Access the full text.
Sign up today, get DeepDyve free for 14 days.
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
Hindawi Journal of Robotics Volume 2022, Article ID 7115551, 9 pages https://doi.org/10.1155/2022/7115551 Research Article Adaptive Image Denoising Method Based on Diffusion Equation and Deep Learning 1,2 1 1,2 Shaobin Ma , Lan Li , and Chengwen Zhang School of Digital Media, Lanzhou University of Arts and Science, Lanzhou 730010, China VR Technology R&D and Promotion Center, Lanzhou University of Arts and Science, Lanzhou 730010, China Correspondence should be addressed to Shaobin Ma; 1000265@luas.edu.cn Received 4 November 2021; Revised 23 November 2021; Accepted 24 November 2021; Published 6 January 2022 Academic Editor: Shan Zhong Copyright © 2022 Shaobin Ma et al. (is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Eﬀective noise removal has become a hot topic in image denoising research while preserving important details of an image. An adaptive threshold image denoising algorithm based on ﬁtting diﬀusion is proposed. Firstly, the diﬀusion coeﬃcient in the diﬀusion equation is improved, and the ﬁtting diﬀusion coeﬃcient is established to overcome the defects of texture detail loss and edge degradation caused by excessive diﬀusion intensity. (en, the threshold function is adaptively designed and improved so that it can automatically control the threshold of the function according to the maximum gray value of the image and the number of iterations, so as to further preserve the important details of the image such as edge and texture. A neural network is used to realize image denoising because of its good learning ability of image statistical characteristics, mainly by the diﬀusion equation and deep learning (CNN) algorithm as the foundation, focus on the eﬀects of activation function of network optimization, using multiple feature extraction technology in-depth networks to study the characteristics of the input image richer, and how to better use the adaptive algorithm on the depth of diﬀusion equation and optimization backpropagation learning. (e training speed of the model is accelerated and the convergence of the algorithm is improved. Combined with batch standardization and residual learning technology, the image denoising network model based on deep residual learning of the convolutional network is designed with better denoising performance. Finally, the algorithm is compared with other excellent denoising algorithms. From the comparison results, it can be seen that the improved denoising algorithm in this paper can also improve the detail restoration of denoised images without losing the sharpness. Moreover, it has better PSNR than other excellent denoising algorithms at diﬀerent noise standard deviations. (e PSNR of the new algorithm is greatly improved compared with the classical algorithm, which can eﬀectively suppress the noise and protect the image edge and detail information. Image denoising can improve the accuracy of human 1. Introduction visual recognition information and is a necessary condition (e noise image is mainly caused by the imperfect system for us to correctly identify images. In nature, due to various internal or external reasons, it is almost impossible to ﬁnd and equipment. In the process of transmission, the image polluted by noise will aﬀect people’s visual sense to varying natural pictures that are completely free of noise pollution, degrees, sometimes even leading to the loss of many image and the images are more or less polluted. (is will make it features, making the image blurred, aﬀecting the useful harder for us to identify the images. In particular, some noise information of the image, and thus hindering people’s images, such as medical images and security images, which normal recognition. (e image polluted by noise will have a aﬀect our signiﬁcant judgment, need us to carry out image great adverse eﬀect on the subsequent image processing, noise reduction to obtain clear image features. For those mainly including image segmentation, extraction, detection, heavily polluted images, they lose the original content of the and recognition. (erefore, it is very necessary and im- image, so eﬀectively improving the accuracy of image rec- portant to use a good denoising algorithm for image ognition is a necessary condition for image recognition. denoising. Image denoising can improve image quality and is a 2 Journal of Robotics prerequisite for further image processing. In image pro- edge of the image according to the prior information of the cessing, image denoising is often the ﬁrst and most im- image, so as to remove the noise from the image and protect portant step. Obtaining high-quality and high-deﬁnition the information at the edge [3]. (erefore, we use the images through noise reduction is a strong guarantee and gradient operator as the operator of the edge detection to good foundation for subsequent image processing. construct a monotone decreasing function [4] in which the Traditional image denoising methods have