Image Recovery Via Fusion Of Deep Convolutional Neural Network And Compressed Sensing

With the booming information industry and technology,we are dealing with huge amounts of image and video data on a daily basis.The problem of how to transmit,store and compute these massive amounts of high-dimensional data on limited hardware resources has become a pressing problem.Compressed Sensing(CS),a new data sampling technique,is able to reconstruct high quality original images from measurements well below the Nyquist sampling frequency.The design of the measurement matrix and the performance of the recovery algorithm are the two main challenges in the application of CS theory to image recovery.Specifically,1.When the image size increases,the dimensionality of the corresponding measure-ment matrix increases dramatically,and block-wise measurement has to be used in practice,which leads to block artifact in the recovered image.2.Deep Convolu-tional Neural Network(DCNN)based recovery algorithms have been continuously proposed in the CS recovery phase with good recovery results.However,this data-driven design does not take into account the priori knowledge of natural images.In this paper,we investigate how to remove block artifact from reconstructed images by improving the measurement matrix based on the theoretical framework of CS,and design the structure of the convolutional neural network in the recovery phase taking into account the sparse prior of the images.The main elements are as follows.1.the underlying theory of DCNN and CS is described,and the connec-tion between the sparse representation model Multi-Layered Convolutional Sparse Coding(ML-CSC)and DCNN is described.2.A novel Convolutional Measurement(CM)method is proposed,which not only reduces the computational and storage costs of the measurement matrix,but al-so utilizes hardware implementation.The problem of block artifact in the recovered image due to the block-wise measurement of the existing measurement matrix when the image size increases is solved.In addition,we give a decomposition procedure for convolutional measurements and demonstrate that its expansion to a Toeplitz-type matrix satisfies the Restricted Isometry Property(RIP),giving theoretical guaran-tees for the CM method.3.The structure of the recovery stage DCNN is designed with the princi-ple of multi-layered threshold projection algorithm to reconstruct the image,which achieves the integration of the algorithm and deep learning and overcomes the lack of theoretical support for the previous DCNN-based recovery design.Combining this recovery algorithm with CM methods,the model Convolutional Measurement Com-pressed Sensing using deep convolutional neural network(CMCS-net)is proposed.Experiments comparing CMCS-net method with several excellent compressed sens-ing methods under different measurement rates show that the proposed method is not only improved in speed,but also greatly improved under different quality evaluation indicators.Block artifact can also be eliminated even at low measure-ment rates.Specifically,compared to the recently proposed model Deep Residual Reconstruction Network(DR~2-Net),CMCS-net achieved the Peak Signal to Noise Ratio(PSNR)and Structural SIMilarity(SSIM)metrics of reconstructed images11.20%-17.09%(2–3d B)and 10.57%-34.81%(0.0891–0.1958)improvement for dif-ferent measurement rates.Moreover,the average recovery time of CMCS-net is shortened by a factor of 4 compared to DR~2-Net.4.A learning-based convolutional measurement,i.e.Compressed Sensing using Fully deep Convolution Neural Network(FCNN-CS)framework,is proposed.So that the measurement matrix is no longer designed independently of the data,the use of data-adaptive measurements can retain more information at the same mea-surement rate and improve the quality of the reconstructed image.In the training phase,the convolutional measurement process and the DCNN-based recovery pro-cess are jointly trained.In the application phase,the measurement network acts as an encoder to produce CS measurements and the recovery network acts as a decoder for image reconstruction.The effectiveness and advancement of our pro-posed compressed perception model based entirely on convolutional neural networks is subsequently verified with extensive numerical experimental comparison results.Specifically,the PSNR and SSIM metrics of the FCNN-CS reconstructed images achieve improvements of 1.06%-3.17%and 1.06%-7.08%at different measurement rates compared to the recently proposed CSNet model based entirely on DCNN.