Research On Greedy Iterative Reconstruction Algorithms Based On Blind Sparse Signal For Compressed Sensing

As a new signal sampling and compression technology emerged in recent years, Compressed Sensing breakthrough the limitation of the traditional Nyquist sampling theorem, in the perception of sparse or compressible signals, it can compress the data directly at the same time, thus the time of sampling and compression and the data storage space could be reduced greatly. As one of the core of CS technology, signal reconstruction algorithm has become a hot topics to many scholars. In this thesis, we have done a series of studies to the greedy iterative classes sparse reconstruction algorithm which based on CS theory, the main work is to study the effective signal reconstruction scheme for the blind sparsity (sparsity unknown) signal, as well as optimizing the atom search strategy of the greedy algorithm to achieve better reconstruction quality. The main tasks includes the following points.At first, this thesis systematically studied some more mature greedy iterative algorithm which has appeared at home and abroad, such as OMP{Orthogonal Matching Pursuit)-. ROMP (Regularize Orthogonal Matching Pursuit)、 CoSaMP (Compressive Sampling Matching Pursuit)、SP(Subspace Pursuit)algorithm, these algorithms are all must be based on the sparse degree as the prior information in order to get a high probability reconstruction of the sparse signal. We have given the basic principle of each algorithm, and then analysis the advantages and disadvantages of each algorithm in detail through experimental results, which leads to the follow-up research content.Secondly the thesis focuses on the sparsity adaptive matching pursuit algorithm, for its defect of easy to appear atoms excessive matching, we have proposed an improved program for blind sparse signal reconstruction algorithm which based on regularization and backtracking method. The improved algorithm has inherited the advantages of SAMP, combined with the optimized regularization method and the backtracking algorithm to optimize the atom matching strategy, so it can further improve the accuracy and adaptability of atom selection through the atom secondary screening, then the reconstruction error could also be reduced, thus this improved algorithm could recover blind sparse signal effectively. Simulation results show that the improved algorithm is better than the original algorithm on the success rate of reconstruction and reconstruction quality, because of regularization processing, the operation time is slightly lower than the original algorithm.Finally, considering the shortcoming of the inner product matching rule in existing greedy iterative algorithm, we introduced Dice coefficient as a new atom similarity measure criterion in to SP and SAMP, then we proposed DSP(Dice-SP)and DSAMP(Dice-SAMP)algorithm. Through the theoretical analysis on Dice coefficient, we know that this atom matching criterion based on Dice coefficient could pick out the best matching atoms more accurately. Then apply these improved algorithm to one-dimensional time domain signal and the two-dimensional image reconstruction, simulation results show that the two kinds of improved algorithm on the sparse signal reconstruction quality are all better than the original algorithm, further verified the Dice coefficient criterion could select much better atoms from sparse dictionary, so it has a better reconstruction performance.