Research On The Measurement Matrix Optimization And Application Of Compressed Sensing

Compressive Sensing sparse compressible signal by sparse transform algorithm; sampling and compressing signal by dimension reduction methods of matrix; the original signal is restored by convex optimization, iterative threshold, greedy algorithms etc. There are two important conditions for compressed sensing theory: first, the signal can be sparsity, which is itself for a signal, being sampled the signal must be sparse in one domain; second is irrelevant characteristic, which is based on the measurement matrix and sparse-based matrix, it impact signal compression ratio and reduction ratio, at the same time, it compress sparse signal by non-adaptive method. Compressed Sensing theory bring a new shock for academia and industry, and is popular used in video image processing, ultrasonic imaging, wireless communications, radar, geological exploration, magnetic resonance imaging and other fields, has been named foreign Technology Review ten scientific and technological progress.It was researched that optimize measurement matrix of compressed sensing, and studied the application of compressed sensing for solving the practical engineering problems, so carried out the following work:First, correlation between the ranks of the random measurement matrix was studied, the experimental results show that obtaining the advantages and disadvantages of reconstruction rate and column coherence in different optimization methods of random measurement matrix. On this basis, collaborative optimization of measurement matrix by gradient reduction and decomposition dimension reduction was proposed, theoretical analysis and simulation results show that the effects of reconstruction after the measurement matrix improvement over the effects of reconstruction before improvement.Secondly, the alternating projection optimization method of measurement matrix based on eigenvalue decomposition was proposed. Optimized measurement matrix by combining the alternative projection of two matrixes, eigenvalue decomposition and singular value decomposition method. The experimental results show that was effective to reduce correlation column of measurement matrix by combining the mathematical methods.Again, it is proposed that the compressed perception is applied to anomaly detection of wind turbines, we get the empirical matrix by computing the historical data, and it can conclude that more accurate information from a small amount of data. The method that combination of compressed sensing and anomaly detection of wind turbines, was applied to engineering practice and expand the application field of compressed sensing, to better solve the problem that find the device which is abnormal in fault detection.