Research On Measurement Matrix Design And Reconstruction Algorithms In Compressed Sensing

The rapid development of information technology and increasing bandwidth of signal hasbrought great challenge to the signal processing system under guidance of the Nyquist samplingtheorem. Compressed sensing is a new signal processing theory and its sampling object is theinformation carried by the signal, making sampling and compression simultaneously. The thesisstudies measurement matrix construction and reconstruction algorithm in compressed sensingtheory and main work is as follows:(1) The thesis proposes an optimized measurement matrix construction method whichcombines theoretical guidance and practical application demands of measurement matrix with linearrepresentation theory of orthogonal basis: select diagonal array with nonzero determinant value asorthogonal basis and Toeplitz matrix representing coefficient matrix to eventually expand to a newmeasurement matrix. Simulation experiments compare the performance of new matrix withGaussian random matrices, Toeplitz matrix and some other commonly used ones to verify the newmeasurement matrix’s good performance.(2) Several reconstruction algorithms are detailed introduced in the thesis, especially sparsityadaptive matching pursuit algorithm. Then introduces the idea of selecting the best atoms duringeach iteration into variable step forward-backward pursuit(VsFBP) algorithm and proposes a newreconstruction algorithm. The new reconstruction algorithm also reduces time consuming bypreselection strategy and pretreatment. Simulation experiments compare the performance of thenew algorithm with commonly used algorithms and verify that the new algorithm has a betterperformance when compression ratio is beyond0.1with relatively low time consuming.(3) The thesis adds a selecting strategy into the regularization criteria for selecting atomicgroups after analyzing the advantages and disadvantages of the criteria. Simulation experimentsprove that algorithm has a better performance when adding the selecting strategy. Then introducesthe new criteria into forward-backward pursuit algorithm and proposes a new reconstructionalgorithm making regularized selecting atoms and sparsity adaptive simultaneously. Simulationexperiments verify that the new algorithm has better performance.