Research On Algorithms And Applications Of Compressed Sensing

Based on the in-depth study of the basic theory of Compressed Sensing, we apply the theory to blind source separation and photoacoustic imaging reconstruction.The design of measurement matrix and recovery algorithm is the two core issues of Compressed Sensing. We first analyze what kind of sequences can be used as observation vectors by the basic properties of Hilbert space and tight frame, and thus leads to the two basic criteria of measurement matrix design: restricted isometry property (RIP) and the coherence of measurement matrix. Then we introduce some random matrices and deterministic matrices and analyze their advantages and disadvantages. After we list several algorithms of Compressed Sensing, a large number of simulation experiments are carried out to compare the performance of these algorithms.Most of the existing methods for blind source separation (BSS) require much prior knowledge and many measurements, aiming at this actuality, Compressed Sensing is proposed to separate blind sources which requires undersampled data. We analyze some similarities between CS and BSS, furthermore, the relationship between them is built by equivalent transformation. And then we analyze how to design the momentous operator of BSS and give some valuable conclusions. At last, sparse random signals and real sound signals are applied to verify the effectiveness of the whole framework.The photoacoustic data acquisition mode we design based on Compressed Sensing is prompted by the single-pixel camera. To have the same performance of traditional methods, the new mode requires only a few number of angles and observations. According to the fact that photoacoustic data is always polluted by noise data, we use Bayesian Compressed Sensing to reconstruct the photoacoustic imaging, the results of simulation experiments show that this algorithm has a good performance on photoacoustic imaging reconstruction. At last, by the multi-angle observation, it can reduce the number of measurements to improve the time resolution for a needed high-quality reconstruction image.