been pro- diﬀusion coeﬃcient changes with the gradient of the original posed for a long time and have been used for a long time image; that is, the magnitude of the gradient is inversely now, but most of these algorithms are not very satisfactory, proportional to the diﬀusion coeﬃcient. (is adaptive especially in the process of denoising, the details of the image denoising method can not only remove the noise in the ﬂat will be lost, and most of the denoising performance and area of the image but also maintain the protection of the edge algorithm complexity are to be improved. Although the deep of the image, which is called the nonuniform diﬀusion learning technology for image denoising has many scholars’ equation. However, this method still has loopholes and research, neural network research, due to the barriers of shortcomings. First, the gradient at the edge is large, so the diﬀusion coeﬃcient is small [5]. (e smaller the diﬀusion hardware, has not been developed, making the neural network technology no longer have complex network model coeﬃcient is, the better the edge is maintained, but the eﬀect of computation for too much worry, because high-perfor- of noise removal cannot be achieved. (en, the gradient will mance GPU multicore parallel computing is well suited for produce deviation for image edge detection aﬀected by the neural network model and is a necessary prerequisite for noise. the rise of deep learning. Although a lot of people are be- A nonlinear diﬀusion equation [6] is proposed, which ginning to study abroad, after all, the direction is the forward takes the gradient operator obtained in the previous step as direction, and theory and technology are not very mature. the edge detection operator in the iterative process to reduce Although the use of the image denoising aspect really has the impact of noise on edge judgment. However, this method achieved good results, there are still many problems, so cannot deal with the noise of the image edge. (e diﬀusion continuing research and perfect image denoising theory and coeﬃcient is improved and designed as a matrix, which makes the diﬀusion coeﬃcient larger in the tangential di- improving the eﬀect of denoising are very necessary. Based on diﬀusion equation and deep learning (CNN) algorithm, rection of the edge and smaller in the vertical direction of the this paper adopts multifeature extraction technology to edge, thus overcoming the shortcomings of the PM model study the richer features of the input image in the deep [7]. A common problem with low-order models is the network and designs an image denoising network model “ladder eﬀect.” In view of the characteristics of the low-order based on deep residual learning of convolutional network, model, a fourth-order diﬀusion equation is introduced [8]. which has better denoising performance. From the com- In this model, Laplace is used to measure marginal areas, so parison results, it can be seen that the improved denoising there is no “ladder eﬀect” in vision. However, the edge algorithm in this paper can also improve the detail resto- protection ability of the model is not good, and it is easy to ration of denoised images without losing sharpness. Under produce speckle noise. In [3], an improved fourth-order diﬀerent noise standard deviations, the PSNR of the pro- diﬀusion equation model is proposed, which uses the posed algorithm is superior to other excellent denoising modulus of a gradient to replace the absolute Laplace value algorithms. as the operator of image edge detection. (is model has a (e ﬁrst part is the introduction, the second part is faster convergence speed and better denoising eﬀect but related work, the third part is the Adaptive Diﬀusion blurred image edges. An anisotropic diﬀusion fourth-order equation and deep learning algorithm for image dryness, the denoising algorithm is proposed [9], which diﬀuses in fourth part is example veriﬁcation, and the ﬁfth part is the diﬀerent degrees in the normal and tangential directions and conclusion. preserves the details of the image well, but this model has gradient artifacts. At present, the research on image denoising algorithms based on diﬀusion equations is also 2. Related Work making continuous progress, mainly focusing on second- Gaussian ﬁltering ﬁrst introduces the diﬀusion equation into order diﬀusion equations, fourth-order diﬀusion equations, and higher-order diﬀusion equations [10]. (e high-order image processing [1]. On the basis of some theoretical and numerical operations, diﬀerential operators can be obtained weighted gradient variation model for image denoising, after the convolution of a ladder as a weighted function of the by transforming local ﬁlter operators. Diﬀerential operators can be transformed by local ﬁlter operators. In the case of second derivative, newly established a high-order variational function and get a fourth-order partial diﬀerential diﬀusion two-dimensional images, the general processing method is to treat the pair diﬀusion as a uniform linear diﬀusion model [11]; the model