Research On The Original Sinal Reconstruction Algorithm Of Compressed Sensing

In recent years, compressed sensing theory has broken through the restrict of sampling frequency which was proposed at the Ne Quist theorem, making compressed sensing theory attract considerable attention. Even now many people are studying compressed sensing theory. People study compressed sensing theory in three main aspects: showing signals sparsely, designing the efficient observation matrix and studying the accurate and fast reconstruction algorithm. The most important aspect is studying reconstruction algorithm, and this thesis mainly studies the reconstruction algorithms including OCMP algorithm, GP algorithm and NSL0 algorithm, and improves those algorithms respectively according to their deficiency. The main works of this thesis is as follows:(1) An improved algorithm of OCMP algorithm is proposed in this thesis, which is named varying step size OCMP algorithm based on L0 norm(L0St OCMP). OCMP algorithm is one of the greedy algorithms. In OCMP algorithm, only one element is selected to join the supporting set each time, and L2 norm is used to select the element, so the convergence rate and recovery precision are not satisfactory. In L0 St OCMP algorithm, the number of elements to be selected to join the supporting set is equal to current step size, which is varying, and the choice of elements is depended on L0 norm which is approximated by arctan function, instead of L2 norm. The simulation result shows that L0 St OCMP algorithm increases the convergence rate and recovery precision at low SNR compared with OCMP algorithm.(2) Two improved algorithms of GP algorithm are proposed in this thesis, named SGP and SWGP respectively. SGP is based on accelerated gradient method, and SWGP is based on SW conjugate gradient method. GP algorithm, one of the greedy algorithms, uses the search direction of steepest descent method to approximate the optimal solution, so it produces sawteeth and affects convergence rate and recovery precision. SGP algorithm approximates the optimal solution through the search direction produced by accelerated gradient method, and SWGP algorithm approximates the optimal solution through the search direction produced by conjugate gradient method. SGP algorithm and SWGP algorithm eliminate sawteeth phenomenon in some degree. The simulation result shows that both two improved methods increase the converge nce rate and recovery precision, and SWGP algorithm improves the performance more obviously.(3) An improved algorithm of NSL0 algorithm is proposed in this thesis, which is named G_NSL0. G_NSL0 algorithm combined NSL0 algorithm with greedy algorithm. NSL0 algorithm is an improved SL0 algorithm, and it uses Newton method to approximate the optimal solution. NSL0 algorithm does not break through the restriction of SL0 algorithm, although it increases the convergence rate and recovery precision compared to SL0 algorithm. G_NSL0 algorithm gets the position of nonzero elements in original signal through fewer times of iteration, then calculate the corresponding value of those position and thus to reconstruct the original signal. The simulation result shows that G_NSL0 algorithm increases the convergence rate and recovery precision obviously compared with NSL0 algorithm.