Research On Theory And Some Applied Technologies Of Compressed Sensing

The compressed sensing (CS) is a brand new theoretical framework about signalacquisition and processing based on the matrix analysis theory, probability statistics theory,topology and functional analysis. It is specific to sparse or compressive signals, and canachieve the compressive processing to signal data in the meantime of sampling. The signalreconstruction is accomplished by adopting a non-linear algorithm. Thanks to the novelty ofthe framework, it provides new ideas for the better solution of many actual signal problems.So far, some important achievements have been obtained in the respect of the study tothe theory and applications of CS theory. However, as a whole, the study to CS is still in theexploratory stage, and many problems still need urgent solution. Especially, after the basictheoretical issues have been proved, the measurement matrices issues, the reconstructionalgorithm issues and the application issues in many fields, etc. are still under continuous studyand exploration. Under this background, starting with the analysis and discussion of the basictheory of CS, the dissertation makes a deep study to the measurement matrices, the signalreconstruction algorithms and some application problems of CS theory.The dissertation makes a detailed study to the Bernoulli measurement matrices, thesignal reconstruction algorithms of iterative greedy, the image encryption method based oncompressed sensing, the image CS reconstruction scheme with blind sparsity, and the radarimaging algorithms based on CS. The contributions of the dissertation are summarized asfollows:First, in the study to the CS measurement matrices, the Bernoulli measurement matricesare studied in details. The dissertation proposes to take random binary matrices as themeasurement matrices, and provids the theoretical conclusion of feasibility and theexperimental results. As for the general singal issues about CS, the random binary matricescan substitute the random symmetric signs matrices as an equivalent. At the same time, thedissertation proposes the semi-Hadamard matrices, and used them as the CS measurementmatrices. The experimental results show that the semi-Hadamard matrices can equivalentlysubstitute partial Hadamard matrices. The above two measurement matrices can effectivelyreduce the storage space and the computation time.Second, in the study to the signal reconstruction algorithms, the iterative greedyreconstruction algorithms are studied in details. The iterative convergence of the iterativegreedy algorithms is studied, and the Stage-wise Orthogonal Convergent Pursuit (StOCP) algorithm is proposed based on the convergence analysis of the iterative greedy algorithms.The StOCP algorithm selects atom based on the convergence and achieves the polyatomselection in single iteration with the stage-wise method, so as to improve the computing speed.The experimental results show that under the condition of the same number of measurementvalues, the new algorithm is superior to the OMP algorithm in reconstruction SNR.Third, as the random structure measurement matrices in CS theory have been widelyapplied, compressed sensing has become a natural encryption means. Upon this background,the study on the application of CS theory to the image encryption is developed. Basing on thesafety analysis of the measurement values, a simple and effective image encryption algorithmbased on CS is proposed. In the new algorithm, the concept of shift resister in the cryptologyis introduced to simplify the secret key. The experimental results proved the effectiveness andthe robust against cropping attack of the new algorithm.Fourth, based on the StOCP algorithm, combining with the CS method of image blocking,the image blind sparsity CS reconstruction scheme based on StOCP algorithm is proposed.When blocking, the scheme takes advantage of the sequence optimization method to increasethe sparsity of the image blocks, and solves the problem of blind sparsity of image using asimple residual threshold based on the sensitivity factor.Fifth, in the study of applications of CS theory to radar imaging, radar imagingalgorithms based on compressed sensing are focused on. The semi-Hadamard matrix andStOCP are adopted in the algorithms. The application of1-D radar imaging is studied firstlyand a range pulse compression algorithm based on compressed sensing is proposed. Thealgorithm introduces the method to establish the basis matrix methods and basic processes ofthe algorithm. Simulations show the superiority of the proposed algorithm. Then, on the basisof several key problems of the combination of CS theory and1-D radar imaging, theapplications of compressed sensing to2-D radar imaging is deeply studied. An azimuthimaging algorithm and a2-D radar imaging algorithm based on compressed sensing areproposed. ISAR is taken as an example to illustrate the constructing methods of basis matricesand the basic processes of the algorithms. At the same time, a sparse aperture imagingalgorithm based on compressed sensing is proposed for the problems of sparse aperture.Simulations verify the superiority of the above algorithms.