is eﬀective in the noise, eliminates the process; that is to say, the diﬀusion coeﬃcients at all points staircase eﬀect, and can have good protection eﬀect on the of the image are the same. However, there are still loopholes edge. An improved semiadaptive threshold anisotropic in this diﬀusion equation [2], whose uniform diﬀusion diﬀusion ﬁlter denoising algorithm is proposed [12, 13]. In this model, the local diﬀerence method is adopted to dis- makes it impossible to retain important details such as edges while removing noise. In view of the defects of the uniform tinguish damaged pixels from noiseless ones, and some damaged pixels are replaced by predenoised pixels of the diﬀusion characteristics of Gaussian ﬁltering, it is natural to come up with an ideal method: reduce the diﬀusion at the Gaussian ﬁlter. (en, an anisotropic diﬀusion model with a Journal of Robotics 3 parameters at the same time in denoising applications. In fact, semiadaptive threshold in the diﬀusion coeﬃcient function is used to obtain the restored image. In order to achieve the the most eﬀective neural network in the ﬁeld of denoising is the most basic multilayer perceptron model. As a popular semiadaptive threshold value of each diﬀusion, the gradient value of the destroyed pixel is introduced into the threshold solution to denoising problems, methods based on image value [14], which makes the diﬀusion of the smooth region priors can extend various methods based on image priors larger and the diﬀusion of the boundary region smaller. (is [23], such as BM3D [24]. (ese methods are used to obtain method can improve PSNR by 30% and structure similarity image prior knowledge directly from the input image for (SSIM) by 5%. It has a good eﬀect on edge protection and image denoising. Although some denoising eﬀects have been noise removal. It overcomes the defect of blurring image achieved, there are still some limitations. Firstly, these methods make use of the prior noise image, which will cause edges by the fourth-order isotropic diﬀusion equation. An adaptive image denoising algorithm based on the fourth- some error, so it is diﬃcult to obtain all the features of the image, resulting in the limitation of denoising performance. order diﬀusion equation [15] is proposed, which uses the image gradient model to construct the measure function of Second, most methods use only the internal information of the input image and do not use any external information, so the image feature information, and uses the feature detection function to adjust the normal and tangential image diﬀusion there is still room for improvement. In addition, for denoising coeﬃcient indexes adaptively according to the diﬀerent methods based on discriminant learning [25, 26], especially features of the image. Isotropic diﬀusion is used to remove those based on diﬀusion equation and deep learning [8, 27, noise in ﬂat and inclined regions, and anisotropic diﬀusion is 28], denoising networks with paired training data sets are used to protect the features of image edge points. Experi- trained and image noise distribution is learned in the hidden mental results show that both denoising and edge preser- layer, thus improving denoising performance. In order to remove the known Gaussian noise level, pairs of training vation are taken into account [16]. A high-order nonlinear diﬀusion image smoothing method based on curvature samples are used to train the denoising network to achieve advanced denoising performance. mode is proposed [17]. Methods such as the combination of gradient and curvature, total variational coupling, and quasi- normal distribution diﬀusion are applied to image 3. Adaptive Diffusion Equation and Deep denoising. Learning Algorithm for Image Dryness Diﬀusion equation and deep learning use Local Receptive Field structure designed for image data [18], compared with 3.1. Image Denoising Based on Diﬀusion Equation. (e Plain Multilayer Perceptrons (MLPs); this structure enables process of recovering a clear image from an image con- diﬀusion equation and deep learning to obtain good results taining noise is called image denoising so that the image while greatly reducing the parameters. (is method is very information after denoising is as close as possible to the useful when the amount of training data is relatively small original clear image information, and the information error because the total number of parameters is relatively small, so it between them is as small as possible. (erefore, image is more diﬃcult to overﬁt the training data. On the other denoising is an inverse process of image processing, as well hand, multilayer perceptron networks have more potential as image deblurring and superresolution reconstruction. (e than diﬀusion equations and deep learning: multilayer per- noise model of the image is shown in Figure 1. ceptron networks can be used to approximate arbitrary (e low rank of hyperspectral images can be explained functions [19], while diﬀusion equations and deep learning from the perspective of the linear spectral mixture