Research On Image Compressive Sensing Methods Driven By Model And Data Collaboratively

In the process of image signal acquisition,processing and transmission,how to sample the signals with the least resources and reconstruct them with high qualities at the receiver is a problem worthy of study.The theory of Compressive sensing is committed to solving the problem of ensuring reconstruction accuracy as much as possible at low sampling frequencies.However,the existing conventional algorithms have high computational complexity and slow reconstruction speed,while deep learning methods have problems such as poor model interpretability and blind design of model structures.These affect the performance of image reconstruction.In view of the above problems,this thesis combines the deep learning method with the optimization theory or mathematical prior knowledge.Compared with the existing model and data hybrid-driven methods,the deep learning method can make the model solving processes of the optimization algorithms efficient.It not only enhances the ability of data fitting and mining signal characteristics of the optimization methods,but also gives the deep learning methods more accurate interpretability.The novel approach truly reflects the effect of model and data driving collaboratively,and theoretically enables high-precision image reconstruction.Based on the collaboratively-driven method,this dissertation designs several deep image compressive sensing(DCS)models.The main contents are as follows.(1)DU-ADMM-Net is proposed based on Alternating Direction Method of Multipliers(ADMM).ADMM is an effective convex optimization method for large-scale data and parallel computing.In the process of ADMM’s splitting and solving variables,a large number of linear and nonlinear operations are involved.Considering that the basic structure of convolutional neural network(CNN),namely convolution and activation function,can essentially play the role of linear and nonlinear calculation,it is possible to use CNN to simulate the above two types of operations,which promotes the overall optimization process to be carried out with higher quality.In addition,the reconstruction part must face the problem of matrix inversion.Direct inversion can increase the computational complexity.This degree paper attempts to expand the Neumann series based on the deep learning method,and replace the terms of the series with multi-convolution layers,so that the matrix inversion can be transformed into polynomial linear accumulation,which is equivalent to multi-convolution hierarchy,which can effectively reduce the computational load.For the nonlinear mapping part,the method in convolutional sparse coding(CSC)is used to replace the sparse base with a convolutional dictionary,and the piecewise linear function(PLF)is used for the sparse regularization term,which is convenient to integrate the sparse regularization process into the neural network and participate in the overall optimization of the model.The model learns various uncertain parameters and functions in an end-to-end training manner.While improving the robustness of the model,the data-driven deep learning method and the model-driven optimization theory work together to reduce the design difficulty of the network model to a certain extent.(2)In order to further improve the accuracy of image reconstruction,RND-Net is proposed based on Range-Null Space Decomposition(RND).RND is a mathematical model constructed for the inverse problem of images,which helps to obtain the low-frequency and high-frequency components of images.In this degree thesis,the deep learning method is combined with it,and the steps of RND are networked to obtain the low-frequency and high-frequency information of images in a novel way.The final reconstructed image is excellent in performance indices and visual effects.(3)In the RND process,generating the null-space extraction term is an important step and is closely related to the acquisition of the null space and the high-probability reconstruction of images.In order to make the null-space extraction term contain more comprehensive feature information and improve the model reconstruction performance,RV-CSNet is proposed.This model flexibly replaces the null-space extraction term with the Variational Autoencoder(VAE),which is widely used in other fields.This deep generation model helps to make the output of the decoder retain more features of the encoder’s input information.In view of this,the decoder of the trained VAE model is used in the generation process of the null-space extraction term,and the sampling information is used as the input.The obtained null-space extraction term contains richer feature information,which is very close to the input image.Besides,the loss function of the network model takes the inherent constraints of RND and VAE into account,and includes the loss conditions of training VAE and the whole end-to-end model.Therefore,the final loss function covers multiple constraints,which improves the image reconstruction abilities of the model after being trained.The two deep learning models based on RND make full use of the synergistic advantages of mathematical prior knowledge and deep learning methods.While enhancing the interpretability of the models,they promote the model performance and image reconstruction accuracy,and greatly reduce the reconstruction time of a single image,which have positive significances when applied in the actual scenes.