Compressed Sensing Observation And Reconstruction Based On Structured Sparse And Convolutional Network

Compressed sensing(CS)is a new sampling theory and breaks the Nyquist sampling theorem.The signal can be reconstructed from the observation that are far less than the original dimension.The theoretical and technical researches on CS have been making a significant impact on signal acquisition,analysis and processing.After more than ten years of development,the original traditional CS gradually turned to structured CS.The processing domain is from one-dimensional signal to two-dimensional image,then three-dimensional video.The sparse representations based on structured redundant dictionaries are paid more attention than that on orthogonal based and frames.The reconstruction constraint is from a single sparse constraint to a more constrained reconstruction with a priori structure.And the non-iterative deep neural network framework is appeared to solve the CS reconstruction problem without iteration.It can be seen from the development process that the domain of CS is becoming more and more extensive and more and more attention has been paid to modeling of structured constraints.Combing with the current academic frontiers,CS shows its new development direction.The dissertation is consistent with the development trend of CS.The research field includes the Wavelet domain CS,the spatial image domian CS and the video domain CS.In the aspect of CS observation,a sketch property and structured observation is proposed to improves the effectiveness of the CS observation effectively.In the reconstruction,the statistical structure,local and non-local similarity of the signal are combined with greedy algorithm,natural evolution algorithm,and deep learning,etc.and a series of structured image or video signal reconstruction frameworks are proposed,including group matching pursuit,direction constraint particle swarm optimization reconstruction,video reconstruction based on internal tensor sparse and combinatorial residual reconstruction neural network with prior constraint.The contributions of the dissertation include:(1)In the Wavelet domain CS,a Group Matching Pursuit(GMP)reconstruction is proposed based on the aggregation of the high frequency coefficients of the wavelet.In GMP,with the neighborhood structure employed as a spatial constraint,the coefficients are organized as groups to restrain each other.The adjacent group coefficients are jointly determined to be large coefficients,which improve the estimation accuracy of the large coefficients location.The large coefficients of the high frequency of the wavelet often appear on the edge,so the edge of the image is extracted to further guide the location of the large coefficients.When solving the group coefficients,the group coefficients are modeled by a multivariate Gaussian distribution,and the value of the group coefficients is obtained by a posteriori probability estimate.Experiments have shown that,the methods based on GMP have a better reconstruction in solving the reconstruction problem of CS.(2)The research of structured CS includes structured observation,structured dictionary and structured reconfiguration.A nonconvex CS based on sketch property and structured observation is proposed by jointly considering the three aspects.In this framework,a structured observation is proposed based on the novel sketch property structured clustering method.In the proposed clustering method,the image are first divided into sketchable blocks and non-sketchable blocks by the Primal Sketch(PS).The sketchable blocks include single direction blocks and multi-direction blocks,and the non-sketchable blocks include smooth blocks and texture blocks.Different clustering methods are designed for different structure type blocks.Specifically,a directional clustering method is proposed for the sketchable blocks with the guidance of the direction of sketch segment.Then in the observation,a space compression observation is proposed to reduce the observation rate of the smooth image blocks,and the Multivariate Measurement Vector(MMV)model is used to obtain the measurement of each the non-smooth class.The class and direction informations which are obtained by the sketch segment are sent to the receivers with the measurements together.In the process of reconstruction,the overcomplete ridgelet redundant dictionary is used for the structured sparse representation.To verify the effectiveness of the proposed observation method,the matching pursuit algorithms are designed for reconstruction.Compared with the random Gaussian observation,a better reconstruction image is obtained.What's more,a Direction Restricted Hybrid Particle Swarm Optimization(DR_HPSO)is proposed based on the proposed observation.In this algorithm,the direction restriction update operation has been put forward to speed up the convergence rate,and the crossover and selection operators are introduced into the particle swarm optimization algorithm.Further,it demonstrates the importance of combining sketch segment direction and dictionary in the reconstruction.Compared with two kinds of evolutionary algorithm,the NR_DG and TS_RS,DR_HPSO achieves faster convergence speed and better reconstruction results.Theoretical analysis and experimental results show that the proposed structured observation and the DR_HPSO reconstruction method performs excellently not only on nature images but also the visualremote sensing images.(3)CS reconstruction based on convolutional network.With the development of neural networks,there appear some CS reconstruction algorithms based on the neural network.Compare with the traditional reconstruction algorithm,they can reconstruct the original images from the compressive measurement quickly and accurately with a low sampling rate.However,the existing CS reconstruction algorithms based on neural network have ignored the image self-similarity which is important prior information for the reconstruction.A Multi-scale Reconstruction Network with Non-local constraint(NL_MRN)is proposed to solve this problem.First,it captures the prior of image non-local similarity by a non-local operation.Then different scale residual reconstruction models which have different convolution kernel size are combined together.At last,the loss function of the whole network is defined as a weighted sum of different reconstruction module's loss function.What's more,the training efficiency of the network is improved by the proposed segmental training method.Theoretical analysis and experimental results show that the proposed P_CRN achieves better reconstruction compares with other reconstruction algorithms,especially at a low sampling rate.(4)The CS reconstruction is extended from the image to the video domain.A video reconstruction model based on the intrinsic tensor sparsity is established by using the similarity between the intra and inter frames.The proposed reconstruction model includes two parts: First,the video tensor sparsity model is formulated by using a spatio-temporal tensor sparse penalty for similar patches.The ITS measure is used as the sparsity measure,which encodes both sparsity insights delivered by the Tucker and CANDECOMP/PARAFAC(CP)decomposition for tensors.Second,3D video patches are modeled as the Gaussian Joint Sparsity(GJS)by exploiting the temporal similarity to obtain an initial image which has distinct direction structure.GJS is a combination of statistical distribution and joint sparsity model.The experimental results show that both the reconstruction models based on ITS and GJS contribute to improving the quality of the video reconstruction.