model. can only learn speciﬁc types of functions due to structural Because of the high correlation between spectral features, constraints. Another class of algorithm denoising autoen- each spectral feature can be represented by a linear com- coder also uses the neural network as a denoising tool [20]. bination of a small number of pure spectral endmembers, Denoising autoencoders are special neural networks that learn that is, a linear spectral mixture model. If each band of by unsupervised learning. Features are represented by the hyperspectral image data is expanded into a vector, then all learned units of the hidden layer. Since the input-output of bands together form a matrix X. this neural network can be easily generated, it only needs to Diﬀusion equations are related to many unknown add noise and other pollution processing to the input, and multivariate functions and their partial derivatives. For ﬁxed good data features can be learned, so denoising autoencoder positive integer k, we use the symbol Dku to represent all k has become a very important algorithm in deep learning. partial derivatives of u. However, the purpose of designing this kind of neural net- Dku work is mainly to extract data features through unsupervised Dk � , (1) learning and to train the deep neural network layer by layer, Dx1, Dx2, . . . , Dxk rather than for denoising. Another diﬀerence is the fact that where (x ,x ,. . ., x ) is any permutations of k elements in the 1 2 n the noise added to the network during learning is usually not set {1,2,3, n}. (erefore, we can regard Dku as a vector in n- Gaussian white noise but pepper and salt noise or the dimensional Euclidean space and write down its length as Dropout of some of the input nodes. For stacked denoising follows: autoencoder [21, 22], which is commonly used in deep Dku learning, the noise will be added to the output node of the Dk u � . (2) previously learned layer, which is diﬀerent from the scheme Dx1, Dx2, . . . , Dxi that only adds noise to the initial input and then learns all 4 Journal of Robotics Noisy picture block RGB2RAW RAW Respectively to dry Go dry aer the Picture block Aggregate picture 1 ppAdaptive Aer drying, picture 1 Color correction Sigmod To dry q q Respectively to dry AlexNet RRG 227×227×3 Aggregate Adaptive dryness control Figure 1: Research framework of adaptive image denoising based on the image block. In particular, when k � 1, we call the n-dimensional 1 vector: 0.9 Du Du Du 0.8 (3) Du � · · · . Dx1 Dx2 Dxi 0.7 (at is the trace of u’s Hessian matrix, the sum of the 0.6 diagonal elements of u’s Hessian matrix. Write the diver- 0.5 gence of F as 0.4 DF i (4) divF � . 0.3 Dx i 0.2 Let the general form of the diﬀusion model be 0.1 DF (5) divFΔI � . DI 0 10 20 30 40 50 60 70 80 90 100 Gradient (e AOS format of the deformable diﬀusion model is g1 n+1 n n (6) F � F − 2ΔI F I . g2 g3 (e block-based denoising algorithm divides the image into small blocks for denoising, and because the noise level Figure 2: Each ﬁtting diﬀusion coeﬃcient. of each image block is diﬀerent, the selection of the denoising threshold is also diﬀerent. In the process of denoising, noise mainly corresponds to a small singular In the process of diﬀusion, pixels’ gray value of the area value. (erefore, the larger the singular value is, the less it and adjacent area has a kind of relationship, usually paying a should shrink as the singular value shrinks. predetermined constant gradient threshold k and adopting the predetermined good constant gradient threshold, which is not conducive to certain areas on the edge of the image 3.2. Diﬀusion Equation Denoising Algorithm. Based on the detail information and images, according to the pixel lo- PM model, the ﬁtting diﬀusion coeﬃcient was established to cation of the dynamic design gradient threshold k. (rough overcome the defects of texture detail information loss and the above analysis, a one-dimensional gradient threshold edge degradation caused by excessive diﬀusion intensity. function k is designed which varies with the diﬀusion time (en, in order to enable the threshold function to control the and the number of diﬀusions. threshold value according to the maximum gray value and iteration times of the image, the threshold function is k(i) � . (8) 1 + ci designed adaptively. Based on the advantages and disad- vantages of the above two diﬀusion coeﬃcients, a new In the tangent direction, the image needs strong diﬀu- diﬀusion coeﬃcient is established, as follows: sion in both the edge and the inner region, where noise can be eliminated and the interrupted edge can be connected on g � χg + cg . (7) i 1 2 the edge. In the normal direction, the inner area of the image (e diﬀusion coeﬃcients of each ﬁt are shown in also needs strong diﬀusion to eliminate noise, but in the Figure 2. edge, no diﬀusion is needed as much as possible to maintain Diﬀusion coeﬃcient Journal of Robotics 5 diverged, and then 0.02 was tried to gradually reduce the the edge features. (erefore, the diﬀusion coeﬃcient B is always set as 1 in the