The Reconstruction Algorithm And Applied Research Of Compressive Sensing Based On I_p Norm

The conventional Nyquist sampling theorem states that analog signal can bereconstructed without distortion only when the sampling frequency is greater than orequal to two times the highest frequency of the signal. High sampling rate will result inthe huge amount of data, the storage and transmission of which is a complex work. Andmoreover, huge amount of data may cause a waste of resources. Compressive sensingtheory, the new research spot in recent years describes that a small group ofnon-adaptive linear projections of a sparse or compressible signal contains enoughinformation for signal reconstruction. The emergence of the compressive sensing theoryhave changed the conventional signal acquisition systems, which need to sample at ahigher rate first, and then compress the signal at a lower bit rate. It completes signalcompression and sampling at the same time, only part of the information need to besampled, and thus significantly saves the system resource.This thesis first introduces the compressive sensing theory, mainly introduces thereconstruction algorithm. When use the existing algorithms to image reconstruction willget lower signal-to-noise. Especially combine with the block compressive sensing;when the sampling rate is lower, the block effect is obviously. In view of thisdisadvantage, a new reconstruction algorithm based onl p(0p1)norm by combiningthe penalty function and revised Hesse sequence quadratic programming is proposed.When the new algorithm is used for image reconstruction, the simulation experimentsshow that the proposed new algorithm can improve the precision of image restoration.When the sampling rate is lower, the block effect is reduced, reconstruction results arebetter than the existing algorithms.In order to better realize the practical application of the compressive sensing theory,this thesis studies the model of microphone array far field DOA estimation based oncompressive sensing. Because the microphone array DOA estimation model firstmeeting the requirement of sparse condition, and moreover, the observation matrixsatisfies the RIP condition for compressive sensing measurement matrix. The simulationexperiments show that the proposed algorithm can be used in far field DOA estimationmodel, and achieves better results. Finally, this thesis put forward the next step work and point out the compressivesensing is used in near-field sound source localization what problem need to solve.