Image Denoising Method Based On Partial Differential Deep Neural Network

As a fundamental task in computer vision and image processing,image denoising possesses important application value in various fields,e.g.,manufacturing,medical health and satellite remote sensing.Being essentially a kind of inverse problem,image denoising is to estimate clean ones from noised images,and enhance its quality to prevent the subsequent image processing and analysis from noise.In the past few decades,a variety of image denoising methods based on different theories have been proposed.In these denoising methods,the traditional ones have definite principles,and lighter computation cost,but usually could not obtain desired denoising performance.Neural networks,especially deep neural networks,made great progress in image denoising,but the denoising methods based on neural networks need a large amount of training data and ones have to spend more time on training networks to their parameters.The partial differential equation based denoising methods possess solid physical significance for dynamic processes and small scale of parameters,but their results often depend on the parameters of equations and have limited generalization.In view of this,combining deep neural networks and partial differential equations,we researched the methods of data driven partial differential equations to explore the physical significance behind image denoising,and realized efficient and explainable image denoising methods.The main work and contributions of the thesis are as follows.(1)An image denoising method based on partial differential deep network was proposed.Based on the ridge regression algorithm,we built a deep neural network for learning and solving partial differential equations with constant coefficients,and designed the cost function by using dynamic time warping.In addition,we applied the proposed network to image denoising and achieved promising results.The details are as follows.We 1)firstly constructed a deep neural network with multiple regression blocks for partial differential equation,introduced dynamic time warping to design cost function to uncouple the dependence of network blocks on the length of training set;2)inspired by transfer learning,fine-tuned the network that is pre-trained on numerical solutions by using real images;and3)took the noise image as the unknown function of the partial differential equation and realized image denoising by forward propagation of the proposed network.The associated experiments illustrate that the proposed network could correctly learn the hidden partial differential equation from the noise images,and achieve promising results on image denoising.(2)An image denoising method based on variable coefficient partial differential deep network is proposed.Aiming to the missing of image details when denoising,we built variable coefficient partial differential deep network by incorporating U-Net,introduced cross entropy into cost function,and realized pixel-wise image denoising.The details are as followed.We 1)designed a new training method to enhance the network`s ability to characterize image features,inspired by U-Net to construct a variable coefficient partial differential deep network;2)introduced weighted cross entropy loss to design a new soft-time regularized distance method as the loss function,improved the stability of network training and the accuracy of image feature learning;3)deconstructed the noisy image into blocks,performed aggregation operation after denoising similar blocks in groups to further improve the effect of image denoising.The associated experiments illustrate that the proposed network could learn the variable coefficient partial differential equations hidden in real data pixel by pixel,and its application in image denoising could better preserve the texture and details in the image.In summary,aiming to learn partial differential equations by deep neural networks and improve the performance of image denoising,we researched the structure,cost function and training of data driven partial differential equations,and proposed a partial differential deep neural network and a variable coefficient partial differential deep neural network.Possessing the advantages of partial differential equations and deep neural networks,the aforementioned two networks could learn the coefficients of partial differential equations,save the training time of networks,have fewer parameters compared with the-state-of-the-art deep neural networks,and relax the requirement for training set;they could finish training networks in shorter time,improve the accuracy of coefficients by collaborating the errors in numerical solutions,and have better explainability.Our thesis provides new research thoughts for researching partial differential equations and image denoising,generalize the application of partial differential equations,and promotes the exploration of the physical significance of image denoising.