tangential direction, and a new dif- initial learning rate. If the network converges but the training speed is slow, then we try to increase the learning fusion coeﬃcient c is designed by excluding one ill-condi- tioned condition in the normal direction combined with the rate. In order to ensure the convergence of the neural diﬀusion coeﬃcient of Tv ﬂow: network, the current learning rate is multiplied by 0.99 in each cycle when the small-batch processing algorithm is ������� c � . implemented. Inertia parameter is a common acceleration (9) 1 + ΔD method in neural network training, which can help the neural network to leave the ﬂat region in function space (e neural network and deep learning model are very faster. (e speciﬁc operation method is to add part of the last suitable for learning the function from picture block to weight update to each update of the weight matrix, namely, picture block due to their strong expression ability. (e frame of denoising using a neural network is shown in DE W(i + 1) � λ + βW(i). (10) Figure 3. (e hidden layer activation function is distin- DW guished from the output layer activation function because (e relation between the activation value of the element the choice of the output layer activation function depends on and input current is as follows: the needs of the problem. Speciﬁcally, we ﬁrst randomly select a clean image block E + DW − V f(i) � log . (11) knife from the image data set and then artiﬁcially add E + DW − V Gaussian white noise to generate the corresponding noise As shown by the similarity measure, image block X. (en, we take the vector-induced noise image block X as the input of the neural network and the corre- |E − D| (12) sponding vector-induced clean image block as the output of d(E, D) � . k∗ k the neural network, update the parameters of the neural network through backward propagation, and gradually learn (e EPLL algorithm ﬁrst learns the prior knowledge of the required model through iteration. the image and obtains the edge texture characteristics of the image through sample learning, which is constrained by the regular term of image denoising to obtain the denoising 3.3. Adaptive Image Denoising Algorithm Based on Diﬀusion image with obvious texture characteristics. On the other Equation and Deep Learning. (e initial value of the weight hand, the image blocks of the default denoised images in the matrix of the neural network has a signiﬁcant inﬂuence on EPLL algorithm have signiﬁcant similarities with the image the training process and the ﬁnal result. For multilayer blocks in the samples. When the EPLL value is large, the networks, we want the initial values of the network to satisfy denoised image is considered to conform to the charac- randomness while ensuring that the input outputs of each teristics of the sample library, and the subjective vision is hidden layer have the same statistical characteristics as also better. (e sum calculation method of likelihood possible. In order to achieve this, it is necessary to associate probability is as follows: the initial value of parameters of each layer with the number of nodes of the corresponding layer and adjust it adaptively EP(x) � log p∗ P(x). (13) according to the number of nodes of each layer. i All training samples were checked in a cycle, and the (e logarithmic likelihood probability of all image parameters of the whole network were updated by backward blocks is summed to obtain the total likelihood probability of conduction every time one training sample was checked. (e the denoised image and sample database image. (e image advantages are that the updating speed of the weight matrix degradation process is known, and the properties of like- is greatly accelerated, and the network parameters are easier lihood probability are understood. (e image denoising to escape from the subideal local minimum region because problem is transformed into a solution formula: of the strong randomness. (e disadvantage is that the error curve ﬂuctuates more in the training process, the conver- f (x, y) � |Ax − y| − EP(x). (14) gence conditions are more complex, and it is more diﬃcult to converge. Relatively speaking, these shortcomings of (e solution of the target equation is approximated by stochastic gradient descent are easier to solve. For example, introducing the auxiliary variable splitting equation into it is a good solution to solve the problem that the error is semiquadratic partition: diﬃcult to converge by gradually decreasing the learning C(x, y) � |Ax − y| − log p(y). (15) rate with the increase of the number of iterations. Due to the advantages of training speed, a stochastic gradient descent algorithm has been widely used. (e adaptive image drying model has higher denoising (e setting of learning rate: a larger learning rate may intensity, which solves the “blocky” eﬀect in the denoising make the neural network model learn faster and may also process. In order to further protect the edge texture and make the neural network diverge. In this paper, the initial other details