weak contrast to obtain a wavelet transformation image;
fourthly, performing wavelet shrinkage processing on the wavelet transformed image to obtain a wavelet shrinkage image;
fifthly, reconstructing the wavelet coefficient to obtain a wavelet reconstructed image;
sixthly, adding the wavelet reconstruction image and the strong contrast image to obtain a final de-noised image and finish the reconstruction of the noise image;
and carrying out three iterations on the whole algorithm process, taking the denoised image obtained at the previous time as a guide image, and calculating a filter kernel of bilateral filtering by using the denoised image obtained at the previous time for bilateral filtering in the next iteration.
2. The method for reconstructing a noisy image fused between a spatial domain and a transform domain according to claim 1, wherein in the whole algorithm process, the standard deviation a of white gaussian noise is 26, the radius b of a bilateral filtering window is 16, and the standard deviation a of a geometric measure is 16s6.8, standard deviation of gray scale measure abThe wavelet transform adopts db8 wavelet as wavelet function, the decomposition layer number is 3, the wavelet shrinkage critical value adopts the wavelet shrinkage critical value related to the decomposition layer number of the wavelet, the wavelet shrinkage critical value function adopts the constant non-oscillation critical value function, the best image denoising effect can be obtained after the algorithm flow is iterated for three times, each iteration can further denoise, only micro deviation is introduced, the iteration times are continuously increased after the iteration is iterated for three times, the image denoising effect is improved very little, and the algorithm calculation complexity is increased on the contrary.
3. The method for reconstructing the noise image fused between the spatial domain and the transform domain according to claim 1, wherein for the noise removal of typical white gaussian noise, after the noise image is subjected to bilateral filtering to obtain an image strong contrast image, the low contrast image is subjected to wavelet transform and wavelet shrinkage, and a wavelet shrinkage critical value associated with the number of wavelet decomposition layers is selected, so that the influence of the total number of wavelet coefficients is weakened and is associated with the number of wavelet decomposition layers; when selecting the wavelet shrinkage critical value function, a constant non-oscillation critical value function is provided on the basis of the soft critical value function and the hard critical value function; and finally, iterating the whole algorithm process, and eliminating the ringing phenomenon caused by wavelet shrinkage by utilizing bilateral filtering.
4. A method for reconstructing a noisy image fused between a spatial domain and a transform domain according to claim 1, characterized in that, in the first step, the noisy image is subjected to a spatial domain bilateral filtering process, wherein a bilateral filter is implemented in a weighted manner, taking into account both the distance between the pixels of the image and the intensity between the pixels, the weighting coefficient of the bilateral filter is the product of two filtering kernels, the first filtering kernel function is determined by the geometric distance between the neighborhood pixels of the center sampled pixel and is called spatial geometric measure; the second filtering kernel function is determined by the difference between the gray value of the central pixel and the gray value of the neighboring pixels, and is called gray measurement;
the bilateral filter fully protects the image edge while smoothing the image, the gray value of the pixel processed at present is the weighted average of the neighborhood pixels after filtering, the weighting coefficient is equal to the product of the space geometric measure and the gray measure, and the filtering output of the central pixel point is influenced only by the neighborhood pixels with close space distance and small gray value difference.
5. The method of claim 4, wherein the gray-level value of the image A at the pixel point c (x, y) is defined as AcAnd the gray value of the image B obtained after filtering at the pixel point c (x, y) is BcThe formula of bilateral filtering is:
Dc＝BEBF
in the above formula, D is the neighborhood pixel of the center pixel c, I is the set of neighborhood pixels, DcFor bilateral filtering kernels, BEIs a geometric measure, BFIs a measure of the gray level, the expression is:
in the expression, E is a geometric measure standard deviation obtained through a Gaussian function, F is a gray measure standard deviation obtained through the Gaussian function, and the two determine the shapes of two filtering kernel functions;
each pixel point of the image replaces the original gray value of the pixel point by the average value of pixels with similar geometric distances and small gray value differences in the neighborhood, the gray value of the pixel point changes slowly in the area containing a large amount of details, the bilateral filter is degraded into a low-pass filter at the moment, and the difference of the pixel values with weak correlation caused by noise can be weakened and eliminated by solving the average value of the pixel points in the neighborhood; in the area with severe image change, the gray value similarity factor of the pixel point on the same side of the edge approaches 1, the gray value similarity factor of the pixel point on the different side of the edge approaches 0, and at the moment, after bilateral filtering, the gray value of the pixel point to be processed on the edge of the image is replaced by the gray average value of the pixel points with similar gray in the neighborhood;
two parameters E and F of the bilateral filter directly determine the integral smoothness degree of the image, respectively express the size and contrast of the kept image characteristics, and are key factors for determining the performance of the bilateral filter; namely, when the E value is larger, the neighborhood pixel points far away from each other can also influence the center pixel point, and when the F value is larger, the gray value of the pixel points in the neighborhood can also act on the output of the center pixel point even if the difference between the gray value of the pixel points in the neighborhood and the center pixel is larger;
the larger the values of the parameters E and F are, the stronger the smoothing effect of the bilateral filter is; when the values of the two parameters E and F are close to 0, the value of the bilateral filter kernel approaches to 0, and the bilateral filter cannot generate a smoothing effect on an input image; the parameter F controls the degree of the bilateral filter for keeping the image edge, the change of the parameter F can influence the edge characteristic of the image more than that of the parameter E, and the parameter E determines the smoothness of the bilateral filter to the image detail;
the denoising performance of the bilateral filter is reduced along with the increase of the filtering radius, and when the filtering radius is 3, the bilateral filtering denoising image obtains the best visual effect.
