Research On Compressive Sensing Theory And Its Applications

With the advent of the era of big data,the problem of pattern recognition under various noises has become increasingly prominent.On this background,many scholars dedicate to the research of the related theory and arithmetic of pattern recognition and machine learning.As the continuous development of compressed sensing in recent years,sparse representation classification(SRC)has attracted more and more attention.A distinguishing feature of SRC lies in its anti-noise ability since it has the inherent sparsity or collaboration when reconstructing the test samples.However,SRC does not fully consider the priors of the error caused by noises.This usually leads to the instability of the recognition performance of SRC for practical classification.Therefore,it is necessary to propose algorithms with more flexibility,adaptability and robustness,which will be meaningful for the research of compressive sensing theory,complex image classification,flow velocity measurement and so on.This doctoral dissertation started from the current existing problems in sparse representation classification algorithms and proposed new algorithms,new constraints and new uses.The main work is as followings:1.Aiming at the problem of norm normalization and suboptimal solution,a new classifier named kernel group sparse representation via structural and non-convex constraints(KGSRSN)is proposed.KGSRSN alleviates the so-called norm normalization problem by mapping the training samples into the kernel space.Furthermore,it integrates both group sparsity and structure locality in the kernel feature space and then penalties a non-convex function to the representation coefficients.Meanwhile,an interval for the parameter of penalty function is provided to promote more sparsity without sacrificing the uniqueness of the solution and robustness of convex optimization.Finally,due to the utilization of the alternating direction method of multipliers(ADMM)and majorization-minimization(MM),KGSRSN can get global optimum solution.Experimental results on three real-world benchmark datasets,i.e.,AR face database,PIE face database and MNIST handwritten digits database,demonstrate that KGSRSN can achieve more discriminative sparse coefficients,and it outperforms many classical algorithm with respect to both recognition rates and running time.2.Aiming at the problem of the most current approaches ignore the internal structure information of image data for the error matrix needs to be stretched into a vector and each element is assumed to be independently corrupted,another new classifier named nonsmooth sparse representation classifier via matrix variate distribution(NSRMVD)is proposed.NSRMVD emphasizes the dependence between pixels of noise and it is assumed that the error matrix is a random matrix variate and follows the matrix multivariate elliptical distribution.Then,several helper variables are introduced to smooth the objective function,which makes the model easily to obtain a globally optimal solution.Finally,the iteratively reweighted least square is adopted to solve the NSRMVD model efficiently.Experimental results on the AR,ExYaleB and PubFig databases demonstrate that the proposed algorithm is a robust discriminative classifier with excellent performance.3.Aiming at the problem of most vector-based methods(eg.KGSRSN)and some matrix-based regression methods(eg.NSRMVD)may fail in dealing with the image-wise noises,i.e.,the contiguous noise plus the noncontiguous noise,another new classifier named weighted mixed norm regression(WMNR)is proposed.Firstly,a unified formula,which contains the loss function,low-rank constraint and coefficients regularization,is provided.Then,WMNR generalizes possible distributions of the residual into a unified feature weighted loss function and treats the structure of corrupted image as low-rank constraints which can be quantified values.Finally,a new reweighted ADMM approach is provided to derive an iterative scheme since the proposed WMNR is formulated as a mixed norm optimization problem.The method exhibits great computational efficiency due to the division of original optimization problem into certain subproblems,which can achieve analytic solution or computes in a parallel manner.Extensive experimental results verify that WMNR is more robust to pose variations,pixel corruption,block occlusion,real disguise,and mixture noises compared to state-of-the-art regression based approaches for image recognition.4.Aiming at the localization of the traditional river flow measurement methods for natural river whose surrounding environment is complex,an emerging non-contact river surface flow velocity estimation method based on sparse representation classification algorithms is proposed.Based on the fundamental principle of feature recognition for water image,this method has realized the integration of image acquisition,image pre-processing,implicit mapping between class labels and the flow velocity as well as data analysis.Moreover,the proposed classifiers in this doctoral dissertation are used for image analysis to estimate the surface flow velocity of Jiepai River.Experimental results not only verify the feasibility of the method,but also demonstrate the proposed classifiers can be used for noisy water images.In conclusion,this doctoral dissertation mainly researches on sparse representation classification algorithms in compressive sensing theory,and applies the proposed algorithms to the classification and recognition of water images to realize the estimation of river surface velocity.All the algorithms have an advantaged superiority and can handle images with different types of noise.