and give consideration to denoising intensity, learning rate was selected by the experimental method: 0.1 an adaptive orthogonal diﬀusion ﬁltering model was pro- was initially tried, 0.05 was selected if the neural network posed to overcome the disadvantages of high denoising 6 Journal of Robotics Input Layer Feature Feature Text Classiﬁer Text Classiﬁer extractor extractor Base Base class class weights weights Text Feature Feature Denoising W=w+r extractor extractor Autoencoder Text Figure 3: Frame of denoising using neural network. texture, noises of diﬀerent sizes and variances were ﬁrst intensity of the orthogonal diﬀusion model and the loss of edge texture and other details. (e experimental results added to the image, and the results are shown in Figure 4. show that the PSNR model improves about 30 dB compared Based on the PM model, the diﬀusion coeﬃcient in the with the classical model (TV ﬂow diﬀusion model). Com- diﬀusion equation is improved, and the ﬁtting diﬀusion pared with the TV stream diﬀusion model, the new model is coeﬃcient is established to overcome the defects of texture more ﬂexible than the TV stream diﬀusion model, which can detail loss and edge degradation caused by excessive adjust the diﬀusion system according to diﬀerent parts of the strength. (en, according to the maximum gray value of the image processing, control the smoothness degree, and image and the number of iterations, the threshold function is process clear images more reasonably. designed automatically. Experimental results show that the peak signal-to-noise ratio of the new algorithm is improved by about 16 dB compared with the classical algorithm. (e 4. Example Verification proposed algorithm can eﬀectively suppress the noise and In order to verify the rationality and eﬀectiveness of the protect the edge and detail information of the image. above algorithms, Lady (600 × 600) and Nudist graphs with Notice that the side length P of the noisy image block can Gaussian random noise were analyzed, and experimental be inconsistent with the side length Q of the denoised image simulation was carried out with Matlab software and semi- block. Such setting is similar to the convolution operation of implicit additive operator splitting numerical algorithm, and the image. For the pixel in the middle of the image block, the their MSE and PSNR were compared. In order to study the information of surrounding pixels can be used more than suppression eﬀect of diﬀusion coeﬃcient on noise and the that of the pixel from the corner of the image block. retention degree of important details such as image edge (erefore, the prediction of the original value of the pixel in Picture fast 2 Journal of Robotics 7 60 0.06 0.05 0.04 0.03 10 20 30 40 50 60 70 0.02 Noise solution 0.01 g4 g2 g3 g1 Figure 5: Mean square error at each position of the 12 ×12 image block after denoising. 10 20 30 40 50 60 70 MSE in training set Noise solution 0.2 g1 g3 0.15 g2 g4 0.1 Figure 4: PSNR and MSE simulation diagrams of diﬀerent vari- 0.05 ances of diﬀusion coeﬃcients in lady image. 0 50 100 150 the middle part of the image block will be more accurate, Epochs of Training while the error of the edge part will be relatively larger. (e actual situation in the image block is an example of mean MSE in validation set 0.5 square error (MSE) in each position as shown in Figure 5; in the case where the original noise block size is 12 ×12 images, 0.4 we use the fourth chapter putting forward the algorithm of denoising model of training, more after denoising images 0.3 after denoising and ideal cleaning image blocks of error, and 0.2 perform statistics after getting the picture. 0 10 20 30 40 50 60 70 80 As can be seen from Figure 5, the mean square error in Epochs of Training the middle of the image block is the lowest, and the mean square error becomes higher toward the edge, among which Figure 6: Changes of mean square error of diﬀusion equation and the mean square error at the corner is the highest. Nu- deep learning in the training set and test set with the number of iteration cycles during training. merically, the mean square error (MSE) in the corner of the image block is approximately 25% greater than that in the middle. On the other hand, in many algorithms, the edge length of the noisy image block is the same as that of the function. Secondly, it only takes a few iterations for the denoised image block. Considering that there will be some former to stabilize the mean square error on the test set, and overlap in the process of splitting and aggregation, the same then the error on the training set continues to decline, while size of denoised image block and noise image block means the error on the test set slowly rises; that is, slight overﬁtting that the same number of noise image blocks provides more appears. However, the latter ﬂuctuates more and the range is estimates of the clean value of each pixel. larger in the training process, and there is no overﬁtting Figure 6 records the curves of the mean square error of trend in the whole