6. The method for reconstructing a noise image fused between a spatial domain and a transform domain as claimed in claim 1, wherein the wavelet shrinkage denoising is most critical for estimating a wavelet shrinkage threshold, and the number of wavelet coefficients affects the performance of the wavelet shrinkage threshold and needs to weaken its effect; the low frequency sub-band in the image contains key information of the image, while the image noise exists more in the high frequency sub-band, a critical value larger than the low frequency sub-band is selected in the high frequency sub-band, and H is increased along with the increase of the decomposition layer number kkIs correspondingly reduced, HkIs the adjustment coefficient of the k layer in the wavelet domain.
7. The method for reconstructing a noise image fused between a spatial domain and a transform domain as claimed in claim 6, wherein for the estimation of the wavelet shrinkage threshold, the invention provides a wavelet shrinkage threshold associated with the wavelet decomposition layer number, and the threshold formula is:
wherein J is the wavelet shrinkage threshold, anIs the standard deviation of noise, N is the number of wavelet coefficients, HkIs the adjustment coefficient of the k-th layer in the wavelet domain, ak，fIs the standard deviation, e, of the noise-free image f at the k-th layer after wavelet transform1，e2As adjustable parameters, the sum of the two adjustable parameter parameters is 1, and for the wavelet shrinkage critical value function of the related wavelet decomposition layer number, the standard deviation of noise and the standard deviation of a noise-free image f at the k-th layer after wavelet transformation, and the standard deviation a of noise are required to be obtainednThe following formula is given:
wherein the content of the first and second substances,
wavelet coefficients for noisy images，
Taking wavelet coefficient of noise image in highest sub-band
To find the standard deviation a of the noisen；
Wavelet coefficients of noisy images
The sum of the wavelet coefficients represented as a noise-free image and the noise wavelet coefficients, i.e.:
according to the linear characteristic of wavelet transformation, the relation among the standard deviations of the wavelet coefficient of the noise image, the wavelet coefficient of the noiseless image and the noise wavelet coefficient on the kth layer is obtained, namely:
standard deviation a of noise image wavelet coefficient at k-th layeri，kWavelet coefficient at k-th layer capable of passing image i
To obtain:
wherein M and n are the number of rows and columns of wavelet coefficients, and M is the total number of wavelet coefficients, and the standard deviation of the wavelet coefficients of the k-th layer of the noiseless image is obtained as follows:
thus, a wavelet shrinkage threshold value J associated with the number of wavelet decomposition layers is calculated.
8. The method of claim 1, wherein the wavelet de-noising algorithm first estimates a proper threshold value and then obtains wavelet coefficients by a threshold value function, and the wavelet shrinkage algorithm comprises a hard threshold value method and a soft threshold value method, and the hard threshold value method has the following formula:
in the formula, hk，eExpressing the wavelet transform coefficients of the noisy image, the critical value is denoted by J, Ghard(hk，e) Expressing the function value of a hard critical value, eliminating the coefficient smaller than the critical value in all the coefficient amplitudes after wavelet transformation, and keeping the wavelet domain coefficient of which the coefficient amplitude is larger than the critical value unchanged;
the mathematical expression for the soft threshold function is as follows:
in the formula, sgn (h)k，e) Expressing the wavelet coefficients hk，eSign function of Gsoft(hk，e) In order to correspond to wavelet coefficients after soft thresholding, the soft threshold function is to eliminate coefficients whose wavelet coefficient magnitudes are less than the threshold, but not to retain wavelet coefficients whose magnitudes are greater than the threshold magnitude, but to retain their difference from the threshold absolute value.
9. A method for reconstructing a noisy image fused between a spatial domain and a transform domain according to claim 8, characterized in that, for the deficiency of the hard and soft threshold methods, the following improvements are made:
threshold function method one, the threshold function is shown as follows:
the threshold function is set continuously at-J and J, no oscillation is generated at the abrupt change position when the image is reconstructed, and the difference between the wavelet coefficient subjected to threshold processing and the real wavelet coefficient is along with the wavelet coefficient hk，eGradually decreases and finally approaches to the real wavelet coefficient, but the first critical value function method has no adjusting factor;
in the second threshold function method, a threshold function between the hard threshold and the soft threshold can be obtained by appropriately changing the parameter p, but the second threshold function method does not solve the problem of constant deviation of the wavelet coefficients well.
10. The method for reconstructing a noisy image fused between a spatial domain and a transform domain according to claim 9, wherein the invention provides a constant shockless threshold function in combination with the first threshold function method and the second threshold function method:
adjustable parameters p and q are added into a constant vibration-free critical value function, the constant vibration-free critical value function is continuous at-J and J, and does not generate vibration during image reconstruction, and the constant vibration-free critical value function is used for
Is an asymptotic line, and follows with hk，eThe wavelet coefficient after the critical value processing gradually approaches to the real wavelet coefficient, so that the problem of constant deviation of the wavelet coefficient is solved; by adjusting the parameters p and q, a constant no-shock threshold function can be obtainedThe soft and hard critical values are adjusted, so that the flexibility is better.
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| CN116907677A (en) * | 2023-09-15 | 2023-10-20 | 山东省科学院激光研究所 | Distributed optical fiber temperature sensing system for concrete structure and measuring method thereof |
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