process. As the learning rate decreases denoising image blocks in the training of the two models (multiplied by 0.99 per cycle), it gradually converges. during the ﬁrst 150 cycles with the number of iterations. It Based on the diﬀusion equation and deep learning, the should be noted that from the 150th cycle to the 1000th Adam algorithm is used to replace the traditional gradient cycle, the shape of each curve is basically the same as that descent algorithm in the backpropagation algorithm like the from the 100th cycle to the 150th cycle. DnCNN algorithm, multifeature extraction technology is It can be seen from Figure 6 that the model using linear adopted for feature extraction of the ﬁrst layer of the neural rectiﬁcation function can ﬁt the training data set better than network model, and the improved linear rectiﬁer function is the model using hyperbolic tangent function. Firstly, in the used as the activation function. Deep learning technology whole training process, the model using linear rectifying promotes the training speed and convergence speed of the whole model and has great advantages in convergence and function has a lower mean square error in both training set and test set than the model using hyperbolic tangent speed. Picture fast 1 PSNR MSE Mean square error Mean square error Mean square error 8 Journal of Robotics denoising performance of this algorithm reaches the best level at present, especially suitable for image denoising in a 8 high noise environment. Data Availability (e data used to support the ﬁndings of this study are available from the corresponding author upon request. Conflicts of Interest (ere are no conﬂicts of interest in this article. Acknowledgments -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 (is study was supported by the Industrial Support and Set12 Guidance Project of Colleges and Universities in Gansu Province: Research and implementation of digital com- BM3D prehensive display system for Dadiwan prehistoric civili- WNNM zation based on virtual reality (Grant no. 2019C-09). Figure 7: Loss function diagram. References As shown in Figure 7, we can ﬁnd from the curve that the [1] K. Satya and T. Jayachandra, “Deep learning approach for loss value of the blue line with low noise standard after image denoising and image demosaicing,” International convergence is much lower than that of the blue line with Journal of Computer Application, vol. 168, no. 9, pp. 18–26, high noise standard after convergence, which conforms to the objective law, because the bigger the noise is, the greater [2] S. Kumar, M. Sar Fa Raz, and M. K. Ahmad, “Denoising the interference between pixels is, and the more diﬃcult the method based on wavelet coeﬃcients via diﬀusion equation,” model optimization is. In addition, when the noise is 35, we Iranian Journal of Science and Technology. Transaction A, found that after 316 times of iteration the curve almost tends Science, vol. 42, no. 6, pp. 41–56, 2017. to be convergent, while a curve in high noise for 75, almost [3] X. Y. Meng, L. Che, and Z. H. Liu, “Towards a partial dif- ferential equation remote sensing image method based on 1000 times or so, tends to be convergent, and the iteration is adaptive degradation diﬀusion parameter,” Multimedia Tools only a small drop, tens of thousands of times compared with and Applications, vol. 76, pp. 17651–17667, 2017. diﬀusion equation and deep learning model with almost [4] K. M. Santosh, “Denoising method based on wavelet coeﬃ- 4000 times. (e loss function curve converges and becomes cients via diﬀusion equation,” Iranian Journal of Science & stable. (e improved diﬀusion equation and deep learning Technology. Transaction A Science, vol. 42, no. 6, pp. 98–104, model based on adaptive dryness in this paper have ad- vantages in convergence speed and model training speed. [5] S. Zhai, Z. Weng, and X. Feng, “An adaptive local grid re- ﬁnement method for 2D diﬀusion equation with variable coeﬃcients based on block-centered ﬁnite diﬀerences,” Ap- 5. Conclusion plied Mathematics and Computation, vol. 268, pp. 284–294, In this paper, the diﬀusion coeﬃcient in the diﬀusion [6] J. Yu, J. Yin, J. Yin, S. Zhou, S. Huang, and X. Xie, “An image equation is improved and the ﬁtting diﬀusion coeﬃcient is super-resolution reconstruction model based on fractional- established to overcome the defects of texture detail loss and order anisotropic diﬀusion equation,” Mathematical Biosci- edge degradation caused by excessive diﬀusion intensity. ences and Engineering, vol. 18, no. 5, pp. 6581–6607, 2021. (en, the threshold function is adaptively designed and [7] J. Yu, L. Tan, and S. Zhou, “Image denoising based on adaptive improved so that it can automatically control the threshold fractional order anisotropic diﬀusion,” KSII Transactions on of the function according to the maximum gray value of the Internet and Information Systems, vol. 11, no. 1, pp. 436–450, image and the number of iterations, so as to further preserve [8] M. Jin, X. Feng, and K. Wang, “Gradient recovery-based the important details of the image such as edge and texture. adaptive stabilized mixed FEM for the convection-diﬀusion- Finally, the simulation results show that the peak signal-to- reaction equation on surfaces,” Computer Methods in Applied noise ratio of the new algorithm is greatly improved com- Mechanics and Engineering, vol. 380, no. 255, pp. 113798– pared with the classical algorithm, which can eﬀectively 113809, 2021. suppress the noise while protecting the image edge and detail [9] R. Li, T. Zeng, H. Peng, and S. Ji, “Deep learning segmentation information. On the basis of image denoising based on of optical microscopy images improves 3-D neuron recon- neural network denoising, a linear correction function is struction,” IEEE Transactions on Medical Imaging, vol. 36, proposed as the activation function of the neural network no. 7, pp. 1533–1541, 2017. hidden layer, and the parameter setting of the model is [10] R. Lin, R. Zhang, C. Wang, X.-Q. Yang, and H. L. Xin, discussed in detail. Experimental results show that the “TEMImageNet training library and AtomSegNet deep- Diﬀerence between the PSNR Journal of Robotics 9 learning models for high-precision atom segmentation, lo- [27] X. Xiao, C. Yang, and X. Yang, “Adaptive learning-based calization, denoising, and deblurring of atomic-resolution projection method for smoke simulation: adaptive Projection images,” Scientiﬁc Reports, vol. 11, no. 1, pp. 5386–5398, 2021. Method based on Machine Learning,” Computer Animations and Virtual Worlds, vol. 29, no. 3-4, pp. e1837–e1845, 2018. [11] L. Wang, S. Zhou, and X. Lin, “A novel adaptive image zooming method based on nonlocal Cahn-Hilliard equation,” [28] B. Li and W. Xie, “Image denoising and enhancement based Knowledge-Based Systems, vol. 166, pp. 166–189, 2018. on adaptive fractional calculus of small probability strategy,” [12] Y. Jin, X. B. Jiang, Z. K. Wei, and Y. Li, “Chest X-ray image Neurocomputing, vol. 175, no. 29, pp. 704–714, 2016. denoising method based on deep convolution neural net- work,” IET Image Processing, vol. 13, no. 11, pp. 1970–1978, [13] F. Zhang, N. Cai, J. Wu, G. Cen, H. Wang, and X. Chen, “Image denoising method based on a deep convolution neural network,” IET Image Processing, vol. 12, no. 4, pp. 485–493, [14] N. Salamat, M. Missen, and V. Prasath, “Recent developments in computational color image denoising with PDEs to deep learning: a review,” Artiﬁcial Intelligence Review, vol. 54, no. 8, pp. 1–32, 2021. [15] D. Liu, W. Wang, and X. Wang, “Poststack seismic data denoising based on 3-D convolutional neural network,” IEEE Transactions on Geoscience and Remote Sensing, vol. 8, no. 9, pp. 1–32, 2019. [16] Z. Li, S. Zhou, and J. Huang, “Investigation of low-dose CT image denoising using unpaired deep learning methods,” IEEE Transactions on Radiation and Plasma Medical Sciences, vol. 5, no. 6, pp. 51–81, 2020. [17] M. Xie, Z. Zhang, W. Zheng, Y. Li, and K. Cao, “Multi-frame star image denoising algorithm based on deep reinforcement learning and mixed Poisson-Gaussian likelihood,” Sensors, vol. 20, no. 21, pp. 5983–5998, 2020. [18] R. Cai, “Research progress in image denoising algorithms based on deep learning,” Journal of Physics: Conference Series, vol. 1345, pp. 42055–42067, 2019. [19] W. Lu, J. A. Onofrey, Y. Lu et al., “An investigation of quantitative accuracy for deep learning based denoising in oncological PET,” Physics in Medicine and Biology, vol. 64, no. 16, pp. 165019–171335, 2019. [20] C. Wu and T. Gao, “Image denoise methods based on deep 1eaming,” Journal of Physics: Conference Series, vol. 1883, no. 1, pp. 12112–12123, 2021. [21] K. Yan, L. Chang, M. Andrianakis, V. Tornari, and Y. Yu, “Deep learning-based wrapped phase denoising method for application in digital holographic speckle pattern interfer- ometry,” Applied Sciences, vol. 10, no. 11, pp. 4044–4057, 2020. [22] C. Alla Takam, O. Samba, A. Tchagna Kouanou, and D. Tchiotsop, “Spark Architecture for deep learning-based dose optimization in medical imaging,” Informatics in Medicine Unlocked, vol. 19, pp. 100335–100355, 2020. [23] S. Zhong, W. Weng, K. Chen, and J. Lai, “Deep-learning steganalysis for removing document images on the basis of geometric median pruning,” Symmetry, vol. 12, no. 9, pp. 1426–1438, 2020. [24] S. Zhang, S. Xu, and L. Tan, “Stroke lesion detection and analysis in MRI images based on deep learning,” Journal of Healthcare Engineering, vol. 2021, no. 5, 9 pages, Article ID 5524769, 2021. [25] D.-I. Eun, R. Jang, W. S. Ha, H. Lee, S. C. Jung, and N. Kim, “Deep-learning-based image quality enhancement of com- pressed sensing magnetic resonance imaging of vessel wall: comparison of self-supervised and unsupervised approaches,” Scientiﬁc Reports, vol. 10, no. 1, pp. 13950–13967, 2020. [26] C. Chen and Z. Xu, “Aerial-image denoising based on con- volutional neural network with multi-scale residual learning approach,” Information, vol. 9, no. 7, pp. 324–345, 2018.
Journal of Robotics – Hindawi Publishing Corporation
Published: Jan 6, 2022
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.